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Decompose Fractions

Grade 4 · Fractions · Worksheet 2

  1. Emma is making a batch of 9 muffins. She needs 7/9 of a cup of blueberries. She only has a 1/9 cup measuring scoop. How many scoops of blueberries does Emma need to add to get the correct amount? Answer: ______________
  2. 4/5 = 1/5 + 1/5 + ?/5 Answer: ______________
  3. 5/8 = 1/8 + 1/8 + ?/8 Answer: ______________
  4. Noah draws a large square on grid paper and divides it into 9 equal smaller squares. He colors 7 of those smaller squares blue. Write the fraction of the large square that is blue as a sum of unit fractions. Answer: ______________
  5. Liam is baking cookies for his class party. He has 3/4 cup of chocolate chips and 2/3 cup of walnuts. He wants to combine them in one bowl. What is the total amount of these two ingredients that Liam will have in the bowl? Answer: ______________
  6. 9/12 = 3/12 + 4/12 + ?/12 Answer: ______________
  7. 6/11 = 1/11 + 1/11 + 1/11 + ?/11 Answer: ______________
  8. 11/12 = 5/12 + ?/12 Answer: ______________
  9. Tane is helping his grandmother prepare kawakawa balm. The recipe requires 7/10 of a cup of coconut oil. Tane only has a 1/10 cup measuring spoon. How many scoops of the 1/10 cup measuring spoon will Tane need to measure out the 7/10 cup of coconut oil? Answer: ______________
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Answer Key & Explanations

Decompose Fractions · Grade 4 · Worksheet 2

  1. Emma is making a batch of 9 muffins. She needs 7/9 of a cup of blueberries. She only has a 1/9 cup measuring scoop. How many scoops of blueberries does Emma need to add to get the correct amount? Answer: 7 Solution: Emma needs 7/9 cup of blueberries. Step 2: Her scoop holds 1/9 cup. Step 3: To find the number of scoops, think: 7/9 = 1/9 + 1/9 + 1/9 + 1/9 + 1/9 + 1/9 + 1/9.
    Full step-by-step solution

    Step 1: Emma needs 7/9 cup of blueberries. Step 2: Her scoop holds 1/9 cup. Step 3: To find the number of scoops, think: 7/9 = 1/9 + 1/9 + 1/9 + 1/9 + 1/9 + 1/9 + 1/9. Step 4: This is 7 scoops of 1/9 cup each. Step 5: So Emma needs 7 scoops of blueberries. Answer: 7

  2. 4/5 = 1/5 + 1/5 + ?/5 Answer: 2/5 Solution: The problem shows 4/5 = 1/5 + 1/5 + ?/5 Add the known fractions: 1/5 + 1/5 = 2/5 To reach 4/5 total, we need: 4/5 - 2/5 = 2/5 Therefore, the missing fraction is 2/5 The answer is 2/5.
    Full step-by-step solution

    Step 1: The problem shows 4/5 = 1/5 + 1/5 + ?/5 Step 2: Add the known fractions: 1/5 + 1/5 = 2/5 Step 3: To reach 4/5 total, we need: 4/5 - 2/5 = 2/5 Step 4: Therefore, the missing fraction is 2/5 The answer is 2/5.

  3. 5/8 = 1/8 + 1/8 + ?/8 Answer: 3/8 Solution: The problem shows 5/8 = 1/8 + 1/8 + ?/8. Add the known eighths: 1/8 + 1/8 = 2/8. To reach the total of 5/8, we need: 5/8 - 2/8 = 3/8.
    Full step-by-step solution

    Step 1: The problem shows 5/8 = 1/8 + 1/8 + ?/8. Step 2: Add the known eighths: 1/8 + 1/8 = 2/8. Step 3: To reach the total of 5/8, we need: 5/8 - 2/8 = 3/8. Step 4: Therefore, the missing fraction is 3/8. The answer is 3/8.

  4. Noah draws a large square on grid paper and divides it into 9 equal smaller squares. He colors 7 of those smaller squares blue. Write the fraction of the large square that is blue as a sum of unit fractions. Answer: 1/9 + 1/9 + 1/9 + 1/9 + 1/9 + 1/9 + 1/9 Solution: The large square is divided into 9 equal smaller squares. So each small square is 1/9 of the whole. Noah colors 7 of these squares blue.
    Full step-by-step solution

    Step 1: The large square is divided into 9 equal smaller squares. So each small square is 1/9 of the whole. Step 2: Noah colors 7 of these squares blue. That means 7 out of 9 squares are blue, or 7/9. Step 3: To write 7/9 as a sum of unit fractions, we add 1/9 seven times. Step 4: 1/9 + 1/9 + 1/9 + 1/9 + 1/9 + 1/9 + 1/9 = 7/9. The answer is 1/9 + 1/9 + 1/9 + 1/9 + 1/9 + 1/9 + 1/9.

  5. Liam is baking cookies for his class party. He has 3/4 cup of chocolate chips and 2/3 cup of walnuts. He wants to combine them in one bowl. What is the total amount of these two ingredients that Liam will have in the bowl? Answer: 1 5/12 cups Solution: To find the total amount of ingredients, we need to add 3/4 cup and 2/3 cup. Identify the fractions to add. We are adding 3/4 and 2/3.
    Full step-by-step solution

    To find the total amount of ingredients, we need to add 3/4 cup and 2/3 cup. Step 1: Identify the fractions to add. We are adding 3/4 and 2/3. Step 2: Find a common denominator. The denominators are 4 and 3. The smallest number that both 4 and 3 divide into is 12. So, the common denominator is 12. Step 3: Convert each fraction to have the denominator of 12. For 3/4: To change the denominator 4 into 12, we multiply by 3. So we multiply both the numerator and denominator by 3. 3/4 = (3 * 3) / (4 * 3) = 9/12. For 2/3: To change the denominator 3 into 12, we multiply by 4. So we multiply both the numerator and denominator by 4. 2/3 = (2 * 4) / (3 * 4) = 8/12. Step 4: Add the converted fractions. Now we add 9/12 and 8/12. When adding fractions with the same denominator, we keep the denominator and add the numerators. 9/12 + 8/12 = (9 + 8)/12 = 17/12. Step 5: Simplify the result. The fraction 17/12 is an improper fraction (the numerator is larger than the denominator). We can convert it to a mixed number. To do this, we see how many whole groups of 12/12 are in 17/12. 17 divided by 12 is 1 with a remainder of 5 (because 12 * 1 = 12, and 17 - 12 = 5). So, 17/12 = 1 and 5/12. Therefore, the total amount of ingredients Liam will have in the bowl is 1 5/12 cups.

  6. 9/12 = 3/12 + 4/12 + ?/12 Answer: 2/12 Solution: The equation is 9/12 = 3/12 + 4/12 + ?/12. Add the known fractions on the right side: 3/12 + 4/12 = 7/12. Subtract the sum of the known fractions from the total: 9/12 - 7/12 = 2/12.
    Full step-by-step solution

    Step 1: The equation is 9/12 = 3/12 + 4/12 + ?/12. Step 2: Add the known fractions on the right side: 3/12 + 4/12 = 7/12. Step 3: Subtract the sum of the known fractions from the total: 9/12 - 7/12 = 2/12. Step 4: Therefore, the missing fraction is 2/12. The answer is 2/12.

  7. 6/11 = 1/11 + 1/11 + 1/11 + ?/11 Answer: 3/11 Solution: The equation is 6/11 = 1/11 + 1/11 + 1/11 + ?/11. Add the known unit fractions: 1/11 + 1/11 + 1/11 = 3/11. Subtract the sum from the total: 6/11 - 3/11 = 3/11.
    Full step-by-step solution

    Step 1: The equation is 6/11 = 1/11 + 1/11 + 1/11 + ?/11. Step 2: Add the known unit fractions: 1/11 + 1/11 + 1/11 = 3/11. Step 3: Subtract the sum from the total: 6/11 - 3/11 = 3/11. Step 4: So the missing fraction is 3/11. The answer is 3/11.

  8. 11/12 = 5/12 + ?/12 Answer: 6/12 Solution: The equation is 11/12 = 5/12 + ?/12 Subtract the known fraction from the total: 11/12 - 5/12 = 6/12 So the missing fraction is 6/12 The answer is 6/12.
    Full step-by-step solution

    Step 1: The equation is 11/12 = 5/12 + ?/12 Step 2: Subtract the known fraction from the total: 11/12 - 5/12 = 6/12 Step 3: So the missing fraction is 6/12 The answer is 6/12.

  9. Tane is helping his grandmother prepare kawakawa balm. The recipe requires 7/10 of a cup of coconut oil. Tane only has a 1/10 cup measuring spoon. How many scoops of the 1/10 cup measuring spoon will Tane need to measure out the 7/10 cup of coconut oil? Answer: 7 Solution: Understand that the total amount needed is 7/10 of a cup. Step 2: Each scoop is 1/10 of a cup. Step 3: To find the number of scoops, divide the total amount by the size of one scoop: 7/10 divided by 1/10 = 7.
    Full step-by-step solution

    Step 1: Understand that the total amount needed is 7/10 of a cup. Step 2: Each scoop is 1/10 of a cup. Step 3: To find the number of scoops, divide the total amount by the size of one scoop: 7/10 divided by 1/10 = 7. Step 4: Alternatively, think of 7/10 as 7 copies of 1/10: 1/10 + 1/10 + 1/10 + 1/10 + 1/10 + 1/10 + 1/10 = 7/10. Step 5: So Tane needs 7 scoops. The answer is 7.