6th Grade 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

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?

6w+86w + 8
4w+84w + 8
3w+43w + 4
2w+42w + 4
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6th Grade Math Quiz

6th Grade Math Quiz: Write Expressions With Numbers And Variables

Practice Write Expressions With Numbers And Variables in 6th Grade 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 6th Grade 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

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 2

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 3

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 4

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 5

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 6

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).

Question 7

Let xx represent a number. Which expression means the sum of twice xx and 7?

  1. 2x+72x+7 (correct answer)
  2. 7−2x7-2x
  3. x+2+7x+2+7
  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 A. A common error is misinterpreting the grouping, like writing 2(x + 7) which means twice the sum instead of sum of twice x and 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 8

Carmen is making bracelets. Each bracelet requires 1515 small beads and 33 large beads. She wants to make bb bracelets, but she already has 2020 small beads and 88 large beads from a previous project. Which expression represents the number of small beads Carmen still needs to buy?

  1. 15(b−20)15(b - 20)
  2. 15b+2015b + 20
  3. 15b−2015b - 20 (correct answer)
  4. 15−20b15 - 20b
Explanation: When you encounter word problems involving expressions, start by identifying what you need to find and then build the expression step by step using the given information. Carmen needs 1515 small beads per bracelet, so for bb bracelets she needs 15b15b small beads total. However, she already has 2020 small beads, which means she needs fewer beads than the full amount. To find how many she still needs to buy, subtract what she already has from what she needs: 15b−2015b - 20. This is answer choice C. Let's examine why the other options are incorrect. Choice A, 15(b−20)15(b - 20), suggests she's making (b−20)(b - 20) bracelets instead of bb bracelets, which changes the entire problem. Choice B, 15b+2015b + 20, adds her existing beads to the total needed, which would give her more beads than necessary rather than finding what she still needs. Choice D, 15−20b15 - 20b, reverses the relationship entirely and doesn't make sense in context since it suggests she needs fewer beads as she makes more bracelets. When solving "how many more do I need" problems, remember the key formula: Total needed minus what you already have equals what you still need. Watch for this pattern in word problems where someone has some materials but needs to buy additional amounts to complete a project.

Question 9

A school is ordering pizza for a field trip. They need 11 pizza for every 44 students, plus 22 extra pizzas for the teachers. If there are ss students going on the trip, which expression represents the total number of pizzas needed?

  1. s+24\frac{s + 2}{4}
  2. s4+2\frac{s}{4} + 2 (correct answer)
  3. 4s+24s + 2
  4. s+84\frac{s + 8}{4}
Explanation: When you see word problems involving rates and additional quantities, break down the problem into parts and translate each piece into mathematical language. Let's work through this step by step. You need 1 pizza for every 4 students, which means you divide the total number of students by 4 to find how many pizzas the students need: s4\frac{s}{4}. Then you need 2 extra pizzas specifically for teachers. Since these are separate requirements, you add them together: s4+2\frac{s}{4} + 2. This matches answer choice B. Now let's see why the other answers don't work. Choice A gives s+24\frac{s + 2}{4}, which incorrectly treats the 2 teacher pizzas as if they follow the same 4-to-1 ratio as the students. This would mean you only get half a pizza for teachers instead of 2 whole pizzas. Choice C gives 4s+24s + 2, which multiplies students by 4 instead of dividing—this would give you way too many pizzas (4 per student instead of 1 per 4 students). Choice D gives s+84\frac{s + 8}{4}, which adds 8 to the number of students before dividing by 4. This treats the teacher pizzas as if they were equivalent to 8 students, but 8 ÷ 4 = 2, so while this coincidentally gives the right number of teacher pizzas, it incorrectly mixes them into the student ratio. Remember: when problems have different rates or rules for different groups, handle each group separately, then combine the results. Don't try to force everything into one ratio.

Question 10

Jake has xx baseball cards. His sister has 33 fewer cards than twice the number Jake has. His brother has 55 more cards than Jake. Which expression represents the total number of cards all three siblings have together?

  1. 2x+82x + 8
  2. 6x−26x - 2
  3. 4x−24x - 2
  4. 4x+24x + 2 (correct answer)
Explanation: When you encounter word problems involving multiple people with different amounts, break down each person's quantity separately before combining them. Let's identify what each sibling has. Jake has xx cards. His sister has "3 fewer cards than twice the number Jake has," which means 2x−32x - 3. His brother has "5 more cards than Jake," which gives us x+5x + 5. To find the total, add all three expressions: x+(2x−3)+(x+5)x + (2x - 3) + (x + 5). Combine like terms: x+2x+x−3+5=4x+2x + 2x + x - 3 + 5 = 4x + 2. This matches answer choice D. Looking at the wrong answers: Choice A (2x+82x + 8) likely comes from misreading the sister's amount as 2x+32x + 3 instead of 2x−32x - 3. Choice B (6x−26x - 2) suggests incorrectly multiplying Jake's cards by 6 instead of properly identifying each person's amount. Choice C (4x−24x - 2) correctly gets 4x4x for the variable terms but miscalculates the constants, probably by treating both the sister's "3 fewer" and brother's "5 more" as negative values. The key strategy here is to translate each phrase carefully into mathematical expressions, then combine systematically. Watch for words like "fewer" (subtract) and "more" (add), and remember that "twice a number" means multiply by 2. Always double-check your translation of each person's amount before adding them together.

Question 11

A notebook costs xx dollars. A pen costs 22 dollars more than the notebook. Which expression represents the cost of the pen?

  1. x2\dfrac{x}{2}
  2. 2x2x
  3. x+2x+2 (correct answer)
  4. x−2x-2
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 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). 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 the cost of the pen which is "2 dollars more than the notebook" where the notebook costs x dollars is x+2x + 2. A common error is confusing "more than" with multiplication like 2x2x, subtraction like x−2x - 2, or division like x/2x/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−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=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\times x instead of 3x3x, acceptable but coefficient notation preferred).

Question 12

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 13

Let mm represent a number of minutes. Which expression means half of mm?

  1. m−2m-2
  2. 2m\dfrac{2}{m}
  3. $2m$
  4. m2\dfrac{m}{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: 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 'half of m' is m/2m/2, which matches choice C. A common error is reversing the division to 2/m2/m, or confusing with multiplication to get $2m$. 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=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×x instead of 3x3x, acceptable but coefficient notation preferred).

Question 14

A water bottle holds xx ounces. Which expression represents the amount of water in the bottle after it is divided equally into 4 cups?

  1. x−4x-4
  2. 4x\dfrac{4}{x}
  3. x÷4x\div 4 (correct answer)
  4. 4x4x
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 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). 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 the amount after "divided equally into 4 cups" where the bottle holds xx ounces is x÷4x ÷ 4 (or x/4x/4, the amount per cup). A common error is reversing the division like 4/x4/x, or confusing with subtraction like x−4x - 4 or multiplication like 4x4x. Writing: (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×x instead of 3x3x, acceptable but coefficient notation preferred).

Question 15

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

  1. 5n5n
  2. n+5n+5 (correct answer)
  3. n−5n-5
  4. 5−n5-n
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 writing 5 - n instead of n - 5 for subtraction phrases, or confusing 'more than' 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 16

Which expression represents the sum of 3 times xx and 5?

  1. 3x+5\dfrac{3}{x}+5
  2. 3+x+53+x+5
  3. 3x+53x+5 (correct answer)
  4. 3(x+5)3(x+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). 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 3 times x and 5' is 3x + 5, which matches choice B. A common error is misinterpreting as multiplying the sum, like 3(x + 5), or using addition without multiplication to get 3 + x + 5. 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 17

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 18

A movie ticket costs xx dollars. You also pay a $3 fee. Which expression represents the total cost?

  1. 3x3x
  2. x+3x+3 (correct answer)
  3. x3\dfrac{x}{3}
  4. x−3x-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, which is x dollars plus a $3 fee, is x + 3, which matches choice C. A common error is using subtraction like x - 3, or multiplication like 3x, instead of addition. 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

A pack has yy stickers. You buy 3 packs. Which expression represents the product of 3 and yy?

  1. 3+y3+y
  2. y÷3y\div 3
  3. 3y3y (correct answer)
  4. y−3y-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 'product of 3 and y' is 3y, which matches choice C. A common error is confusing product with sum, like writing 3 + y, or using division instead to get y ÷ 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).

Question 20

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).