Fraction Operations

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Fraction Operations · Grade 5 · Worksheet 2

1. A recipe uses 3/5 cup of sugar. If you want to make 4/7 of the recipe, how many cups of sugar do you need? Answer: 12/35 Solution: The problem asks for 4/7 of 3/5 cup of sugar. This means we need to multiply the fractions. Multiply the numerators: 4 × 3 = 12.
   Full step-by-step solution

   Step 1: The problem asks for 4/7 of 3/5 cup of sugar. This means we need to multiply the fractions. Step 2: Multiply the numerators: 4 × 3 = 12. Step 3: Multiply the denominators: 7 × 5 = 35. Step 4: This gives us the fraction 12/35. Step 5: Check if the fraction can be simplified. The greatest common factor of 12 and 35 is 1, so 12/35 is already in simplest form. The answer is 12/35 cup of sugar.

2. Sam has a 4 meter long ribbon. Sam cuts it into 4 equal pieces. How long is each piece? Answer: 1 Solution: Total ribbon length: 4 meters. Step 2: Number of equal pieces: 4. Step 3: Divide the total length by the number of pieces: 4 ÷ 4 = 1 meter.
   Full step-by-step solution

   Step 1: Total ribbon length: 4 meters. Step 2: Number of equal pieces: 4. Step 3: Divide the total length by the number of pieces: 4 ÷ 4 = 1 meter. The answer is 1 meter.

3. 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

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

   Step 1: The problem asks for 2/3 of 3/4 cup of sugar. This means we need to multiply the fractions: 2/3 × 3/4. 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 both 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.

5. Liam is baking cookies for a school fundraiser. He needs 3/4 cup of sugar for one batch of chocolate chip cookies and 2/3 cup of sugar for one batch of oatmeal raisin cookies. If he makes one batch of each type, what is the total amount of sugar Liam needs in cups? Answer: 17/12 Solution: To find the total amount of sugar Liam needs, we need to add the sugar required for the chocolate chip cookies and the sugar required for the oatmeal raisin cookies. Write down the amounts. Chocolate chip cookies need 3/4 cup of sugar.
   Full step-by-step solution

   To find the total amount of sugar Liam needs, we need to add the sugar required for the chocolate chip cookies and the sugar required for the oatmeal raisin cookies. Step 1: Write down the amounts. Chocolate chip cookies need 3/4 cup of sugar. Oatmeal raisin cookies need 2/3 cup of sugar. Step 2: Set up the addition. Total sugar = 3/4 + 2/3 Step 3: To add fractions, they must have the same denominator (the bottom number). The denominators here are 4 and 3. The smallest number that both 4 and 3 divide into is 12. This is called the least common denominator. Step 4: Convert each fraction to an equivalent fraction with a denominator of 12. For 3/4: To change the denominator from 4 to 12, we multiply by 3. To keep the value of the fraction the same, we must also multiply the numerator (the top number) by 3. So, 3/4 = (3 x 3)/(4 x 3) = 9/12. For 2/3: To change the denominator from 3 to 12, we multiply by 4. We must also multiply the numerator by 4. So, 2/3 = (2 x 4)/(3 x 4) = 8/12. Step 5: Now add the fractions with the common denominator. Total sugar = 9/12 + 8/12 Step 6: When adding fractions with the same denominator, we add the numerators and keep the denominator the same. 9/12 + 8/12 = (9 + 8)/12 = 17/12 Step 7: The result is 17/12. This is an improper fraction (the numerator is larger than the denominator). The problem asks for the total amount in cups, and this fraction is an acceptable answer. Therefore, the total amount of sugar Liam needs is 17/12 cups.

6. Amelia has a 10 meter long ribbon. Amelia cuts it into 2 equal pieces. How long is each piece? Answer: 5 Solution: Total ribbon length: 10 meters. Step 2: Number of equal pieces: 2. Step 3: Divide the total length by the number of pieces: 10 ÷ 2 = 5 meter.
   Full step-by-step solution

   Step 1: Total ribbon length: 10 meters. Step 2: Number of equal pieces: 2. Step 3: Divide the total length by the number of pieces: 10 ÷ 2 = 5 meter. The answer is 5 meter.

7. A factory produces 840 meters of fabric. They use 3/8 of the fabric to make shirts and then use 2/5 of the remaining fabric to make pants. What fraction of the original 840 meters of fabric is left after making both shirts and pants? Answer: 3/8 Solution: Find the fraction of fabric remaining after making shirts. If 3/8 was used for shirts, then 1 - 3/8 = 5/8 remains. Calculate how much fabric is used for pants.
   Full step-by-step solution

   Step 1: Find the fraction of fabric remaining after making shirts. If 3/8 was used for shirts, then 1 - 3/8 = 5/8 remains. Step 2: Calculate how much fabric is used for pants. They use 2/5 of the remaining fabric, so 2/5 × 5/8 = 10/40 = 1/4 of the original fabric is used for pants. Step 3: Find the total fabric used. Shirts used 3/8 and pants used 1/4 = 2/8, so total used = 3/8 + 2/8 = 5/8. Step 4: Calculate the fraction left. Original fabric is 1 whole, so 1 - 5/8 = 3/8 remains. The answer is 3/8.

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

   Step 1: The problem asks for 3/4 of 2/3 cup of chocolate chips. This means we need to multiply the fractions. Step 2: Multiply the numerators: 3 × 2 = 6. Step 3: Multiply the denominators: 4 × 3 = 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.

9. Emma is making a quilt for her grandmother. She needs 3/4 yard of blue fabric and 2/3 yard of red fabric. If she wants to make one quilt using both colors, what is the total amount of fabric, in yards, that Emma needs? Answer: 17/12 Solution: Identify the fractions to add: 3/4 and 2/3 Find a common denominator for 4 and 3, which is 12 Convert 3/4 to twelfths: (3 × 3)/(4 × 3) = 9/12 Convert 2/3 to twelfths: (2 × 4)/(3 × 4) = 8/12 Add the fractions: 9/12 + 8/12 = 17/12 The total fabric needed is 17/12 yards The answer is 17/12 yards.
   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, which 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 total fabric needed is 17/12 yards The answer is 17/12 yards.