Fraction Operations

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Fraction Operations · Grade 5 · Worksheet 2

1. Noah is drawing a rectangular garden on a coordinate grid. The garden has corners at (1, 1), (6, 1), (6, 6), and (1, 6). Each unit on the grid represents 1 meter. Noah wants to plant flowers in 1/2 of the garden and vegetables in the other 1/2. What is the area of the flower section in square meters? Answer: 12.5 Solution: Find the length and width of the rectangle. The x-coordinates go from 1 to 6, so the length is 6 - 1 = 5 meters. The y-coordinates go from 1 to 6, so the width is 6 - 1 = 5 meters.
   Full step-by-step solution

   Step 1: Find the length and width of the rectangle. The x-coordinates go from 1 to 6, so the length is 6 - 1 = 5 meters. The y-coordinates go from 1 to 6, so the width is 6 - 1 = 5 meters. Step 2: Calculate the total area: Area = length x width = 5 x 5 = 25 square meters. Step 3: The flower section is 1/2 of the garden, so multiply the total area by 1/2: 25 x 1/2 = 25/2 = 12.5 square meters. The answer is 12.5 square meters.

2. Kaia is making a patchwork quilt. She has 7/9 of a meter of blue fabric. Each patch requires 1/6 of a meter. How many patches can she cut? Answer: 4 2/3 Solution: We need to find how many 1/6 meter patches fit into 7/9 meter. This is a division problem: 7/9 ÷ 1/6. To divide fractions, multiply by the reciprocal of the second fraction.
   Full step-by-step solution

   Step 1: We need to find how many 1/6 meter patches fit into 7/9 meter. This is a division problem: 7/9 ÷ 1/6. Step 2: To divide fractions, multiply by the reciprocal of the second fraction. The reciprocal of 1/6 is 6/1. Step 3: So, 7/9 ÷ 1/6 = 7/9 × 6/1. Step 4: Multiply the numerators: 7 × 6 = 42. Step 5: Multiply the denominators: 9 × 1 = 9. Step 6: This gives 42/9. Step 7: Simplify by dividing numerator and denominator by their greatest common factor, which is 3. 42 ÷ 3 = 14 and 9 ÷ 3 = 3. Step 8: So, 42/9 = 14/3. Step 9: Convert the improper fraction to a mixed number. 14 ÷ 3 = 4 with a remainder of 2, so 14/3 = 4 2/3. The answer is 4 2/3 patches.

3. Liam is building a rectangular garden bed that is 3/4 meter long and 2/5 meter wide. He wants to know how much area the garden bed will cover. What is the area of Liam's garden bed in square meters? Answer: 3/10 Solution: To find the area of a rectangle, multiply the length by the width. Write down the length and width. Length = 3/4 meter Width = 2/5 meter Multiply the length by the width.
   Full step-by-step solution

   To find the area of a rectangle, multiply the length by the width. Step 1: Write down the length and width. Length = 3/4 meter Width = 2/5 meter Step 2: Multiply the length by the width. Area = (3/4) * (2/5) Step 3: Multiply the numerators (top numbers) together. 3 * 2 = 6 Step 4: Multiply the denominators (bottom numbers) together. 4 * 5 = 20 Step 5: Write the result as a fraction. Area = 6/20 Step 6: Simplify the fraction by finding the greatest common factor of 6 and 20. The factors of 6 are 1, 2, 3, 6. The factors of 20 are 1, 2, 4, 5, 10, 20. The greatest common factor is 2. Step 7: Divide both the numerator and denominator by 2. 6 ÷ 2 = 3 20 ÷ 2 = 10 Step 8: Write the simplified fraction. Area = 3/10 Therefore, the area of Liam's garden bed is 3/10 square meters.

4. Sam has 4 liters of juice. Sam pours the juice equally into 4 bottles. How many liters of juice are in each bottle? Answer: 1 Solution: Divide the total juice by the number of bottles: 4 ÷ 4. 4 ÷ 4 = 1 liter per bottle.
   Full step-by-step solution

   Step 1: Divide the total juice by the number of bottles: 4 ÷ 4. Step 2: 4 ÷ 4 = 1 liter per bottle.

5. A recipe calls for 3/4 cup of sugar. If you want to make 2/3 of the recipe, how much sugar do you need? Answer: 1/2 Solution: The problem is asking for 2/3 of 3/4 cup of sugar. This means we need to multiply the fractions. Multiply the numerators: 2 × 3 = 6.
   Full step-by-step solution

   Step 1: The problem is asking for 2/3 of 3/4 cup of sugar. This means we need to multiply the fractions. Step 2: Multiply the numerators: 2 × 3 = 6. Step 3: Multiply the denominators: 3 × 4 = 12. Step 4: This gives us the fraction 6/12. Step 5: Simplify 6/12 by dividing the numerator and denominator by their greatest common factor, which is 6. 6 ÷ 6 = 1 and 12 ÷ 6 = 2. Step 6: The simplified fraction is 1/2. The answer is 1/2 cup of sugar.

6. A recipe uses 3/4 cup of chocolate chips. If you want to make 2/3 of the recipe, how many cups of chocolate chips do you need? Answer: 1/2 Solution: The problem asks for 2/3 of 3/4 cup of chocolate chips. This means we need to multiply the fractions. Multiply the numerators: 2 × 3 = 6.
   Full step-by-step solution

   Step 1: The problem asks for 2/3 of 3/4 cup of chocolate chips. This means we need to multiply the fractions. Step 2: Multiply the numerators: 2 × 3 = 6. Step 3: Multiply the denominators: 3 × 4 = 12. Step 4: This gives us the fraction 6/12. Step 5: Simplify 6/12 by dividing the numerator and denominator by their greatest common factor, which is 6. 6 ÷ 6 = 1 and 12 ÷ 6 = 2. Step 6: The simplified fraction is 1/2. The answer is 1/2 cup of chocolate chips.

7. A farmer harvested 750 kilograms of apples from his orchard. He sold 3/5 of the harvest to a grocery store and gave 1/4 of the remaining apples to a local food bank. What fraction of the original harvest did the farmer give to the food bank? Answer: 1/10 Solution: The farmer harvested 750 kg of apples. He sold 3/5 of the harvest to a grocery store. Then, he gave 1/4 of the *remaining* apples to a food bank.
   Full step-by-step solution

   Let's go step-by-step. --- **Step 1: Understand the problem** The farmer harvested 750 kg of apples. He sold 3/5 of the harvest to a grocery store. Then, he gave 1/4 of the *remaining* apples to a food bank. We want the *fraction of the original harvest* given to the food bank. --- **Step 2: Find the amount sold to the grocery store** He sold 3/5 of 750 kg. Amount sold = (3/5) × 750 = 3 × 150 = 450 kg. --- **Step 3: Find the remaining apples after selling to the grocery store** Remaining = 750 − 450 = 300 kg. --- **Step 4: Find the amount given to the food bank** He gave 1/4 of the remaining (300 kg) to the food bank. Amount to food bank = (1/4) × 300 = 75 kg. --- **Step 5: Find the fraction of the original harvest given to the food bank** Original harvest = 750 kg. Food bank amount = 75 kg. Fraction = 75 / 750. Simplify: divide numerator and denominator by 75. 75 ÷ 75 = 1, 750 ÷ 75 = 10. So fraction = 1/10. --- **Step 6: Explanation without total weight (direct fraction method)** We can solve without using 750 kg: - Sold 3/5 initially, so remaining fraction = 1 − 3/5 = 2/5 of original. - Gave 1/4 of remaining to food bank: (1/4) × (2/5) = 2/20 = 1/10 of original. This matches our earlier answer. --- **Final answer:** 1/10

8. 3/5 + 2/3 = ? Answer: 19/15 Solution: Find a common denominator for 3/5 and 2/3. The least common multiple of 5 and 3 is 15.
   Full step-by-step solution

   Step 1: Find a common denominator for 3/5 and 2/3. The least common multiple of 5 and 3 is 15. Step 2: Convert 3/5 to have denominator 15: (3 × 3)/(5 × 3) = 9/15 Step 3: Convert 2/3 to have denominator 15: (2 × 5)/(3 × 5) = 10/15 Step 4: Add the fractions: 9/15 + 10/15 = 19/15 Step 5: The fraction 19/15 is already in simplest form. The answer is 19/15.

9. Liam is building a rectangular garden bed that measures 3/4 meter by 2/5 meter. He wants to cover the entire garden bed with soil. What is the area of the garden bed in square meters? Answer: 3/10 Solution: To find the area of a rectangle, we multiply the length by the width. The length is 3/4 meter and the width is 2/5 meter.
   Full step-by-step solution

   To find the area of a rectangle, we multiply the length by the width. The length is 3/4 meter and the width is 2/5 meter. So, the area is: (3/4) * (2/5) When multiplying fractions, we multiply the numerators together and the denominators together. Multiply the numerators: 3 * 2 = 6 Multiply the denominators: 4 * 5 = 20 This gives us the fraction 6/20. Now, we simplify this fraction. Both the numerator (6) and the denominator (20) can be divided by 2. 6 divided by 2 is 3. 20 divided by 2 is 10. So, 6/20 simplifies to 3/10. Therefore, the area of the garden bed is 3/10 square meters.