Decompose Fractions

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Answer Key & Explanations

Decompose Fractions · Grade 4 · Worksheet 1

1. 9/12 = 2/12 + 4/12 + ?/12 Answer: 3/12 Solution: The equation is 9/12 = 2/12 + 4/12 + ?/12 Add the known fractions: 2/12 + 4/12 = 6/12 Subtract the sum of the known fractions from the total: 9/12 - 6/12 = 3/12 Therefore, the missing fraction is 3/12 The answer is 3/12.
   Full step-by-step solution

   Step 1: The equation is 9/12 = 2/12 + 4/12 + ?/12 Step 2: Add the known fractions: 2/12 + 4/12 = 6/12 Step 3: Subtract the sum of the known fractions from the total: 9/12 - 6/12 = 3/12 Step 4: Therefore, the missing fraction is 3/12 The answer is 3/12.

2. Liam is baking cookies and needs 3/4 cup of sugar for one batch. He only has a 1/4 cup measuring cup. How many scoops of the 1/4 cup does Liam need to measure out 3/4 cup of sugar? Answer: 3 Solution: We need to find how many 1/4 cup scoops make 3/4 cup of sugar. Liam needs 3/4 cup of sugar. He has a 1/4 cup measuring cup.
   Full step-by-step solution

   We need to find how many 1/4 cup scoops make 3/4 cup of sugar. Step 1: Understand the problem. Liam needs 3/4 cup of sugar. He has a 1/4 cup measuring cup. We want to know: how many 1/4 cups equal 3/4 cup? Step 2: Set up the calculation. Let the number of scoops be x. Each scoop is 1/4 cup. So, x scoops = x * (1/4) cup. We want this to equal 3/4 cup. So: x * (1/4) = 3/4 Step 3: Solve for x. Multiply both sides by 4 to eliminate denominators: 4 * [x * (1/4)] = 4 * (3/4) x = 3 Step 4: Interpret the result. x = 3 means Liam needs 3 scoops of the 1/4 cup to get 3/4 cup of sugar. Step 5: Check the reasoning. 1/4 + 1/4 + 1/4 = 3/4. Yes, three 1/4 cups make 3/4 cup. Final answer: 3

3. At the pet store, Tane sees 3 kittens in one cage and 2 kittens in another cage. How many kittens are there in total? Answer: 5 Solution: Count the kittens in the first cage: 3 kittens. Count the kittens in the second cage: 2 kittens. Add them together: 3 + 2 = 5 kittens.
   Full step-by-step solution

   Step 1: Count the kittens in the first cage: 3 kittens. Step 2: Count the kittens in the second cage: 2 kittens. Step 3: Add them together: 3 + 2 = 5 kittens. The answer is 5 kittens.

4. Liam is organizing his toy cars into equal groups. He has 7/9 of his toy cars in the red bin. He wants to write this fraction as a sum of unit fractions (fractions with numerator 1) to show how many equal parts make up the whole. How can Liam write 7/9 as a sum of unit fractions? Answer: 1/9 + 1/9 + 1/9 + 1/9 + 1/9 + 1/9 + 1/9 Solution: Understand that 7/9 means 7 parts out of 9 equal parts. A unit fraction has numerator 1, so for ninths, the unit fraction is 1/9. To make 7/9, you need 7 copies of 1/9.
   Full step-by-step solution

   Step 1: Understand that 7/9 means 7 parts out of 9 equal parts. Step 2: A unit fraction has numerator 1, so for ninths, the unit fraction is 1/9. Step 3: To make 7/9, you need 7 copies of 1/9. Step 4: Write the sum: 1/9 + 1/9 + 1/9 + 1/9 + 1/9 + 1/9 + 1/9. Step 5: Check: 1/9 + 1/9 = 2/9, plus another 1/9 = 3/9, and so on until you reach 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 needs 3/4 cup of sugar for the chocolate chip cookies and 2/3 cup of sugar for the oatmeal raisin cookies. What is the total amount of sugar Liam needs for both cookie recipes? Answer: 1 5/12 cups Solution: Identify the amounts needed. Chocolate chip cookies: 3/4 cup of sugar Oatmeal raisin cookies: 2/3 cup of sugar Add the fractions. 3/4 + 2/3 To add fractions, they must have the same denominator (a common denominator).
   Full step-by-step solution

   Let's find the total amount of sugar Liam needs. Step 1: Identify the amounts needed. Chocolate chip cookies: 3/4 cup of sugar Oatmeal raisin cookies: 2/3 cup of sugar Step 2: Add the fractions. 3/4 + 2/3 To add fractions, they must have the same denominator (a common denominator). Step 3: Find a common denominator. The denominators are 4 and 3. The least common multiple of 4 and 3 is 12. So we will convert both fractions to have a denominator of 12. Step 4: Convert 3/4 to a fraction with denominator 12. To change 4 to 12, we multiply by 3. So multiply both numerator and denominator by 3. 3/4 = (3 × 3)/(4 × 3) = 9/12 Step 5: Convert 2/3 to a fraction with denominator 12. To change 3 to 12, we multiply by 4. So multiply both numerator and denominator by 4. 2/3 = (2 × 4)/(3 × 4) = 8/12 Step 6: Add the converted fractions. 9/12 + 8/12 = (9 + 8)/12 = 17/12 Step 7: Convert the improper fraction to a mixed number. 17/12 means 17 divided by 12. 12 goes into 17 one full time (1 × 12 = 12), with a remainder of 5. So 17/12 = 1 5/12 Step 8: State the final answer. The total amount of sugar Liam needs is 1 5/12 cups.

6. Maria is making lemonade for a school fair. She needs 2 3/4 cups of sugar for the recipe. She only has a 1/4 cup measuring cup. How many scoops of the 1/4 cup does Maria need to measure out 2 3/4 cups of sugar? Answer: 11 Solution: Convert 2 3/4 cups to an improper fraction: 2 3/4 = (2 × 4 + 3)/4 = (8 + 3)/4 = 11/4 cups Since each scoop is 1/4 cup, divide the total amount by the scoop size: (11/4) ÷ (1/4) = 11/4 × 4/1 = 11 Maria needs 11 scoops of the 1/4 cup measuring cup.
   Full step-by-step solution

   Step 1: Convert 2 3/4 cups to an improper fraction: 2 3/4 = (2 × 4 + 3)/4 = (8 + 3)/4 = 11/4 cups Step 2: Since each scoop is 1/4 cup, divide the total amount by the scoop size: (11/4) ÷ (1/4) = 11/4 × 4/1 = 11 Step 3: Maria needs 11 scoops of the 1/4 cup measuring cup. The answer is 11.

7. A rectangular garden is divided into 12 equal sections. If 4 sections are planted with corn, 3 sections are planted with beans, and 2 sections are planted with squash, what fraction of the garden is planted with vegetables? Write your answer as a fraction in simplest form. Answer: 3/4 Solution: Find the total number of sections planted with vegetables Corn: 4 sections Beans: 3 sections Squash: 2 sections Total vegetable sections = 4 + 3 + 2 = 9 sections Total garden sections = 12 Fraction = 9/12 Both 9 and 12 can be divided by 3 9 ÷ 3 = 3 12 ÷ 3 = 4 Simplified fraction = 3/4 The answer…
   Full step-by-step solution

   Step 1: Find the total number of sections planted with vegetables Corn: 4 sections Beans: 3 sections Squash: 2 sections Total vegetable sections = 4 + 3 + 2 = 9 sections Step 2: Write this as a fraction of the total garden Total garden sections = 12 Fraction = 9/12 Step 3: Simplify the fraction Both 9 and 12 can be divided by 3 9 ÷ 3 = 3 12 ÷ 3 = 4 Simplified fraction = 3/4 The answer is 3/4.

8. A construction crew needs 7/8 of a ton of concrete for a project. They have 3/8 of a ton already mixed. What fraction of a ton do they still need to mix to complete the project? Answer: 1/2 Solution: The crew needs 7/8 of a ton total They already have 3/8 of a ton Subtract what they have from what they need: 7/8 - 3/8 When subtracting fractions with the same denominator, subtract the numerators: 7 - 3 = 4 Keep the same denominator: 4/8 Simplify 4/8 by dividing numerator and denominator by 4:…
   Full step-by-step solution

   Step 1: The crew needs 7/8 of a ton total Step 2: They already have 3/8 of a ton Step 3: Subtract what they have from what they need: 7/8 - 3/8 Step 4: When subtracting fractions with the same denominator, subtract the numerators: 7 - 3 = 4 Step 5: Keep the same denominator: 4/8 Step 6: Simplify 4/8 by dividing numerator and denominator by 4: 4 ÷ 4 = 1, 8 ÷ 4 = 2 Step 7: The simplified fraction is 1/2 The answer is 1/2.

9. 7/9 = 1/9 + 1/9 + 1/9 + ?/9 Answer: 4/9 Solution: The equation is 7/9 = 1/9 + 1/9 + 1/9 + ?/9. Add the known unit fractions: 1/9 + 1/9 + 1/9 = 3/9. Subtract the sum from the total: 7/9 - 3/9 = 4/9.
   Full step-by-step solution

   Step 1: The equation is 7/9 = 1/9 + 1/9 + 1/9 + ?/9. Step 2: Add the known unit fractions: 1/9 + 1/9 + 1/9 = 3/9. Step 3: Subtract the sum from the total: 7/9 - 3/9 = 4/9. Step 4: So the missing fraction is 4/9. The answer is 4/9.