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Decompose Fractions

Grade 4 · Fractions · Worksheet 2

  1. 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: ______________
  2. 9/12 = 3/12 + 4/12 + ?/12 Answer: ______________
  3. Emma is painting a wooden board that is divided into 9 equal sections. She paints 7 of the sections blue. Emma wants to write the fraction of the board that is blue as a sum of unit fractions. How can Emma write 7/9 as a sum of unit fractions? Answer: ______________
  4. Isabella is making a batch of homemade granola bars. The recipe calls for 7/8 cup of oats. She only has a 1/8 cup measuring cup. How many scoops of the 1/8 cup does Isabella need to measure out the 7/8 cup of oats? Answer: ______________
  5. A rectangular field is 120 meters long and 80 meters wide. The field is divided into equal square sections, each with a side length of 20 meters. What fraction of the field is represented by 3 of these square sections? Write your answer in simplest form.
    Answer: ______________
  6. 6/8 = 2/8 + ?/8 Answer: ______________
  7. 7/9 = 2/9 + 3/9 + ?/9 Answer: ______________
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Answer Key & Explanations

Decompose Fractions · Grade 4 · Worksheet 2

  1. 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.

  2. 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.

  3. Emma is painting a wooden board that is divided into 9 equal sections. She paints 7 of the sections blue. Emma wants to write the fraction of the board that is blue as a sum of unit fractions. How can Emma 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: The board is divided into 9 equal sections, so each section is 1/9 of the whole board. This is a unit fraction. Emma painted 7 sections blue.
    Full step-by-step solution

    Step 1: The board is divided into 9 equal sections, so each section is 1/9 of the whole board. This is a unit fraction. Step 2: Emma painted 7 sections blue. That means the blue part is 7/9 of the board. Step 3: To write 7/9 as a sum of unit fractions, we add 1/9 together 7 times. Step 4: 7/9 = 1/9 + 1/9 + 1/9 + 1/9 + 1/9 + 1/9 + 1/9. The answer is 1/9 + 1/9 + 1/9 + 1/9 + 1/9 + 1/9 + 1/9.

  4. Isabella is making a batch of homemade granola bars. The recipe calls for 7/8 cup of oats. She only has a 1/8 cup measuring cup. How many scoops of the 1/8 cup does Isabella need to measure out the 7/8 cup of oats? Answer: 7 Solution: The recipe needs 7/8 cup of oats. Step 2: The measuring cup holds 1/8 cup. Step 3: To find how many scoops, divide the total amount by the size of one scoop: 7/8 divided by 1/8.
    Full step-by-step solution

    Step 1: The recipe needs 7/8 cup of oats. Step 2: The measuring cup holds 1/8 cup. Step 3: To find how many scoops, divide the total amount by the size of one scoop: 7/8 divided by 1/8. Step 4: Dividing by 1/8 is the same as multiplying by 8: 7/8 x 8 = 7. Step 5: So Isabella needs 7 scoops of the 1/8 cup to get 7/8 cup of oats. The answer is 7.

  5. A rectangular field is 120 meters long and 80 meters wide. The field is divided into equal square sections, each with a side length of 20 meters. What fraction of the field is represented by 3 of these square sections? Write your answer in simplest form. Answer: 1/16 Solution: Calculate the area of the entire field: 120 m × 80 m = 9,600 square meters Calculate the area of one square section: 20 m × 20 m = 400 square meters Find how many square sections fit in the field: 9,600 ÷ 400 = 24 sections Determine what fraction 3 sections represent: 3/24 Simplify the fraction:…
    Full step-by-step solution

    Step 1: Calculate the area of the entire field: 120 m × 80 m = 9,600 square meters Step 2: Calculate the area of one square section: 20 m × 20 m = 400 square meters Step 3: Find how many square sections fit in the field: 9,600 ÷ 400 = 24 sections Step 4: Determine what fraction 3 sections represent: 3/24 Step 5: Simplify the fraction: 3/24 = 1/8 The answer is 1/8.

  6. 6/8 = 2/8 + ?/8 Answer: 4/8 Solution: The equation is 6/8 = 2/8 + ?/8. The total is 6/8. One part is 2/8.
    Full step-by-step solution

    Step 1: The equation is 6/8 = 2/8 + ?/8. Step 2: The total is 6/8. One part is 2/8. Step 3: To find the missing part, subtract the known part from the total: 6/8 - 2/8 = 4/8. Step 4: So the missing fraction is 4/8. The answer is 4/8.

  7. 7/9 = 2/9 + 3/9 + ?/9 Answer: 2/9 Solution: The equation is 7/9 = 2/9 + 3/9 + ?/9 Add the known fractions: 2/9 + 3/9 = 5/9 Subtract the sum of the known fractions from the total: 7/9 - 5/9 = 2/9 Therefore, the missing fraction is 2/9 The answer is 2/9.
    Full step-by-step solution

    Step 1: The equation is 7/9 = 2/9 + 3/9 + ?/9 Step 2: Add the known fractions: 2/9 + 3/9 = 5/9 Step 3: Subtract the sum of the known fractions from the total: 7/9 - 5/9 = 2/9 Step 4: Therefore, the missing fraction is 2/9 The answer is 2/9.