Elementary School Math Quiz: Add And Subtract Unlike Fractions
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Add And Subtract Unlike FractionsQuestion 1 of 20

A recipe uses the same-sized whole cup as the unit. Maya pours 23\tfrac{2}{3} cup of milk and then adds 14\tfrac{1}{4} cup more. What is the total amount of milk she poured?

37\tfrac{3}{7} cup
912\tfrac{9}{12} cup
1112\tfrac{11}{12} cup
312\tfrac{3}{12} cup
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Elementary School Math Quiz

Elementary School Math Quiz: Add And Subtract Unlike Fractions

Practice Add And Subtract Unlike Fractions in Elementary 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 Add And Subtract Unlike Fractions, giving you a quick way to practice the rules, question types, and explanations that matter most for Elementary 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

A recipe uses the same-sized whole cup as the unit. Maya pours 23\tfrac{2}{3} cup of milk and then adds 14\tfrac{1}{4} cup more. What is the total amount of milk she poured?

  1. 37\tfrac{3}{7} cup
  2. 912\tfrac{9}{12} cup
  3. 1112\tfrac{11}{12} cup (correct answer)
  4. 312\tfrac{3}{12} cup
Explanation: To add or subtract unlike fractions, which have different denominators, we must first convert them to equivalent fractions with the same denominator to ensure they refer to parts of the same-sized whole. We find a common denominator by identifying a common multiple of the two denominators, preferably the least common multiple, such as 12 for 3 and 4 in this milk-pouring scenario. To rewrite the fractions, multiply both the numerator and denominator of each by the same number; for example, multiply 2/3 by 4/4 to get 8/12, and 1/4 by 3/3 to get 3/12. Once they have the same denominator, add the numerators while keeping the denominator the same, resulting in 11/12 cup of milk total. A common misconception is that you can simply add the numerators and denominators separately, but this doesn't account for the different part sizes. Using equivalent fractions allows us to combine or compare parts accurately by making them comparable. This method ensures that operations on fractions are meaningful and applicable in real-world measurements like recipes.

Question 2

A ribbon is cut from the same-sized roll. Maya uses 34\frac{3}{4} meter, and Jordan uses 23\frac{2}{3} meter. What is the total length of ribbon they use?

  1. 57\frac{5}{7} meter
  2. 1712\frac{17}{12} meter (correct answer)
  3. 512\frac{5}{12} meter
  4. 1124\frac{11}{24} meter
Explanation: When adding or subtracting unlike fractions, which have different denominators, we need to convert them to equivalent fractions with the same denominator. To do this, find a common denominator, such as the least common multiple of 4 and 3, which is 12. Rewrite each fraction by multiplying the numerator and denominator by the same number: 3/4 becomes (3×3)/(4×3) = 9/12, and 2/3 becomes (2×4)/(3×4) = 8/12. Now, add the numerators while keeping the common denominator: 9/12 + 8/12 = 17/12 meter, which is the total ribbon used by Maya and Jordan. A common misconception is that you can just add the numerators and denominators separately, but this doesn't account for the different part sizes. Using equivalent fractions allows us to combine amounts accurately by ensuring the pieces are the same size. This equivalence principle makes addition and subtraction of any fractions possible, as it aligns the units for fair computation.

Question 3

A recipe serves 6 people and calls for 1131\frac{1}{3} cups of milk and 34\frac{3}{4} cup of cream. Maria wants to make enough for 9 people. How much total liquid (milk and cream combined) will she need?

  1. 2582\frac{5}{8} cups of liquid
  2. 3183\frac{1}{8} cups of liquid (correct answer)
  3. 3143\frac{1}{4} cups of liquid
  4. 3583\frac{5}{8} cups of liquid
Explanation: For 6 people, total liquid is 113+34=43+34=1612+912=25121\frac{1}{3} + \frac{3}{4} = \frac{4}{3} + \frac{3}{4} = \frac{16}{12} + \frac{9}{12} = \frac{25}{12} cups. For 9 people, multiply by 96=32\frac{9}{6} = \frac{3}{2}: 2512×32=7524=258=318\frac{25}{12} \times \frac{3}{2} = \frac{75}{24} = \frac{25}{8} = 3\frac{1}{8} cups. Choice A uses an incorrect scaling factor. Choice C represents just scaling the milk or cream individually. Choice D adds extra liquid beyond the correct scaling.

Question 4

A recipe calls for 2162\frac{1}{6} cups of flour. James accidentally added 2342\frac{3}{4} cups instead. If he removes 13\frac{1}{3} cup to try to fix his mistake, how much flour will he have compared to the original recipe?

  1. 34\frac{3}{4} cup more than the recipe calls for
  2. 512\frac{5}{12} cup more than the recipe calls for
  3. 712\frac{7}{12} cup more than the recipe calls for
  4. 14\frac{1}{4} cup more than the recipe calls for (correct answer)
Explanation: When you encounter word problems involving mixed numbers and fractions, you need to track each step carefully and work with a common denominator to compare amounts accurately. Let's follow James's flour adventure step by step. First, find how much flour James has after removing some. He started with 2342\frac{3}{4} cups and removed 13\frac{1}{3} cup. To subtract these, convert to improper fractions with a common denominator of 12: 234=33122\frac{3}{4} = \frac{33}{12} and 13=412\frac{1}{3} = \frac{4}{12}. So James has 3312412=2912\frac{33}{12} - \frac{4}{12} = \frac{29}{12} cups remaining. Now compare this to the original recipe amount of 216=25122\frac{1}{6} = \frac{25}{12} cups. The difference is 29122512=412=14\frac{29}{12} - \frac{25}{12} = \frac{4}{12} = \frac{1}{4} cup more than needed. Choice A (34\frac{3}{4} cup more) likely comes from incorrectly finding the difference between 2342\frac{3}{4} and 2162\frac{1}{6} without accounting for the removal step. Choice B (512\frac{5}{12} cup more) might result from calculation errors when finding common denominators. Choice C (712\frac{7}{12} cup more) could come from adding instead of subtracting the removed flour, or other arithmetic mistakes. The correct answer is D: James has 14\frac{1}{4} cup more flour than the recipe calls for. Strategy tip: In multi-step fraction problems, convert everything to the same denominator early and double-check each operation. Track what you're adding versus subtracting at each step.

Question 5

On a hike, Noah walked 35\frac{3}{5} mile and then 12\frac{1}{2} mile. Both distances are parts of the same 1-mile whole. He rewrote them as 35=610\frac{3}{5}=\frac{6}{10} and 12=510\frac{1}{2}=\frac{5}{10}. Which statement about the size of the result is correct?

  1. The total is less than 1 mile because the denominators are different.
  2. The total is exactly 1 mile because 3+1=43+1=4 and 5+2=75+2=7.
  3. The total is greater than 1 mile because 610+510=1110\frac{6}{10}+\frac{5}{10}=\frac{11}{10}. (correct answer)
  4. The total is 47\frac{4}{7} mile because you add the numerators and denominators.
Explanation: When adding or subtracting unlike fractions, we first need to find equivalent fractions with the same denominator. To do this, identify a common denominator, such as 10 for denominators 5 and 2, which is the least common multiple. Then, rewrite each fraction: multiply the numerator and denominator of 35\frac{3}{5} by 2 to get 610\frac{6}{10}, and of 12\frac{1}{2} by 5 to get 510\frac{5}{10}. Once the fractions have the same denominator, add the numerators 6+5=116 + 5 = 11 while keeping the denominator 10, resulting in 1110\frac{11}{10} mile, which is greater than 1. A common misconception is that different denominators mean the sum is less than 1, but equivalents show otherwise. Using equivalent fractions ensures accurate size comparisons of the result. This method generalizes to estimating totals in activities like hiking, providing reliable insights into quantities.

Question 6

A garden bed is the same whole garden bed for both measurements. One section is 78\frac{7}{8} full of soil, and another section adds 25\frac{2}{5} of the bed more. The fractions must refer to the same whole (one garden bed). A student rewrites them as 78=3540\frac{7}{8}=\frac{35}{40} and 25=1640\frac{2}{5}=\frac{16}{40}. What is the total fraction of the garden bed filled?

  1. 913\frac{9}{13} of the bed
  2. 3713\frac{37}{13} of the bed
  3. 5140\frac{51}{40} of the bed (correct answer)
  4. 940\frac{9}{40} of the bed
Explanation: When adding or subtracting unlike fractions, which have different denominators, we need to convert them to equivalent fractions with the same denominator. To do this, find a common denominator, such as the least common multiple of 8 and 5, which is 40. Rewrite each fraction by multiplying the numerator and denominator by the same number: 7/8 becomes (7×5)/(8×5) = 35/40, and 2/5 becomes (2×8)/(5×8) = 16/40. Now, add the numerators while keeping the common denominator: 35/40 + 16/40 = 51/40 of the bed filled. A common misconception is that adding fractions means adding numerators while keeping one denominator, but this ignores equivalence. Using equivalent fractions allows precise combination by equalizing part sizes. This principle generalizes to enable addition and subtraction across any unlike fractions.

Question 7

A recipe uses flour measured with the same 1-cup measuring cup. You already added 1141\frac{1}{4} cups of flour, but the recipe needs 2132\frac{1}{3} cups total. The fractions must refer to the same whole (1 cup). Using equivalent fractions, 14=312\frac{1}{4}=\frac{3}{12} and 13=412\frac{1}{3}=\frac{4}{12}. How much more flour is needed?

  1. 11121\frac{1}{12} cups (correct answer)
  2. 112\frac{1}{12} cup
  3. 1271\frac{2}{7} cups
  4. 37\frac{3}{7} cup
Explanation: When adding or subtracting unlike fractions, which have different denominators, we need to convert them to equivalent fractions with the same denominator. To do this, find a common denominator, such as the least common multiple of 3 and 4, which is 12. Rewrite each fraction by multiplying the numerator and denominator by the same number: 2132 \frac{1}{3} is 73\frac{7}{3}, which becomes (7×4)/(3×4)=2812(7\times4)/(3\times4) = \frac{28}{12}, and 1141 \frac{1}{4} is 54\frac{5}{4}, which becomes (5×3)/(4×3)=1512(5\times3)/(4\times3) = \frac{15}{12}. Now, subtract the numerators while keeping the common denominator: 28121512=1312=1112\frac{28}{12} - \frac{15}{12} = \frac{13}{12} = 1 \frac{1}{12} cups more needed. A common misconception is subtracting mixed numbers by only handling wholes or fractions separately without equivalence. Using equivalent fractions makes subtraction possible by standardizing denominators. This equivalence allows for accurate operations on fractions in various contexts.

Question 8

Two pitchers each hold the same 1-liter whole (fractions must refer to the same-sized whole). One pitcher has 78\frac{7}{8} liter of juice. Another has 13\frac{1}{3} liter of juice. A student writes equivalent fractions: 78=2124\frac{7}{8}=\frac{21}{24} and 13=824\frac{1}{3}=\frac{8}{24}. What is the difference 7813\frac{7}{8}-\frac{1}{3} liters?

  1. 65\frac{6}{5} liter
  2. 2011\frac{20}{11} liter
  3. 1324\frac{13}{24} liter (correct answer)
  4. 611\frac{6}{11} liter
Explanation: When subtracting unlike fractions such as 7/8 and 1/3, we need to find equivalent fractions with the same denominator to compare precisely. To find a common denominator, use the least common multiple of 8 and 3, which is 24. Rewrite 7/8 as 21/24 by multiplying numerator and denominator by 3, and 1/3 as 8/24 by multiplying by 8. Subtract the numerators: 21 - 8 = 13, over 24, giving 13/24 liter difference. A common misconception is using the wrong common denominator, but LCM ensures efficiency. Equivalents make fractions compatible, enabling subtraction or addition. This principle generalizes to all fraction operations, ensuring correctness.

Question 9

A science class pours water into a container, using the same 1-liter measuring cup each time. They pour 56\frac{5}{6} liter, then pour 14\frac{1}{4} liter more. The fractions must refer to the same whole (1 liter). One student rewrites them as equivalent fractions: 56=1012\frac{5}{6}=\frac{10}{12} and 14=312\frac{1}{4}=\frac{3}{12}. What is the total amount of water poured?

  1. 610\frac{6}{10} liter
  2. 1124\frac{11}{24} liter
  3. 1312\frac{13}{12} liter (correct answer)
  4. 612\frac{6}{12} liter
Explanation: When adding or subtracting unlike fractions, which have different denominators, we need to convert them to equivalent fractions with the same denominator. To do this, find a common denominator, such as the least common multiple of 6 and 4, which is 12. Rewrite each fraction by multiplying the numerator and denominator by the same number: 5/6 becomes (5×2)/(6×2) = 10/12, and 1/4 becomes (1×3)/(4×3) = 3/12. Now, add the numerators while keeping the common denominator: 10/12 + 3/12 = 13/12 liter, the total water poured. A common misconception is that fractions with larger denominators are always smaller, but equivalence shows value depends on both numerator and denominator. Using equivalent fractions makes it possible to operate on them by standardizing the part sizes. This method generalizes to all fraction additions and subtractions, allowing accurate comparisons and calculations.

Question 10

Liam filled a water bottle that holds 1 whole liter. He drank 78\frac{7}{8} liter and then drank 13\frac{1}{3} liter more from another identical full bottle. The fractions refer to the same-sized whole liter. He rewrote 78=2124\frac{7}{8}=\frac{21}{24} and 13=824\frac{1}{3}=\frac{8}{24}. What is the total amount he drank?

  1. 811\frac{8}{11} liter
  2. 2224\frac{22}{24} liter
  3. 2924\frac{29}{24} liter (correct answer)
  4. 824\frac{8}{24} liter
Explanation: When adding or subtracting unlike fractions, we first need to find equivalent fractions with the same denominator. To do this, identify a common denominator, such as 24 for denominators 8 and 3, which is the least common multiple. Then, rewrite each fraction: multiply the numerator and denominator of 78\frac{7}{8} by 3 to get 2124\frac{21}{24}, and of 13\frac{1}{3} by 8 to get 824\frac{8}{24}. Once the fractions have the same denominator, add the numerators 21+8=2921 + 8 = 29 while keeping the denominator 24, resulting in 2924\frac{29}{24} liter drunk. A common misconception is that adding improper fractions directly without equivalents gives a valid result, but this ignores the different part sizes. Using equivalent fractions ensures we combine equal portions of the liter accurately. This method generalizes to adding any unlike fractions, supporting calculations in everyday situations like totaling liquid consumption.

Question 11

On a number line from 0 to 1 (the same whole), a student wants to add 38\frac{3}{8} and 12\frac{1}{2}. The student writes equivalent fractions: 12=48\frac{1}{2}=\frac{4}{8}. Which statement correctly explains how the fractions were combined?

  1. Add the denominators: 8+2=108+2=10, so the sum is 410\frac{4}{10}.
  2. Make equivalent fractions with a common denominator of 8, then add: 38+48=78\frac{3}{8}+\frac{4}{8}=\frac{7}{8}. (correct answer)
  3. Add the numerators and denominators: 3+18+2=410\frac{3+1}{8+2}=\frac{4}{10}.
  4. Add only the numerators and keep 8: 3+18=48\frac{3+1}{8}=\frac{4}{8}.
Explanation: When adding unlike fractions such as 3/8 and 1/2, we need to find equivalent fractions with the same denominator to combine them effectively. To find a common denominator, note that 8 is a multiple of 2, so use 8. Rewrite 1/2 as 4/8 by multiplying numerator and denominator by 4, while 3/8 stays the same. Add the numerators over the common denominator: 3 + 4 = 7, giving 7/8. A common misconception is adding numerators and denominators separately, like (3+1)/(8+2) = 4/10, but this distorts the values. Equivalent fractions align the parts, making addition possible. This method generalizes to subtracting unlike fractions too, ensuring accurate results.

Question 12

A runner jogged 56\frac{5}{6} mile on Monday and 14\frac{1}{4} mile on Tuesday. Both distances are parts of the same 1-mile whole. Which statement correctly explains how to find a common denominator using equivalent fractions before adding?

  1. Use 10 as the common denominator because 6+4=106+4=10.
  2. Keep the denominators 6 and 4 and add the numerators: 5+1=65+1=6.
  3. Use 24 as the common denominator by rewriting 56\frac{5}{6} as 2024\frac{20}{24} and 14\frac{1}{4} as 624\frac{6}{24}. (correct answer)
  4. Rewrite 56\frac{5}{6} as 1012\frac{10}{12} and keep 14\frac{1}{4} as 14\frac{1}{4} because both are fractions.
Explanation: When adding or subtracting unlike fractions, we first need to find equivalent fractions with the same denominator. To do this, identify a common denominator, such as 24 for denominators 6 and 4, which is the least common multiple. Then, rewrite each fraction: multiply the numerator and denominator of 56\frac{5}{6} by 4 to get 2024\frac{20}{24}, and of 14\frac{1}{4} by 6 to get 624\frac{6}{24}. Once the fractions have the same denominator, you can add the numerators while keeping the denominator the same to find the total distance. A common misconception is adding the denominators instead of finding a common one, like using 10 because 6+4=106 + 4 = 10, but this doesn't create equivalent fractions. Using equivalent fractions ensures that the parts of the mile are the same size for accurate addition. This method generalizes to all fraction operations, allowing reliable calculations in contexts like totaling jogging distances.

Question 13

A water bottle holds 1 whole liter (the same-sized whole). A student drank 1121\frac{1}{2} liters over the day from refills, then drank 23\frac{2}{3} liter more. These amounts refer to the same unit (liters). The student rewrites 12=36\frac{1}{2}=\frac{3}{6} and 23=46\frac{2}{3}=\frac{4}{6}. What is 112+231\frac{1}{2}+\frac{2}{3} liters?

  1. 2162\frac{1}{6} liters (correct answer)
  2. 1351\frac{3}{5} liters
  3. 1361\frac{3}{6} liters
  4. 35\frac{3}{5} liter
Explanation: When adding unlike fractions in mixed numbers like 1 1/2 and 2/3, we need to find equivalents for the fractional parts with the same denominator. To find a common denominator, use the least common multiple of 2 and 3, which is 6. Rewrite 1/2 as 3/6 by multiplying numerator and denominator by 3, and 2/3 as 4/6 by multiplying by 2. Add the fractions to the whole: 1 + 3/6 + 4/6 = 1 + 7/6 = 2 1/6 liters. A common misconception is forgetting to handle the whole number separately, but mixed numbers require combining like parts. Equivalent fractions make both parts comparable, facilitating addition or subtraction. This approach works broadly for unlike fractions, allowing seamless operations across various contexts.

Question 14

Two students ate parts of the same-sized pizza. One ate 1121\frac{1}{2} pizzas and the other ate 34\frac{3}{4} of a pizza. The fractions must refer to the same whole (one pizza). Using equivalent fractions, 12=24\frac{1}{2}=\frac{2}{4}. What is the total amount of pizza eaten?

  1. 2142\frac{1}{4} pizzas (correct answer)
  2. 1461\frac{4}{6} pizzas
  3. 1481\frac{4}{8} pizzas
  4. 1261\frac{2}{6} pizzas
Explanation: When adding or subtracting unlike fractions, which have different denominators, we need to convert them to equivalent fractions with the same denominator. To do this, find a common denominator, such as the least common multiple of 2 and 4, which is 4. Rewrite each fraction by multiplying the numerator and denominator by the same number: 1 1/2 is 3/2, which becomes (3×2)/(2×2) = 6/4, and 3/4 stays 3/4. Now, add the numerators while keeping the common denominator: 6/4 + 3/4 = 9/4 = 2 1/4 pizzas, the total eaten. A common misconception is to add mixed numbers without converting the fractions properly, leading to errors in the whole parts. Using equivalent fractions allows us to combine values precisely by making the denominators match. This equivalence enables fraction operations in general, ensuring consistent units across different expressions.

Question 15

Two students are measuring the same 1-yard strip of fabric (fractions must refer to the same-sized whole). One student used 56\frac{5}{6} yard. The other student used 14\frac{1}{4} yard. They find equivalent fractions: 56=1012\frac{5}{6}=\frac{10}{12} and 14=312\frac{1}{4}=\frac{3}{12}. What is the difference 5614\frac{5}{6}-\frac{1}{4}?

  1. 410\frac{4}{10} yard
  2. 924\frac{9}{24} yard
  3. 712\frac{7}{12} yard (correct answer)
  4. 610\frac{6}{10} yard
Explanation: When subtracting unlike fractions such as 5/6 and 1/4, we need to find equivalent fractions with the same denominator to compare them correctly. To find a common denominator, identify the least common multiple of 6 and 4, which is 12. Rewrite 5/6 as 10/12 by multiplying numerator and denominator by 2, and 1/4 as 3/12 by multiplying by 3. Subtract the numerators over the common denominator: 10 - 3 = 7, resulting in 7/12 yard difference. A common misconception is subtracting denominators too, but denominators define part sizes and stay the same when common. Using equivalents ensures fractions refer to identical part sizes, enabling subtraction. This equivalence enables precise operations on unlike fractions in any addition or subtraction scenario.

Question 16

A recipe uses the same 1-cup measuring cup as the whole. You have 2142\frac{1}{4} cups of flour and you add 23\frac{2}{3} cup more. You rewrite 14=312\frac{1}{4}=\frac{3}{12} and 23=812\frac{2}{3}=\frac{8}{12}. What is 214+232\frac{1}{4}+\frac{2}{3} cups?

  1. 211122\frac{11}{12} cups (correct answer)
  2. 2372\frac{3}{7} cups
  3. 23122\frac{3}{12} cups
  4. 37\frac{3}{7} cup
Explanation: When adding unlike fractions in mixed numbers like 2 1/4 and 2/3, we need to find equivalents for the fractional parts with the same denominator. To find a common denominator, use the least common multiple of 4 and 3, which is 12. Rewrite 1/4 as 3/12 by multiplying numerator and denominator by 3, and 2/3 as 8/12 by multiplying by 4. Add to the whole: 2 + 3/12 + 8/12 = 2 + 11/12 = 2 11/12 cups. A common misconception is adding wholes and fractions without converting, but unlike denominators prevent direct combination. Equivalents make parts uniform, allowing proper addition or subtraction. This principle applies universally to fraction operations, promoting consistency.

Question 17

A science class uses the same 1-meter strip as the whole length. One group measures 58\tfrac{5}{8} meter. Another group measures 14\tfrac{1}{4} meter. They add the lengths and use equivalent fractions: 14=28\tfrac{1}{4}=\tfrac{2}{8}. Which statement about the size of the result is correct?

  1. The sum is less than 58\tfrac{5}{8} because adding a fraction always makes the total smaller.
  2. The sum is exactly 11 meter because 8+4=128+4=12.
  3. The sum is greater than 58\tfrac{5}{8} meter and less than 11 meter because 58+28=78\tfrac{5}{8}+\tfrac{2}{8}=\tfrac{7}{8}. (correct answer)
  4. The sum is greater than 11 meter because 5+1=65+1=6 and 8+4=128+4=12.
Explanation: To add or subtract unlike fractions, which have different denominators, we must first convert them to equivalent fractions with the same denominator to ensure they refer to parts of the same-sized whole. We find a common denominator by identifying a common multiple of the two denominators, preferably the least common multiple, such as 8 for 8 and 4 in this meter strip addition. To rewrite the fractions, multiply both the numerator and denominator of each by the same number; for example, 1/4 becomes 2/8. Once they have the same denominator, add the numerators to get 7/8 meter, which is between 5/8 and 1. A common misconception is that adding fractions makes the total smaller, but it actually increases it. Using equivalent fractions allows us to combine or compare parts accurately by making them comparable. This method ensures that operations on fractions are meaningful and applicable in measurements like lengths in science.

Question 18

Two students are measuring water from the same-sized 1-liter bottle, so the fractions refer to the same whole. They need to subtract: 56\tfrac{5}{6} liter minus 14\tfrac{1}{4} liter. Which statement correctly explains how to find a common denominator using equivalent fractions?

  1. Use 1010 as the denominator because 6+4=106+4=10.
  2. Rewrite 56\tfrac{5}{6} as 1012\tfrac{10}{12} and 14\tfrac{1}{4} as 312\tfrac{3}{12} because 1212 is a common multiple of 66 and 44. (correct answer)
  3. Subtract 515-1 and 646-4 to get 42\tfrac{4}{2}.
  4. Keep the denominators and subtract the numerators: 516\tfrac{5-1}{6}.
Explanation: To add or subtract unlike fractions, which have different denominators, we must first convert them to equivalent fractions with the same denominator to ensure they refer to parts of the same-sized whole. We find a common denominator by identifying a common multiple of the two denominators, preferably the least common multiple, such as 12 for 6 and 4 in this water-measuring problem. To rewrite the fractions, multiply both the numerator and denominator of each by the same number; for example, 5/6 becomes 10/12 and 1/4 becomes 3/12. Once they have the same denominator, subtract the numerators while keeping the denominator the same to find the difference. A common misconception is adding the denominators instead of finding a common multiple, like thinking 6+4=10 is the denominator. Using equivalent fractions allows us to combine or compare parts accurately by making them comparable. This method ensures that operations on fractions are meaningful and applicable in precise measurements like liters of water.

Question 19

A baker uses the same whole tray of brownies. She has 2132\tfrac{1}{3} trays made and gives away 34\tfrac{3}{4} tray. She rewrites 13\tfrac{1}{3} as 412\tfrac{4}{12} and 34\tfrac{3}{4} as 912\tfrac{9}{12} so the fractions refer to the same-sized whole tray. How many trays does she have left?

  1. 17121\tfrac{7}{12} trays (correct answer)
  2. 11121\tfrac{1}{12} trays
  3. 2672\tfrac{6}{7} trays
  4. 1171\tfrac{1}{7} trays
Explanation: To add or subtract unlike fractions, which have different denominators, we must first convert them to equivalent fractions with the same denominator to ensure they refer to parts of the same-sized whole. We find a common denominator by identifying a common multiple of the two denominators, preferably the least common multiple, such as 12 for 3 and 4 in this brownie tray subtraction. To rewrite the fractions, multiply both the numerator and denominator of each by the same number; for example, 1/3 becomes 4/12 and 3/4 becomes 9/12. Once they have the same denominator, subtract the numerators, borrowing from the whole number if needed, to get 1 7/12 trays left. A common misconception is subtracting mixed numbers without converting the fractional parts properly. Using equivalent fractions allows us to combine or compare parts accurately by making them comparable. This method ensures that operations on fractions are meaningful and applicable in quantities like trays of food.

Question 20

A class has 1 whole hour for a science lab. They spent 25\frac{2}{5} hour setting up and 12\frac{1}{2} hour doing the experiment. Both fractions refer to the same 1-hour whole. The teacher rewrote them as equivalent fractions: 25=410\frac{2}{5}=\frac{4}{10} and 12=510\frac{1}{2}=\frac{5}{10}. How much time did they spend in all?

  1. 37\frac{3}{7} hour
  2. 910\frac{9}{10} hour (correct answer)
  3. 310\frac{3}{10} hour
  4. 615\frac{6}{15} hour
Explanation: When adding or subtracting unlike fractions, we first need to find equivalent fractions with the same denominator. To do this, identify a common denominator, such as 10 for denominators 5 and 2, which is the least common multiple. Then, rewrite each fraction: multiply the numerator and denominator of 2/5 by 2 to get 4/10, and of 1/2 by 5 to get 5/10. Once the fractions have the same denominator, add the numerators 4 + 5 = 9 while keeping the denominator 10, resulting in 9/10 hour spent. A common misconception is that the sum of two fractions less than 1 must be less than 1, but here it exceeds 1/2 + 1/2 without being improper yet. Using equivalent fractions ensures the time parts are comparable for correct addition. This method generalizes to time management problems, making fraction operations straightforward and precise.