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. Aroha is making a traditional Maori kete (basket) and needs 7/9 of a metre of flax cord. She only has a 1/9 metre measuring stick. How many 1/9 metre lengths does Aroha need to measure out to get 7/9 metre of flax cord? Answer: 7 Solution: The total length needed is 7/9 metre. The measuring stick is 1/9 metre long. To find how many 1/9 pieces make 7/9, we need to decompose 7/9 into a sum of unit fractions: 7/9 = 1/9 + 1/9 + 1/9 + 1/9 + 1/9 + 1/9 + 1/9.
   Full step-by-step solution

   Step 1: The total length needed is 7/9 metre. Step 2: The measuring stick is 1/9 metre long. Step 3: To find how many 1/9 pieces make 7/9, we need to decompose 7/9 into a sum of unit fractions: 7/9 = 1/9 + 1/9 + 1/9 + 1/9 + 1/9 + 1/9 + 1/9. Step 4: Count the number of unit fractions: there are 7. Step 5: So, Aroha needs 7 scoops of the 1/9 metre measuring stick. The answer is 7.

3. A rectangular field is 120 meters long and 80 meters wide. The field is divided into 8 equal rectangular sections. What is the area of each section in square meters? Answer: 1200 Solution: Area = length × width = 120 m × 80 m = 9600 square meters 9600 square meters ÷ 8 sections = 1200 square meters per section 1200 × 8 = 9600, which matches our total area The answer is 1200 square meters.
   Full step-by-step solution

   Step 1: Find the total area of the rectangular field Area = length × width = 120 m × 80 m = 9600 square meters Step 2: Divide the total area by the number of sections 9600 square meters ÷ 8 sections = 1200 square meters per section Step 3: Verify the calculation 1200 × 8 = 9600, which matches our total area The answer is 1200 square meters.

4. 9/11 = 1/11 + 1/11 + 1/11 + ?/11 Answer: 6/11 Solution: The equation is 9/11 = 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: 9/11 - 3/11 = 6/11.
   Full step-by-step solution

   Step 1: The equation is 9/11 = 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: 9/11 - 3/11 = 6/11. Step 4: So the missing fraction is 6/11. The answer is 6/11.

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 12 equal square sections. The gardener plants flowers in 4 sections and vegetables in 3 sections. What fraction of the garden is planted? Write your answer as a fraction in simplest form. Answer: 7/12 Solution: Identify the total number of sections in the garden: 12 sections Count the sections planted with flowers: 4 sections Count the sections planted with vegetables: 3 sections Add the planted sections: 4 + 3 = 7 sections Write the fraction of planted sections: 7/12 Check if the fraction can be…
   Full step-by-step solution

   Step 1: Identify the total number of sections in the garden: 12 sections Step 2: Count the sections planted with flowers: 4 sections Step 3: Count the sections planted with vegetables: 3 sections Step 4: Add the planted sections: 4 + 3 = 7 sections Step 5: Write the fraction of planted sections: 7/12 Step 6: 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 the recipe. He only has a 1/4 cup measuring cup. How many times does Liam need to fill his 1/4 cup measuring cup to get the 3/4 cup of sugar he needs? Answer: 3 Solution: Liam needs 3/4 cup of sugar. He has a 1/4 cup measuring cup. We need to find how many 1/4 cups make 3/4 cup.
   Full step-by-step solution

   Liam needs 3/4 cup of sugar. He has a 1/4 cup measuring cup. Step 1: Understand the relationship between the amounts. We need to find how many 1/4 cups make 3/4 cup. Step 2: Set up the problem. Let x = number of times Liam fills the 1/4 cup. Then: (1/4) * x = 3/4 Step 3: Solve for x. Multiply both sides by 4 to clear denominators: 1 * x = 3 So x = 3. Step 4: Interpret the result. Liam needs to fill his 1/4 cup measuring cup 3 times to get 3/4 cup of sugar. Answer: 3