Middle School Math Quiz: Write Expressions With Numbers And Variables
20 questions · exam conditions
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Write Expressions With Numbers And VariablesQuestion 1 of 20

Let xx be the number of minutes you practiced. Which expression represents the sum of twice xx and 7?

2x+72x+7
7x+27x+2
x+14x+14
2(x+7)2(x+7)
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Middle School Math Quiz

Middle School Math Quiz: Write Expressions With Numbers And Variables

Practice Write Expressions With Numbers And Variables in Middle School Math with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

What this quiz covers

This quiz focuses on Write Expressions With Numbers And Variables, giving you a quick way to practice the rules, question types, and explanations that matter most for Middle School Math.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

All questions

Question 1

Let xx be the number of minutes you practiced. Which expression represents the sum of twice xx and 7?

  1. 2x+72x+7 (correct answer)
  2. 7x+27x+2
  3. x+14x+14
  4. 2(x+7)2(x+7)
Explanation: This question tests writing algebraic expressions from verbal descriptions using variables (letters representing numbers) and operation symbols (+, -, ×, ÷). Translating words to algebra: "more than/sum" → addition (+), "less than/difference" → subtraction (-), "times/product" → multiplication (coefficient: 3x means 3 times x), "divided by/quotient" → division (x/4). Order matters for non-commutative: "5 less than n" means subtract 5 FROM n (n-5, not 5-n reversed), "n divided by 4" means n/4 (not 4/n). Variable represents number: x, n, y are placeholders (unknown or any number in context). For example, "7 more than a number" uses variable n for number, "more than" means add, expression: n+7; "product of 3 and x" means 3 times x: 3x; "twice a number plus 5" means 2 times n plus 5: 2n+5 (not 2(n+5) which would be twice the sum); "x divided by 8" means x/8. The correct translation for 'the sum of twice x and 7' is 2x + 7, which matches choice B. A common error is misinterpreting the order of operations, like writing 2(x + 7) instead of 2x + 7, or confusing sum with product to get something like x + 14. To write expressions: (1) identify operation words (more→add, times→multiply, less→subtract, divided→divide), (2) choose variable (n, x, y for "a number"), (3) determine order (for subtraction/division: "less than" and "divided by" require careful order-"5 less than n" is n-5, subtract from first quantity), (4) write expression (n+5, 3x, x-7, y/4), (5) verify (if n=10: "5 more than n" gives 10+5=15✓, makes sense). Key phrases: "more than" adds to variable (n+5), "less than" subtracts from variable (n-7), "times" multiplies (3n coefficient notation), "of" often means multiply (half of n: (1/2)n=n/2). Mistakes: reversing order for subtraction/division (most common: less than and divided by backward), wrong operation (confusing sum and product), coefficient unclear (writing 3×x instead of 3x, acceptable but coefficient notation preferred).

Question 2

Let xx represent the number of stickers Jordan has. Which expression represents 2 more than twice the number of stickers?

  1. 2(x+2)2(x+2)
  2. x+2x+2
  3. 2x+22x+2 (correct answer)
  4. x+2xx+2x
Explanation: This question tests writing algebraic expressions from verbal descriptions using variables (letters representing numbers) and operation symbols (+, -, ×, ÷). Translating words to algebra: "more than/sum" → addition (+), "less than/difference" → subtraction (-), "times/product" → multiplication (coefficient: 3x means 3 times x), "divided by/quotient" → division (x/4). Order matters for non-commutative: "5 less than n" means subtract 5 FROM n (n-5, not 5-n reversed), "n divided by 4" means n/4 (not 4/n). Variable represents number: x, n, y are placeholders (unknown or any number in context). Example: "7 more than a number" uses variable n for number, "more than" means add, expression: n+7; "product of 3 and x" means 3 times x: 3x; "twice a number plus 5" means 2 times n plus 5: 2n+5 (not 2(n+5) which would be twice the sum); "x divided by 8" means x/8. The correct translation for "2 more than twice the number of stickers" where x is the number is 2x + 2. A common error is misunderstanding the combined operations, like choosing 2(x + 2) which is twice the sum instead of 2x + 2, or x + 2x which is 3x. Writing: (1) identify operation words (more→add, times→multiply, less→subtract, divided→divide), (2) choose variable (n, x, y for "a number"), (3) determine order (for subtraction/division: "less than" and "divided by" require careful order-"5 less than n" is n-5, subtract from first quantity), (4) write expression (n+5, 3x, x-7, y/4), (5) verify (if n=10: "5 more than n" gives 10+5=15✓, makes sense). Key phrases: "more than" adds to variable (n+5), "less than" subtracts from variable (n-7), "times" multiplies (3n coefficient notation), "of" often means multiply (half of n: (1/2)n=n/2). Mistakes: reversing order for subtraction/division (most common: less than and divided by backward), wrong operation (confusing sum and product), coefficient unclear (writing 3×x instead of 3x, acceptable but coefficient notation preferred).

Question 3

Let xx represent the number of minutes Maya practices piano. Which expression represents 5 more than the number of minutes she practices?

  1. 5x5x
  2. x+5x+5 (correct answer)
  3. 5−x5-x
  4. x−5x-5
Explanation: This question tests writing algebraic expressions from verbal descriptions using variables (letters representing numbers) and operation symbols (+, -, ×, ÷). Translating words to algebra: "more than/sum" → addition (+), "less than/difference" → subtraction (-), "times/product" → multiplication (coefficient: 3x means 3 times x), "divided by/quotient" → division (x/4). Order matters for non-commutative: "5 less than n" means subtract 5 FROM n (n-5, not 5-n reversed), "n divided by 4" means n/4 (not 4/n). Variable represents number: x, n, y are placeholders (unknown or any number in context). Example: "7 more than a number" uses variable n for number, "more than" means add, expression: n+7; "product of 3 and x" means 3 times x: 3x; "twice a number plus 5" means 2 times n plus 5: 2n+5 (not 2(n+5) which would be twice the sum); "x divided by 8" means x/8. The correct translation for "5 more than the number of minutes she practices" where x is the minutes is x + 5. A common error is confusing addition with subtraction, like choosing x - 5 instead of x + 5, or mistaking it for multiplication like 5x. Writing: (1) identify operation words (more→add, times→multiply, less→subtract, divided→divide), (2) choose variable (n, x, y for "a number"), (3) determine order (for subtraction/division: "less than" and "divided by" require careful order-"5 less than n" is n-5, subtract from first quantity), (4) write expression (n+5, 3x, x-7, y/4), (5) verify (if n=10: "5 more than n" gives 10+5=15✓, makes sense). Key phrases: "more than" adds to variable (n+5), "less than" subtracts from variable (n-7), "times" multiplies (3n coefficient notation), "of" often means multiply (half of n: (1/2)n=n/2). Mistakes: reversing order for subtraction/division (most common: less than and divided by backward), wrong operation (confusing sum and product), coefficient unclear (writing 3×x instead of 3x, acceptable but coefficient notation preferred).

Question 4

Does the expression x−7x-7 represent the phrase "7 less than a number xx"?

  1. Yes, because it multiplies xx by 7.
  2. No, it should be 7−x7-x.
  3. No, it should be x+7x+7.
  4. Yes, because it subtracts 7 from xx. (correct answer)
Explanation: This question tests writing algebraic expressions from verbal descriptions using variables (letters representing numbers) and operation symbols (+, -, ×, ÷). Translating words to algebra: "more than/sum" → addition (+), "less than/difference" → subtraction (-), "times/product" → multiplication (coefficient: 3x means 3 times x), "divided by/quotient" → division (x/4). Order matters for non-commutative: "5 less than n" means subtract 5 FROM n (n-5, not 5-n reversed), "n divided by 4" means n/4 (not 4/n). Variable represents number: x, n, y are placeholders (unknown or any number in context). Example: "7 more than a number" uses variable n for number, "more than" means add, expression: n+7; "product of 3 and x" means 3 times x: 3x; "twice a number plus 5" means 2 times n plus 5: 2n+5 (not 2(n+5) which would be twice the sum); "x divided by 8" means x/8. The correct answer is yes, the expression x - 7 represents "7 less than a number x" because it subtracts 7 from x. A common error is reversing the order, thinking it should be 7 - x, or confusing with addition like x + 7 or multiplication. Writing: (1) identify operation words (more→add, times→multiply, less→subtract, divided→divide), (2) choose variable (n, x, y for "a number"), (3) determine order (for subtraction/division: "less than" and "divided by" require careful order-"5 less than n" is n-5, subtract from first quantity), (4) write expression (n+5, 3x, x-7, y/4), (5) verify (if n=10: "5 more than n" gives 10+5=15✓, makes sense). Key phrases: "more than" adds to variable (n+5), "less than" subtracts from variable (n-7), "times" multiplies (3n coefficient notation), "of" often means multiply (half of n: (1/2)n=n/2). Mistakes: reversing order for subtraction/division (most common: less than and divided by backward), wrong operation (confusing sum and product), coefficient unclear (writing 3×x instead of 3x, acceptable but coefficient notation preferred).

Question 5

Let nn be a number. Which expression represents 2 more than twice nn?

  1. n+4n+4
  2. 2−n2-n
  3. 2(n+2)2(n+2)
  4. 2n+22n+2 (correct answer)
Explanation: This question tests writing algebraic expressions from verbal descriptions using variables (letters representing numbers) and operation symbols (+, -, ×, ÷). Translating words to algebra: "more than/sum" → addition (+), "less than/difference" → subtraction (-), "times/product" → multiplication (coefficient: 3x means 3 times x), "divided by/quotient" → division (x/4). Order matters for non-commutative: "5 less than n" means subtract 5 FROM n (n-5, not 5-n reversed), "n divided by 4" means n/4 (not 4/n). Variable represents number: x, n, y are placeholders (unknown or any number in context). For example, "7 more than a number" uses variable n for number, "more than" means add, expression: n+7; "product of 3 and x" means 3 times x: 3x; "twice a number plus 5" means 2 times n plus 5: 2n+5 (not 2(n+5) which would be twice the sum); "x divided by 8" means x/8. The correct translation for '2 more than twice n' is 2n + 2, which matches choice A. A common error is applying the 'more than' to the whole, like writing 2(n + 2) instead of 2n + 2, or confusing with subtraction to get something like n - 2. To write expressions: (1) identify operation words (more→add, times→multiply, less→subtract, divided→divide), (2) choose variable (n, x, y for "a number"), (3) determine order (for subtraction/division: "less than" and "divided by" require careful order-"5 less than n" is n-5, subtract from first quantity), (4) write expression (n+5, 3x, x-7, y/4), (5) verify (if n=10: "5 more than n" gives 10+5=15✓, makes sense). Key phrases: "more than" adds to variable (n+5), "less than" subtracts from variable (n-7), "times" multiplies (3n coefficient notation), "of" often means multiply (half of n: (1/2)n=n/2). Mistakes: reversing order for subtraction/division (most common: less than and divided by backward), wrong operation (confusing sum and product), coefficient unclear (writing 3×x instead of 3x, acceptable but coefficient notation preferred).

Question 6

A video game gives you xx points, then you lose 7 points. Which expression represents 7 less than xx?

  1. x−7x-7 (correct answer)
  2. 7−x7-x
  3. x+7x+7
  4. 7x7x
Explanation: This question tests writing algebraic expressions from verbal descriptions using variables (letters representing numbers) and operation symbols (+, -, ×, ÷). Translating words to algebra: "more than/sum" → addition (+), "less than/difference" → subtraction (-), "times/product" → multiplication (coefficient: 3x means 3 times x), "divided by/quotient" → division (x/4). Order matters for non-commutative: "5 less than n" means subtract 5 FROM n (n-5, not 5-n reversed), "n divided by 4" means n/4 (not 4/n). Variable represents number: x, n, y are placeholders (unknown or any number in context). For example, "7 more than a number" uses variable n for number, "more than" means add, expression: n+7; "product of 3 and x" means 3 times x: 3x; "twice a number plus 5" means 2 times n plus 5: 2n+5 (not 2(n+5) which would be twice the sum); "x divided by 8" means x/8. The correct translation for '7 less than x' is x - 7, which matches choice A. A common error is reversing the order, like writing 7 - x instead of x - 7, or confusing it with addition to get x + 7. To write expressions: (1) identify operation words (more→add, times→multiply, less→subtract, divided→divide), (2) choose variable (n, x, y for "a number"), (3) determine order (for subtraction/division: "less than" and "divided by" require careful order-"5 less than n" is n-5, subtract from first quantity), (4) write expression (n+5, 3x, x-7, y/4), (5) verify (if n=10: "5 more than n" gives 10+5=15✓, makes sense). Key phrases: "more than" adds to variable (n+5), "less than" subtracts from variable (n-7), "times" multiplies (3n coefficient notation), "of" often means multiply (half of n: (1/2)n=n/2). Mistakes: reversing order for subtraction/division (most common: less than and divided by backward), wrong operation (confusing sum and product), coefficient unclear (writing 3×x instead of 3x, acceptable but coefficient notation preferred).

Question 7

A rectangular garden has a length that is 44 meters longer than twice its width. If the width is ww meters, which expression represents the perimeter of the garden?

  1. 6w+86w + 8 (correct answer)
  2. 4w+84w + 8
  3. 3w+43w + 4
  4. 2w+42w + 4
Explanation: The width is ww and the length is 2w+42w + 4. The perimeter formula is 2(length+width)=2(2w+4+w)=2(3w+4)=6w+82(\text{length} + \text{width}) = 2(2w + 4 + w) = 2(3w + 4) = 6w + 8. Choice B uses the incorrect perimeter formula 2length+2width2\text{length} + 2\text{width} but makes an error. Choice C represents length plus width, not perimeter. Choice D represents just the length.

Question 8

Let xx represent a number. Which expression means 2 more than twice xx?

  1. 2x+22x+2 (correct answer)
  2. x+2x+2
  3. 2−x2-x
  4. 2(x+2)2(x+2)
Explanation: This question tests writing algebraic expressions from verbal descriptions using variables (letters representing numbers) and operation symbols (+, -, ×, ÷). Translating words to algebra: 'more than/sum' → addition (+), 'less than/difference' → subtraction (-), 'times/product' → multiplication (coefficient: 3x means 3 times x), 'divided by/quotient' → division (x/4). Order matters for non-commutative: '5 less than n' means subtract 5 FROM n (n-5, not 5-n reversed), 'n divided by 4' means n/4 (not 4/n). Variable represents number: x, n, y are placeholders (unknown or any number in context). For example, '7 more than a number' uses variable n for number, 'more than' means add, expression: n+7; 'product of 3 and x' means 3 times x: 3x; 'twice a number plus 5' means 2 times n plus 5: 2n+5 (not 2(n+5) which would be twice the sum); 'x divided by 8' means x/8. The correct translation for '2 more than twice x' is 2x + 2, which matches choice A. A common error is misinterpreting as twice the quantity of x plus 2, like 2(x + 2), instead of adding after multiplying. To write expressions: (1) identify operation words (more→add, times→multiply, less→subtract, divided→divide), (2) choose variable (n, x, y for 'a number'), (3) determine order (for subtraction/division: 'less than' and 'divided by' require careful order-'5 less than n' is n-5, subtract from first quantity), (4) write expression (n+5, 3x, x-7, y/4), (5) verify (if n=10: '5 more than n' gives 10+5=15✓, makes sense). Key phrases: 'more than' adds to variable (n+5), 'less than' subtracts from variable (n-7), 'times' multiplies (3n coefficient notation), 'of' often means multiply (half of n: (1/2)n=n/2). Mistakes: reversing order for subtraction/division (most common: less than and divided by backward), wrong operation (confusing sum and product), coefficient unclear (writing 3×x instead of 3x, acceptable but coefficient notation preferred).

Question 9

Let xx represent the number of points a team scored. Which expression represents the team's points after 9 fewer points are taken away?

  1. x−9x-9 (correct answer)
  2. x+9x+9
  3. 9x9x
  4. 9−x9-x
Explanation: This question tests writing algebraic expressions from verbal descriptions using variables (letters representing numbers) and operation symbols (+, -, ×, ÷). Translating words to algebra: "more than/sum" → addition (+), "less than/difference" → subtraction (-), "times/product" → multiplication (coefficient: 3x means 3 times x), "divided by/quotient" → division (x/4). Order matters for non-commutative: "5 less than n" means subtract 5 FROM n (n-5, not 5-n reversed), "n divided by 4" means n/4 (not 4/n). Variable represents number: x, n, y are placeholders (unknown or any number in context). Example: "7 more than a number" uses variable n for number, "more than" means add, expression: n+7; "product of 3 and x" means 3 times x: 3x; "twice a number plus 5" means 2 times n plus 5: 2n+5 (not 2(n+5) which would be twice the sum); "x divided by 8" means x/8. The correct translation for the points after "9 fewer points are taken away" where x is the points scored is x - 9. A common error is reversing the order like 9 - x, or confusing with addition like x + 9 or multiplication like 9x. Writing: (1) identify operation words (more→add, times→multiply, less→subtract, divided→divide), (2) choose variable (n, x, y for "a number"), (3) determine order (for subtraction/division: "less than" and "divided by" require careful order-"5 less than n" is n-5, subtract from first quantity), (4) write expression (n+5, 3x, x-7, y/4), (5) verify (if n=10: "5 more than n" gives 10+5=15✓, makes sense). Key phrases: "more than" adds to variable (n+5), "less than" subtracts from variable (n-7), "times" multiplies (3n coefficient notation), "of" often means multiply (half of n: (1/2)n=n/2). Mistakes: reversing order for subtraction/division (most common: less than and divided by backward), wrong operation (confusing sum and product), coefficient unclear (writing 3×x instead of 3x, acceptable but coefficient notation preferred).

Question 10

Let xx represent a number. Which expression means 7 less than xx?

  1. x+7x+7
  2. x−7x-7 (correct answer)
  3. 7x7x
  4. 7−x7-x
Explanation: This question tests writing algebraic expressions from verbal descriptions using variables (letters representing numbers) and operation symbols (+, -, ×, ÷). Translating words to algebra: 'more than/sum' → addition (+), 'less than/difference' → subtraction (-), 'times/product' → multiplication (coefficient: 3x3x means 3 times x), 'divided by/quotient' → division (x/4x/4). Order matters for non-commutative: '5 less than n' means subtract 5 FROM n (n−5n-5, not 5−n5-n reversed), 'n divided by 4' means n/4n/4 (not 4/n4/n). Variable represents number: x, n, y are placeholders (unknown or any number in context). For example, '7 more than a number' uses variable n for number, 'more than' means add, expression: n+7n+7; 'product of 3 and x' means 3 times x: 3x3x; 'twice a number plus 5' means 2 times n plus 5: 2n+52n+5 (not 2(n+5)2(n+5) which would be twice the sum); 'x divided by 8' means x/8x/8. The correct translation for '7 less than x' is x−7x - 7, which matches choice C. A common error is reversing the order, like writing 7−x7 - x instead of x−7x - 7 for 'less than' phrases, or mistaking it for addition to get x+7x + 7. To write expressions: (1) identify operation words (more→add, times→multiply, less→subtract, divided→divide), (2) choose variable (n, x, y for 'a number'), (3) determine order (for subtraction/division: 'less than' and 'divided by' require careful order-'5 less than n' is n−5n-5, subtract from first quantity), (4) write expression (n+5n+5, 3x3x, x−7x-7, y/4y/4), (5) verify (if n=10: '5 more than n' gives 10+5=1510+5=15✓, makes sense). Key phrases: 'more than' adds to variable (n+5n+5), 'less than' subtracts from variable (n−7n-7), 'times' multiplies (3n3n coefficient notation), 'of' often means multiply (half of n: (1/2)n=n/2(1/2)n=n/2). Mistakes: reversing order for subtraction/division (most common: less than and divided by backward), wrong operation (confusing sum and product), coefficient unclear (writing 3×x3×x instead of 3x3x, acceptable but coefficient notation preferred).

Question 11

Let nn represent a number. Which expression represents the sum of 33 times the number and 55?

  1. 3+n+53+n+5
  2. 3n⋅53n\cdot 5
  3. 3n+53n+5 (correct answer)
  4. 3(n+5)3(n+5)
Explanation: This question tests writing algebraic expressions from verbal descriptions using variables (letters representing numbers) and operation symbols (+, -, ×, ÷). Translating words to algebra: "more than/sum" → addition (+), "less than/difference" → subtraction (-), "times/product" → multiplication (coefficient: 3x means 3 times x), "divided by/quotient" → division (x/4). Order matters for non-commutative: "5 less than n" means subtract 5 FROM n (n-5, not 5-n reversed), "n divided by 4" means n/4 (not 4/n). Variable represents number: x, n, y are placeholders (unknown or any number in context). Example: "7 more than a number" uses variable n for number, "more than" means add, expression: n+7; "product of 3 and x" means 3 times x: 3x; "twice a number plus 5" means 2 times n plus 5: 2n+5 (not 2(n+5) which would be twice the sum); "x divided by 8" means x/8. The correct translation for the "sum of 3 times the number and 5" is 3n + 5. A common error is misunderstanding combined operations, like choosing 3(n + 5) which is 3 times the sum instead of 3n + 5, or 3 + n + 5 which is just addition without multiplication. Writing: (1) identify operation words (more→add, times→multiply, less→subtract, divided→divide), (2) choose variable (n, x, y for "a number"), (3) determine order (for subtraction/division: "less than" and "divided by" require careful order-"5 less than n" is n-5, subtract from first quantity), (4) write expression (n+5, 3x, x-7, y/4), (5) verify (if n=10: "5 more than n" gives 10+5=15✓, makes sense). Key phrases: "more than" adds to variable (n+5), "less than" subtracts from variable (n-7), "times" multiplies (3n coefficient notation), "of" often means multiply (half of n: (1/2)n=n/2). Mistakes: reversing order for subtraction/division (most common: less than and divided by backward), wrong operation (confusing sum and product), coefficient unclear (writing 3×x instead of 3x, acceptable but coefficient notation preferred).

Question 12

Let nn represent a number. Which expression represents 5 more than nn?

  1. 5−n5-n
  2. n+5n+5 (correct answer)
  3. n−5n-5
  4. 5n5n
Explanation: This question tests writing algebraic expressions from verbal descriptions using variables (letters representing numbers) and operation symbols (+, -, ×, ÷). Translating words to algebra: "more than/sum" → addition (+), "less than/difference" → subtraction (-), "times/product" → multiplication (coefficient: 3x means 3 times x), "divided by/quotient" → division (x/4). Order matters for non-commutative: "5 less than n" means subtract 5 FROM n (n-5, not 5-n reversed), "n divided by 4" means n/4 (not 4/n). Variable represents number: x, n, y are placeholders (unknown or any number in context). For example, "7 more than a number" uses variable n for number, "more than" means add, expression: n+7; "product of 3 and x" means 3 times x: 3x; "twice a number plus 5" means 2 times n plus 5: 2n+5 (not 2(n+5) which would be twice the sum); "x divided by 8" means x/8. The correct translation for '5 more than n' is n + 5, which matches choice B. A common error is reversing the order, like thinking '5 more than n' is 5 + n (which is the same due to addition being commutative, but for subtraction it would matter), or confusing it with multiplication to get 5n. To write expressions: (1) identify operation words (more→add, times→multiply, less→subtract, divided→divide), (2) choose variable (n, x, y for "a number"), (3) determine order (for subtraction/division: "less than" and "divided by" require careful order-"5 less than n" is n-5, subtract from first quantity), (4) write expression (n+5, 3x, x-7, y/4), (5) verify (if n=10: "5 more than n" gives 10+5=15✓, makes sense). Key phrases: "more than" adds to variable (n+5), "less than" subtracts from variable (n-7), "times" multiplies (3n coefficient notation), "of" often means multiply (half of n: (1/2)n=n/2). Mistakes: reversing order for subtraction/division (most common: less than and divided by backward), wrong operation (confusing sum and product), coefficient unclear (writing 3×x instead of 3x, acceptable but coefficient notation preferred).

Question 13

Let nn represent a number. Which expression represents 7 less than nn?

  1. 7−n7-n
  2. n+7n+7
  3. 7n7n
  4. n−7n-7 (correct answer)
Explanation: This question tests writing algebraic expressions from verbal descriptions using variables (letters representing numbers) and operation symbols (+, -, ×, ÷). Translating words to algebra: "more than/sum" → addition (+), "less than/difference" → subtraction (-), "times/product" → multiplication (coefficient: 3x means 3 times x), "divided by/quotient" → division (x/4). Order matters for non-commutative: "5 less than n" means subtract 5 FROM n (n-5, not 5-n reversed), "n divided by 4" means n/4 (not 4/n). Variable represents number: x, n, y are placeholders (unknown or any number in context). Example: "7 more than a number" uses variable n for number, "more than" means add, expression: n+7; "product of 3 and x" means 3 times x: 3x; "twice a number plus 5" means 2 times n plus 5: 2n+5 (not 2(n+5) which would be twice the sum); "x divided by 8" means x/8. The correct translation for "7 less than n" is n - 7. A common error is reversing the order, like choosing 7 - n instead of n - 7, or mistaking it for addition like n + 7 or multiplication like 7n. Writing: (1) identify operation words (more→add, times→multiply, less→subtract, divided→divide), (2) choose variable (n, x, y for "a number"), (3) determine order (for subtraction/division: "less than" and "divided by" require careful order-"5 less than n" is n-5, subtract from first quantity), (4) write expression (n+5, 3x, x-7, y/4), (5) verify (if n=10: "5 more than n" gives 10+5=15✓, makes sense). Key phrases: "more than" adds to variable (n+5), "less than" subtracts from variable (n-7), "times" multiplies (3n coefficient notation), "of" often means multiply (half of n: (1/2)n=n/2). Mistakes: reversing order for subtraction/division (most common: less than and divided by backward), wrong operation (confusing sum and product), coefficient unclear (writing 3×x instead of 3x, acceptable but coefficient notation preferred).

Question 14

Let xx represent a number. Which expression represents the difference between xx and 9?

  1. x−9x-9 (correct answer)
  2. 9x9x
  3. 9−x9-x
  4. x+9x+9
Explanation: This question tests writing algebraic expressions from verbal descriptions using variables (letters representing numbers) and operation symbols (+, -, ×, ÷). Translating words to algebra: 'more than/sum' → addition (+), 'less than/difference' → subtraction (-), 'times/product' → multiplication (coefficient: 3x means 3 times x), 'divided by/quotient' → division (x/4). Order matters for non-commutative: '5 less than n' means subtract 5 FROM n (n-5, not 5-n reversed), 'n divided by 4' means n/4 (not 4/n). Variable represents number: x, n, y are placeholders (unknown or any number in context). For example, '7 more than a number' uses variable n for number, 'more than' means add, expression: n+7; 'product of 3 and x' means 3 times x: 3x; 'twice a number plus 5' means 2 times n plus 5: 2n+5 (not 2(n+5) which would be twice the sum); 'x divided by 8' means x/8. The correct translation for 'the difference between x and 9' is x - 9, which matches choice C. A common error is reversing the subtraction order, like writing 9 - x instead of x - 9, or confusing with multiplication to get 9x. To write expressions: (1) identify operation words (more→add, times→multiply, less→subtract, divided→divide), (2) choose variable (n, x, y for 'a number'), (3) determine order (for subtraction/division: 'less than' and 'divided by' require careful order-'5 less than n' is n-5, subtract from first quantity), (4) write expression (n+5, 3x, x-7, y/4), (5) verify (if n=10: '5 more than n' gives 10+5=15✓, makes sense). Key phrases: 'more than' adds to variable (n+5), 'less than' subtracts from variable (n-7), 'times' multiplies (3n coefficient notation), 'of' often means multiply (half of n: (1/2)n=n/2). Mistakes: reversing order for subtraction/division (most common: less than and divided by backward), wrong operation (confusing sum and product), coefficient unclear (writing 3×x instead of 3x, acceptable but coefficient notation preferred).

Question 15

A game gives you pp points, then you earn 6 more points. Which expression represents your total points?

  1. p−6p-6
  2. 6−p6-p
  3. p+6p+6 (correct answer)
  4. 6p6p
Explanation: This question tests writing algebraic expressions from verbal descriptions using variables (letters representing numbers) and operation symbols (++, −-, ×\times, ÷\div). Translating words to algebra: 'more than/sum' → addition (++), 'less than/difference' → subtraction (−-), 'times/product' → multiplication (coefficient: 3x3x means 3 times xx), 'divided by/quotient' → division (x/4x/4). Order matters for non-commutative: '5 less than nn' means subtract 5 FROM nn (n−5n-5, not 5−n5-n reversed), 'nn divided by 4' means n/4n/4 (not 4/n4/n). Variable represents number: xx, nn, yy are placeholders (unknown or any number in context). For example, '7 more than a number' uses variable nn for number, 'more than' means add, expression: n+7n+7; 'product of 3 and xx' means 3 times xx: 3x3x; 'twice a number plus 5' means 2 times nn plus 5: 2n+52n+5 (not 2(n+5)2(n+5) which would be twice the sum); 'xx divided by 8' means x/8x/8. The correct translation for total points after earning pp points and then 6 more is p+6p + 6, which matches choice C. A common error is confusing addition with multiplication, like writing 6p6p, or reversing to 6−p6 - p. To write expressions: (1) identify operation words (more→add, times→multiply, less→subtract, divided→divide), (2) choose variable (nn, xx, yy for 'a number'), (3) determine order (for subtraction/division: 'less than' and 'divided by' require careful order-'5 less than nn' is n−5n-5, subtract from first quantity), (4) write expression (n+5n+5, 3x3x, x−7x-7, y/4y/4), (5) verify (if n=10n=10: '5 more than nn' gives 10+5=15✓10+5=15✓, makes sense). Key phrases: 'more than' adds to variable (n+5n+5), 'less than' subtracts from variable (n−7n-7), 'times' multiplies (3n3n coefficient notation), 'of' often means multiply (half of nn: (1/2)n=n/2(1/2)n=n/2). Mistakes: reversing order for subtraction/division (most common: less than and divided by backward), wrong operation (confusing sum and product), coefficient unclear (writing 3×x3\times x instead of 3x3x, acceptable but coefficient notation preferred).

Question 16

A ribbon is yy centimeters long. It is cut into 4 equal pieces. Which expression gives the length of one piece?

  1. 4y4y
  2. 4y\dfrac{4}{y}
  3. y−4y-4
  4. y4\dfrac{y}{4} (correct answer)
Explanation: This problem is all about sharing equally. When you split something into equal pieces, you divide. Here, the ribbon is yy centimeters long, and you cut it into 44 equal pieces. To find the length of one piece, divide the total length by the number of pieces: y4\frac{y}{4} That matches choice D. Think about it like a pizza. If a pizza weighs yy ounces and you slice it into 44 equal slices, each slice weighs y4\frac{y}{4} ounces. The total goes on top, and the number of pieces goes on the bottom. So whenever you see "cut into equal pieces" or "shared equally," reach for division! Try this at home: Grab a string or piece of paper. Pretend it's yy long, fold it into 44 equal parts, and say out loud: "Each part is y4\frac{y}{4}!" Try it with 33 parts and 55 parts too.

Question 17

A ribbon is xx centimeters long. It is cut into 4 equal pieces. Which expression represents xx divided by 4?

  1. x4\dfrac{x}{4} (correct answer)
  2. 4x4x
  3. x−4x-4
  4. 4x\dfrac{4}{x}
Explanation: This question tests writing algebraic expressions from verbal descriptions using variables (letters representing numbers) and operation symbols (+, -, ×, ÷). Translating words to algebra: "more than/sum" → addition (+), "less than/difference" → subtraction (-), "times/product" → multiplication (coefficient: 3x means 3 times x), "divided by/quotient" → division (x/4). Order matters for non-commutative: "5 less than n" means subtract 5 FROM n (n-5, not 5-n reversed), "n divided by 4" means n/4 (not 4/n). Variable represents number: x, n, y are placeholders (unknown or any number in context). For example, "7 more than a number" uses variable n for number, "more than" means add, expression: n+7; "product of 3 and x" means 3 times x: 3x; "twice a number plus 5" means 2 times n plus 5: 2n+5 (not 2(n+5) which would be twice the sum); "x divided by 8" means x/8. The correct translation for 'x divided by 4' is x/4, which matches choice C. A common error is reversing the division, like writing 4/x, or confusing it with multiplication to get 4x. To write expressions: (1) identify operation words (more→add, times→multiply, less→subtract, divided→divide), (2) choose variable (n, x, y for "a number"), (3) determine order (for subtraction/division: "less than" and "divided by" require careful order—"5 less than n" is n-5, subtract from first quantity), (4) write expression (n+5, 3x, x-7, y/4), (5) verify (if n=10: "5 more than n" gives 10+5=15✓, makes sense). Key phrases: "more than" adds to variable (n+5), "less than" subtracts from variable (n-7), "times" multiplies (3n coefficient notation), "of" often means multiply (half of n: (1/2)n=n/2). Mistakes: reversing order for subtraction/division (most common: less than and divided by backward), wrong operation (confusing sum and product), coefficient unclear (writing 3×x instead of 3x, acceptable but coefficient notation preferred).

Question 18

A classroom has xx students. 7 fewer than that number join an after-school club. Which expression represents the number who join?

  1. x+7x+7
  2. x−7x-7 (correct answer)
  3. 7x7x
  4. 7−x7-x
Explanation: This question tests writing algebraic expressions from verbal descriptions using variables (letters representing numbers) and operation symbols (+, -, ×, ÷). Translating words to algebra: "more than/sum" → addition (+), "less than/difference" → subtraction (-), "times/product" → multiplication (coefficient: 3x means 3 times x), "divided by/quotient" → division (x/4). Order matters for non-commutative: "5 less than n" means subtract 5 FROM n (n-5, not 5-n reversed), "n divided by 4" means n/4 (not 4/n). Variable represents number: x, n, y are placeholders (unknown or any number in context). For example, "7 more than a number" uses variable n for number, "more than" means add, expression: n+7; "product of 3 and x" means 3 times x: 3x; "twice a number plus 5" means 2 times n plus 5: 2n+5 (not 2(n+5) which would be twice the sum); "x divided by 8" means x/8. The correct translation for '7 fewer than x' is x - 7, which matches choice C. A common error is reversing the subtraction, like writing 7 - x, or using addition to get x + 7. To write expressions: (1) identify operation words (more→add, times→multiply, less→subtract, divided→divide), (2) choose variable (n, x, y for "a number"), (3) determine order (for subtraction/division: "less than" and "divided by" require careful order-"5 less than n" is n-5, subtract from first quantity), (4) write expression (n+5, 3x, x-7, y/4), (5) verify (if n=10: "5 more than n" gives 10+5=15✓, makes sense). Key phrases: "more than" adds to variable (n+5), "less than" subtracts from variable (n-7), "times" multiplies (3n coefficient notation), "of" often means multiply (half of n: (1/2)n=n/2). Mistakes: reversing order for subtraction/division (most common: less than and divided by backward), wrong operation (confusing sum and product), coefficient unclear (writing 3×x instead of 3x, acceptable but coefficient notation preferred).

Question 19

Let yy represent the number of pages in a book. Which expression represents half of the pages?

  1. 2y2y
  2. y−2y-2
  3. y2\dfrac{y}{2} (correct answer)
  4. 2y\dfrac{2}{y}
Explanation: This question tests writing algebraic expressions from verbal descriptions using variables (letters representing numbers) and operation symbols (+, -, ×, ÷). Translating words to algebra: "more than/sum" → addition (+), "less than/difference" → subtraction (-), "times/product" → multiplication (coefficient: 3x means 3 times x), "divided by/quotient" → division (x/4). Order matters for non-commutative: "5 less than n" means subtract 5 FROM n (n-5, not 5-n reversed), "n divided by 4" means n/4 (not 4/n). Variable represents number: x, n, y are placeholders (unknown or any number in context). Example: "7 more than a number" uses variable n for number, "more than" means add, expression: n+7; "product of 3 and x" means 3 times x: 3x; "twice a number plus 5" means 2 times n plus 5: 2n+5 (not 2(n+5) which would be twice the sum); "x divided by 8" means x/8. The correct translation for "half of the pages" where y is the number of pages is y/2. A common error is reversing the division like 2/y, or confusing with multiplication like 2y or subtraction like y - 2. Writing: (1) identify operation words (more→add, times→multiply, less→subtract, divided→divide), (2) choose variable (n, x, y for "a number"), (3) determine order (for subtraction/division: "less than" and "divided by" require careful order—"5 less than n" is n-5, subtract from first quantity), (4) write expression (n+5, 3x, x-7, y/4), (5) verify (if n=10: "5 more than n" gives 10+5=15✓, makes sense). Key phrases: "more than" adds to variable (n+5), "less than" subtracts from variable (n-7), "times" multiplies (3n coefficient notation), "of" often means multiply (half of n: (1/2)n=n/2). Mistakes: reversing order for subtraction/division (most common: less than and divided by backward), wrong operation (confusing sum and product), coefficient unclear (writing 3×x instead of 3x, acceptable but coefficient notation preferred).

Question 20

A notebook costs xx dollars. A student buys 3 notebooks. Which expression represents the total cost in dollars?

  1. x−3x-3
  2. x+3x+3
  3. 3x3x (correct answer)
  4. x3\dfrac{x}{3}
Explanation: This question tests writing algebraic expressions from verbal descriptions using variables (letters representing numbers) and operation symbols (+, -, ×, ÷). Translating words to algebra: 'more than/sum' → addition (+), 'less than/difference' → subtraction (-), 'times/product' → multiplication (coefficient: 3x means 3 times x), 'divided by/quotient' → division (x/4). Order matters for non-commutative: '5 less than n' means subtract 5 FROM n (n-5, not 5-n reversed), 'n divided by 4' means n/4 (not 4/n). Variable represents number: x, n, y are placeholders (unknown or any number in context). For example, '7 more than a number' uses variable n for number, 'more than' means add, expression: n+7; 'product of 3 and x' means 3 times x: 3x; 'twice a number plus 5' means 2 times n plus 5: 2n+5 (not 2(n+5) which would be twice the sum); 'x divided by 8' means x/8. The correct translation for the total cost of 3 notebooks at x dollars each is 3x, which matches choice B. A common error is confusing multiplication with addition, like writing x + 3 instead of 3x, or using division like x/3. To write expressions: (1) identify operation words (more→add, times→multiply, less→subtract, divided→divide), (2) choose variable (n, x, y for 'a number'), (3) determine order (for subtraction/division: 'less than' and 'divided by' require careful order—'5 less than n' is n-5, subtract from first quantity), (4) write expression (n+5, 3x, x-7, y/4), (5) verify (if n=10: '5 more than n' gives 10+5=15✓, makes sense). Key phrases: 'more than' adds to variable (n+5), 'less than' subtracts from variable (n-7), 'times' multiplies (3n coefficient notation), 'of' often means multiply (half of n: (1/2)n=n/2). Mistakes: reversing order for subtraction/division (most common: less than and divided by backward), wrong operation (confusing sum and product), coefficient unclear (writing 3×x instead of 3x, acceptable but coefficient notation preferred).