Fraction Operations

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Fraction Operations · Grade 5 · Worksheet 3

1. Tane has a 6 meter long ribbon. Tane cuts it into 6 equal pieces. How long is each piece? Answer: 1 Solution: Total ribbon length: 6 meters. Step 2: Number of equal pieces: 6. Step 3: Divide the total length by the number of pieces: 6 ÷ 6 = 1 meter.
   Full step-by-step solution

   Step 1: Total ribbon length: 6 meters. Step 2: Number of equal pieces: 6. Step 3: Divide the total length by the number of pieces: 6 ÷ 6 = 1 meter. The answer is 1 meter.

2. A rectangular prism is drawn with a length of 8 cm, width of 5 cm, and height of 6 cm. What is the volume of this rectangular prism in cubic centimeters? Answer: 240 Solution: The formula for volume of a rectangular prism is length × width × height Substitute the given values: 8 cm × 5 cm × 6 cm First multiply 8 × 5 = 40 Then multiply 40 × 6 = 240 Include the units: 240 cubic centimeters The answer is 240.
   Full step-by-step solution

   Step 1: The formula for volume of a rectangular prism is length × width × height Step 2: Substitute the given values: 8 cm × 5 cm × 6 cm Step 3: First multiply 8 × 5 = 40 Step 4: Then multiply 40 × 6 = 240 Step 5: Include the units: 240 cubic centimeters The answer is 240.

3. A recipe requires 3/4 cup of milk. If you only want to make 2/3 of the recipe, how much milk do you need? Answer: 1/2 Solution: The problem asks for 2/3 of 3/4 cup of milk. 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 milk. 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 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 milk.

4. A recipe uses 3/4 cup of milk. If you only want to make 2/3 of the recipe, how many cups of milk do you need? Answer: 1/2 Solution: The problem asks for 2/3 of 3/4 cup of milk. 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 milk. 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 milk.

5. Emma is making a quilt for her grandmother. She needs 3/4 yard of blue fabric and 5/6 yard of red fabric. If she already has 1/3 yard of blue fabric, how many more yards of blue fabric does Emma need to buy? Answer: 5/12 Solution: Emma needs 3/4 yard of blue fabric total She already has 1/3 yard of blue fabric To find how much more she needs, subtract what she has from what she needs: 3/4 - 1/3 Find a common denominator for 4 and 3, which is 12 Convert 3/4 to 9/12 (3/4 × 3/3 = 9/12) Convert 1/3 to 4/12 (1/3 × 4/4 = 4/12)…
   Full step-by-step solution

   Step 1: Emma needs 3/4 yard of blue fabric total Step 2: She already has 1/3 yard of blue fabric Step 3: To find how much more she needs, subtract what she has from what she needs: 3/4 - 1/3 Step 4: Find a common denominator for 4 and 3, which is 12 Step 5: Convert 3/4 to 9/12 (3/4 × 3/3 = 9/12) Step 6: Convert 1/3 to 4/12 (1/3 × 4/4 = 4/12) Step 7: Subtract: 9/12 - 4/12 = 5/12 Step 8: Emma needs 5/12 yard more of blue fabric

6. A factory produces 840 meters of fabric. They use 5/8 of the fabric to make shirts and then use 2/3 of the remaining fabric to make pants. What fraction of the original fabric was used to make pants? Answer: 1/4 Solution: Find the fabric used for shirts: 5/8 of 840 = (5/8) × 840 = 5 × 105 = 525 meters Find the remaining fabric after shirts: 840 - 525 = 315 meters Find the fabric used for pants: 2/3 of 315 = (2/3) × 315 = 2 × 105 = 210 meters Find the fraction of original fabric used for pants: 210/840 = 21/84 =…
   Full step-by-step solution

   Step 1: Find the fabric used for shirts: 5/8 of 840 = (5/8) × 840 = 5 × 105 = 525 meters Step 2: Find the remaining fabric after shirts: 840 - 525 = 315 meters Step 3: Find the fabric used for pants: 2/3 of 315 = (2/3) × 315 = 2 × 105 = 210 meters Step 4: Find the fraction of original fabric used for pants: 210/840 = 21/84 = 7/28 = 1/4 The answer is 1/4.

7. 3/4 + 2/5 = ? Answer: 23/20 Solution: To add the fractions 3/4 and 2/5, we need a common denominator. Find a common denominator. The denominators are 4 and 5.
   Full step-by-step solution

   To add the fractions 3/4 and 2/5, we need a common denominator. Step 1: Find a common denominator. The denominators are 4 and 5. The smallest number that both 4 and 5 divide into is 20. So, the common denominator is 20. Step 2: Convert the first fraction, 3/4, to have a denominator of 20. To change 4 into 20, we multiply by 5. To keep the value of the fraction the same, we must also multiply the numerator by 5. So, 3/4 = (3 x 5) / (4 x 5) = 15/20. Step 3: Convert the second fraction, 2/5, to have a denominator of 20. To change 5 into 20, we multiply by 4. To keep the value of the fraction the same, we must also multiply the numerator by 4. So, 2/5 = (2 x 4) / (5 x 4) = 8/20. Step 4: Add the two fractions. Now that both fractions have the same denominator (20), we can add them by adding the numerators and keeping the denominator. 15/20 + 8/20 = (15 + 8) / 20 = 23/20. Step 5: Check if the result can be simplified. The fraction 23/20 is already in its simplest form because 23 and 20 have no common factors other than 1. Therefore, the final answer is 23/20.

8. Emma is making a quilt and needs to cut fabric pieces. She has a piece of fabric that is 5/6 yard long. If she cuts off 3/8 yard for one section of the quilt, how much fabric does she have left? Answer: 11/24 Solution: Write the subtraction problem: 5/6 - 3/8 Find a common denominator for 6 and 8. The least common multiple is 24.
   Full step-by-step solution

   Step 1: Write the subtraction problem: 5/6 - 3/8 Step 2: Find a common denominator for 6 and 8. The least common multiple is 24. Step 3: Convert 5/6 to have denominator 24: (5 × 4)/(6 × 4) = 20/24 Step 4: Convert 3/8 to have denominator 24: (3 × 3)/(8 × 3) = 9/24 Step 5: Subtract the fractions: 20/24 - 9/24 = 11/24 Step 6: The answer is 11/24 yard of fabric remaining.