Decompose Fractions

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Decompose Fractions · Grade 4 · Worksheet 1

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. 11/12 = 4/12 + 3/12 + ?/12 Answer: 4/12 Solution: The equation is 11/12 = 4/12 + 3/12 + ?/12. Add the known fractions on the right side: 4/12 + 3/12 = 7/12. Subtract the sum of the known fractions from the total: 11/12 - 7/12 = 4/12.
   Full step-by-step solution

   Step 1: The equation is 11/12 = 4/12 + 3/12 + ?/12. Step 2: Add the known fractions on the right side: 4/12 + 3/12 = 7/12. Step 3: Subtract the sum of the known fractions from the total: 11/12 - 7/12 = 4/12. Step 4: Therefore, the missing fraction is 4/12. The answer is 4/12.

3. Noah is making a batch of homemade granola bars. The recipe calls for 6/8 cup of honey. Noah only has a 1/8 cup measuring spoon. How many scoops of the 1/8 cup measuring spoon does Noah need to add to get the 6/8 cup of honey he needs? Answer: 6 Solution: The recipe needs 6/8 cup of honey. Each scoop is 1/8 cup. To find the number of scoops, think about how many 1/8 cups make 6/8 cup.
   Full step-by-step solution

   Step 1: The recipe needs 6/8 cup of honey. Step 2: Each scoop is 1/8 cup. Step 3: To find the number of scoops, think about how many 1/8 cups make 6/8 cup. Step 4: 6/8 = 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 Step 5: Count the unit fractions: there are 6 of them. Step 6: Noah needs 6 scoops of the 1/8 cup measuring spoon. The answer is 6.

4. A rectangular garden measures 12 feet long and 8 feet wide. The gardener plants flowers in a triangular section that covers exactly half of the garden. If the triangle's base runs along the entire 12-foot length, what is the height of the triangular flower section? Answer: 8 Solution: Find the area of the rectangular garden. Area of rectangle = length × width = 12 ft × 8 ft = 96 square feet The triangular flower section covers half of the garden.
   Full step-by-step solution

   Step 1: Find the area of the rectangular garden. Area of rectangle = length × width = 12 ft × 8 ft = 96 square feet Step 2: The triangular flower section covers half of the garden. Area of triangle = 1/2 × area of rectangle = 1/2 × 96 = 48 square feet Step 3: Use the triangle area formula to find the height. Area of triangle = 1/2 × base × height 48 = 1/2 × 12 × height 48 = 6 × height Step 4: Solve for height. height = 48 ÷ 6 = 8 feet The height of the triangular flower section is 8 feet.

5. Olivia is making a large batch of fruit punch for a family reunion. The recipe calls for 5/8 of a gallon of orange juice. Olivia only has a 1/8 gallon measuring cup. How many times does Olivia need to fill her 1/8 gallon measuring cup to get the 5/8 gallon of orange juice she needs? Answer: 5 Solution: Olivia needs 5/8 gallon of orange juice. Step 2: Her measuring cup holds 1/8 gallon. Step 3: To find how many 1/8 scoops are in 5/8, we add unit fractions: 1/8 + 1/8 + 1/8 + 1/8 + 1/8 = 5/8.
   Full step-by-step solution

   Step 1: Olivia needs 5/8 gallon of orange juice. Step 2: Her measuring cup holds 1/8 gallon. Step 3: To find how many 1/8 scoops are in 5/8, we add unit fractions: 1/8 + 1/8 + 1/8 + 1/8 + 1/8 = 5/8. Step 4: This means she needs 5 scoops. Final answer: 5.

6. A rectangular garden is divided into 8 equal sections. If 3 sections are planted with tomatoes and 2 sections are planted with carrots, what fraction of the garden is planted with vegetables? Write your answer as a fraction in simplest form. Answer: 5/8 Solution: The garden is divided into 8 equal sections. 3 sections have tomatoes, 2 sections have carrots. We want the fraction of the garden planted with vegetables.
   Full step-by-step solution

   Step 1: Understand the problem. The garden is divided into 8 equal sections. 3 sections have tomatoes, 2 sections have carrots. We want the fraction of the garden planted with vegetables. Step 2: Find the total number of sections planted with vegetables. Tomatoes: 3 sections Carrots: 2 sections Total vegetable sections = 3 + 2 = 5 sections. Step 3: Write the fraction of the garden that is vegetables. The garden has 8 equal sections in total, so: Fraction = (Number of vegetable sections) / (Total sections) = 5/8. Step 4: Check if the fraction is in simplest form. 5 and 8 have no common factors other than 1, so 5/8 is already in simplest form. Final Answer: 5/8