Fraction Operations

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Fraction Operations · Grade 5 · Worksheet 1

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 recipe calls for 5/6 cup of sugar. If you want to make 3/4 of the recipe, how many cups of sugar do you need? Answer: 5/8 Solution: The problem asks for 3/4 of 5/6 cup of sugar. This means we need to multiply the fractions: 3/4 × 5/6. Multiply the numerators: 3 × 5 = 15.
   Full step-by-step solution

   Step 1: The problem asks for 3/4 of 5/6 cup of sugar. This means we need to multiply the fractions: 3/4 × 5/6. Step 2: Multiply the numerators: 3 × 5 = 15. Step 3: Multiply the denominators: 4 × 6 = 24. Step 4: This gives us the fraction 15/24. Step 5: Simplify 15/24 by dividing both numerator and denominator by their greatest common factor, which is 3. 15 ÷ 3 = 5 and 24 ÷ 3 = 8. Step 6: The simplified fraction is 5/8. The answer is 5/8 cup of sugar.

3. Kai has 6 liters of juice. Kai pours the juice equally into 3 bottles. How many liters of juice are in each bottle? Answer: 2 Solution: Divide the total juice by the number of bottles: 6 ÷ 3. 6 ÷ 3 = 2 liter per bottle.
   Full step-by-step solution

   Step 1: Divide the total juice by the number of bottles: 6 ÷ 3. Step 2: 6 ÷ 3 = 2 liter per bottle.

4. Emma is making a fruit salad for a class party. She uses 3/4 cup of strawberries and 2/3 cup of blueberries. What is the total amount of fruit, in cups, that Emma uses in her fruit salad? Answer: 17/12 Solution: Identify the fractions to add: 3/4 and 2/3 Find a common denominator.
   Full step-by-step solution

   Step 1: Identify the fractions to add: 3/4 and 2/3 Step 2: Find a common denominator. The least common multiple of 4 and 3 is 12 Step 3: Convert 3/4 to twelfths: 3/4 = (3 × 3)/(4 × 3) = 9/12 Step 4: Convert 2/3 to twelfths: 2/3 = (2 × 4)/(3 × 4) = 8/12 Step 5: Add the fractions: 9/12 + 8/12 = 17/12 Step 6: The answer is 17/12 cups, which can also be written as 1 5/12 cups

5. A rectangular prism is drawn with a length of 12 cm, width of 8 cm, and height of 5 cm. What is the volume of this prism in cubic centimeters? Answer: 480 Solution: The formula for the volume of a rectangular prism is length × width × height. Substitute the given values: Volume = 12 cm × 8 cm × 5 cm. First, multiply 12 and 8: 12 × 8 = 96.
   Full step-by-step solution

   Step 1: The formula for the volume of a rectangular prism is length × width × height. Step 2: Substitute the given values: Volume = 12 cm × 8 cm × 5 cm. Step 3: First, multiply 12 and 8: 12 × 8 = 96. Step 4: Now multiply the result by the height: 96 × 5 = 480. Step 5: The volume is 480 cubic centimeters.

6. A recipe requires 3/4 cup of milk. If you 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.

7. Aroha is weaving a traditional flax basket. She has 5/7 of a roll of flax cord. Each decorative band around the basket requires 3/14 of the roll. How many bands can she weave? Answer: 3 1/3 Solution: We need to find how many 3/14 roll bands fit into 5/7 roll. This is a division problem: 5/7 ÷ 3/14. To divide fractions, multiply by the reciprocal of the second fraction.
   Full step-by-step solution

   Step 1: We need to find how many 3/14 roll bands fit into 5/7 roll. This is a division problem: 5/7 ÷ 3/14. Step 2: To divide fractions, multiply by the reciprocal of the second fraction. The reciprocal of 3/14 is 14/3. Step 3: So, 5/7 ÷ 3/14 = 5/7 × 14/3. Step 4: Multiply the numerators: 5 × 14 = 70. Step 5: Multiply the denominators: 7 × 3 = 21. Step 6: This gives 70/21. Step 7: Simplify by dividing numerator and denominator by their greatest common factor, which is 7. 70 ÷ 7 = 10 and 21 ÷ 7 = 3. Step 8: So, 70/21 = 10/3. Step 9: Convert the improper fraction to a mixed number. 10 ÷ 3 = 3 with a remainder of 1, so 10/3 = 3 1/3. The answer is 3 1/3 bands.

8. Mere walked 2 of a mile to the park. Then Mere walked another 3 of a mile to the library. How far did Mere walk in total? Answer: 5 Solution: Find a common denominator for 2 and 3. Add the two fractions: 2 + 3 = 5. Simplify if needed: 5.
   Full step-by-step solution

   Step 1: Find a common denominator for 2 and 3. Step 2: Add the two fractions: 2 + 3 = 5. Step 3: Simplify if needed: 5. Mere walked 5 of a mile in total. The answer is 5.