Fraction Operations

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Fraction Operations · Grade 5 · Worksheet 1

1. Ben has a 12 meter long ribbon. Ben cuts it into 2 equal pieces. How long is each piece? Answer: 6 Solution: Total ribbon length: 12 meters. Step 2: Number of equal pieces: 2. Step 3: Divide the total length by the number of pieces: 12 ÷ 2 = 6 meter.
   Full step-by-step solution

   Step 1: Total ribbon length: 12 meters. Step 2: Number of equal pieces: 2. Step 3: Divide the total length by the number of pieces: 12 ÷ 2 = 6 meter. The answer is 6 meter.

2. 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.

3. Jordan has a 7 meter long ribbon. Jordan cuts it into 7 equal pieces. How long is each piece? Answer: 1 Solution: Total ribbon length: 7 meters. Step 2: Number of equal pieces: 7. Step 3: Divide the total length by the number of pieces: 7 ÷ 7 = 1 meter.
   Full step-by-step solution

   Step 1: Total ribbon length: 7 meters. Step 2: Number of equal pieces: 7. Step 3: Divide the total length by the number of pieces: 7 ÷ 7 = 1 meter. The answer is 1 meter.

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

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

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

6. A rectangular prism is drawn with dimensions 8 cm by 5 cm by 3 cm. What is the volume of this prism in cubic centimeters? Answer: 120 Solution: The formula for volume of a rectangular prism is length × width × height. Multiply the length (8 cm) by the width (5 cm): 8 × 5 = 40 Multiply that result by the height (3 cm): 40 × 3 = 120 The volume is 120 cubic centimeters.
   Full step-by-step solution

   Step 1: The formula for volume of a rectangular prism is length × width × height. Step 2: Multiply the length (8 cm) by the width (5 cm): 8 × 5 = 40 Step 3: Multiply that result by the height (3 cm): 40 × 3 = 120 Step 4: The volume is 120 cubic centimeters.

7. Liam is making a special trail mix for his hiking trip. He uses 2/3 cup of almonds and 3/4 cup of raisins. What is the total amount of almonds and raisins that Liam uses in his trail mix? Answer: 1 5/12 cups Solution: To find the total amount of almonds and raisins, we need to add the two fractions: 2/3 cup and 3/4 cup. Identify the fractions to add. We have 2/3 and 3/4.
   Full step-by-step solution

   To find the total amount of almonds and raisins, we need to add the two fractions: 2/3 cup and 3/4 cup. Step 1: Identify the fractions to add. We have 2/3 and 3/4. Step 2: Find a common denominator. The denominators are 3 and 4. The smallest number that both 3 and 4 divide into evenly is 12. So, the common denominator is 12. Step 3: Convert each fraction to have the denominator of 12. - For 2/3: To change the denominator 3 into 12, we multiply by 4. So we multiply both the numerator and denominator by 4. This gives us (2 * 4) / (3 * 4) = 8/12. - For 3/4: To change the denominator 4 into 12, we multiply by 3. So we multiply both the numerator and denominator by 3. This gives us (3 * 3) / (4 * 3) = 9/12. Step 4: Add the converted fractions. Now we add 8/12 + 9/12. Since the denominators are the same, we add the numerators: 8 + 9 = 17. We keep the denominator of 12. This gives us 17/12. Step 5: Simplify the result. The fraction 17/12 is an improper fraction (the numerator is larger than the denominator). We can convert it to a mixed number. - Divide 17 by 12. 12 goes into 17 one full time (1 * 12 = 12). - The remainder is 17 - 12 = 5. - So, 17/12 is equal to 1 and 5/12. Therefore, the total amount of almonds and raisins that Liam uses is 1 5/12 cups.

8. 2/3 + 5/6 = ? Answer: 3/2 Solution: Find a common denominator for 3 and 6. Since 6 is a multiple of 3, the common denominator is 6. Convert 2/3 to have a denominator of 6.
   Full step-by-step solution

   Step 1: Find a common denominator for 3 and 6. Since 6 is a multiple of 3, the common denominator is 6. Step 2: Convert 2/3 to have a denominator of 6. Multiply both numerator and denominator by 2: (2 × 2)/(3 × 2) = 4/6. Step 3: Now add the fractions: 4/6 + 5/6 = 9/6. Step 4: Simplify 9/6 by dividing both numerator and denominator by 3: 9 ÷ 3 = 3, 6 ÷ 3 = 2, so 9/6 = 3/2. The answer is 3/2.