Decompose Fractions

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Decompose Fractions · Grade 4 · Worksheet 3

1. A rectangular garden is divided into 12 equal square sections arranged in 3 rows and 4 columns. If 5 sections are planted with sunflowers and 3 sections are planted with roses, what fraction of the garden is planted with flowers? Write your answer as a fraction in simplest form. Answer: 2/3 Solution: The garden has 3 rows × 4 columns = 12 total sections Sunflowers occupy 5 sections and roses occupy 3 sections Total flower sections = 5 + 3 = 8 sections Fraction of garden with flowers = 8/12 Simplify 8/12 by dividing numerator and denominator by 4: 8 ÷ 4 = 2, 12 ÷ 4 = 3 The simplified fraction…
   Full step-by-step solution

   Step 1: The garden has 3 rows × 4 columns = 12 total sections Step 2: Sunflowers occupy 5 sections and roses occupy 3 sections Step 3: Total flower sections = 5 + 3 = 8 sections Step 4: Fraction of garden with flowers = 8/12 Step 5: Simplify 8/12 by dividing numerator and denominator by 4: 8 ÷ 4 = 2, 12 ÷ 4 = 3 Step 6: The simplified fraction is 2/3 The answer is 2/3.

2. 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.

3. Decompose 7/8 into a sum of two fractions with the same denominator. Answer: 3/8 + 4/8 Solution: We need to find two fractions that add up to 7/8. Both fractions must have 8 as the denominator. To find the second fraction, subtract 3/8 from 7/8: 7/8 - 3/8 = 4/8.
   Full step-by-step solution

   Step 1: We need to find two fractions that add up to 7/8. Both fractions must have 8 as the denominator. Step 2: Let's choose a first fraction, for example, 3/8. Step 3: To find the second fraction, subtract 3/8 from 7/8: 7/8 - 3/8 = 4/8. Step 4: Check the sum: 3/8 + 4/8 = 7/8. The decomposition is 3/8 + 4/8.

4. Emma is making a fruit salad for a school picnic. She uses 3/4 cup of strawberries and 2/3 cup of blueberries. What is the total amount of fruit, in cups, that Emma uses for her fruit salad? Answer: 17/12 Solution: Identify the fractions to add: 3/4 and 2/3 Find a common denominator for 4 and 3. The least common denominator is 12.
   Full step-by-step solution

   Step 1: Identify the fractions to add: 3/4 and 2/3 Step 2: Find a common denominator for 4 and 3. The least common denominator is 12. Step 3: Convert 3/4 to twelfths: (3 × 3)/(4 × 3) = 9/12 Step 4: Convert 2/3 to twelfths: (2 × 4)/(3 × 4) = 8/12 Step 5: Add the fractions: 9/12 + 8/12 = 17/12 Step 6: The answer is 17/12 cups, which can also be written as 1 5/12 cups.

5. 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.

6. A rectangular garden is divided into 12 equal sections. If 4 sections are planted with corn and 3 sections are planted with beans, what fraction of the garden is planted with vegetables? Write your answer as a fraction in simplest form. Answer: 7/12 Solution: Find the total number of vegetable sections: 4 corn sections + 3 bean sections = 7 sections The garden has 12 equal sections total The fraction planted with vegetables is 7/12 Check if the fraction can be simplified: 7 and 12 have no common factors other than 1, so 7/12 is already in simplest…
   Full step-by-step solution

   Step 1: Find the total number of vegetable sections: 4 corn sections + 3 bean sections = 7 sections Step 2: The garden has 12 equal sections total Step 3: The fraction planted with vegetables is 7/12 Step 4: Check if the fraction can be simplified: 7 and 12 have no common factors other than 1, so 7/12 is already in simplest form The answer is 7/12.

7. 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

8. 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.

9. 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.