Fraction Operations

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Answer Key & Explanations

Fraction Operations · Grade 5 · Worksheet 3

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

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

2. Aroha is drawing a rectangular sandpit on a coordinate grid where each unit represents 1 meter. The corners of the sandpit are at (9, 10), (17, 10), (17, 19), and (9, 19). She wants to fill exactly 5/8 of the sandpit with play sand. What is the area, in square meters, that will be filled with play sand? Answer: 45 Solution: Find the length. The left side is at x = 9 and the right side is at x = 17. The length is 17 - 9 = 8 meters.
   Full step-by-step solution

   Step 1: Find the length. The left side is at x = 9 and the right side is at x = 17. The length is 17 - 9 = 8 meters. Step 2: Find the width. The bottom is at y = 10 and the top is at y = 19. The width is 19 - 10 = 9 meters. Step 3: Find the total area. Area = length x width = 8 x 9 = 72 square meters. Step 4: Find 5/8 of the total area for play sand. 5/8 of 72 = (5/8) x 72 = (5 x 72)/8 = 360/8 = 45 square meters. The answer is 45 square meters.

3. Max has 3 liters of juice. Max pours the juice equally into 3 bottles. How many liters of juice are in each bottle? Answer: 1 Solution: Divide the total juice by the number of bottles: 3 ÷ 3. 3 ÷ 3 = 1 liter per bottle.
   Full step-by-step solution

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

4. A rectangular prism is drawn with a length of 6 cm, a width of 4.5 cm, and a height of 3.2 cm. What is the volume of this prism in cubic centimeters? Answer: 86.4 Solution: The formula for the volume of a rectangular prism is Volume = length x width x height. Substitute the given values into the formula: Volume = 6 cm x 4.5 cm x 3.2 cm. First, multiply 6 and 4.5.
   Full step-by-step solution

   Step 1: The formula for the volume of a rectangular prism is Volume = length x width x height. Step 2: Substitute the given values into the formula: Volume = 6 cm x 4.5 cm x 3.2 cm. Step 3: First, multiply 6 and 4.5. 6 x 4.5 = 27. Step 4: Now, multiply the result by the height: 27 x 3.2. Step 5: Calculate 27 x 3.2. 27 x 3 = 81, and 27 x 0.2 = 5.4. Adding these gives 81 + 5.4 = 86.4. Step 6: The volume is 86.4 cubic centimeters.

5. Tane is building a model canoe. He has 7/9 of a sheet of balsa wood. Each part of the canoe requires 1/3 of the sheet. How many parts can he make? Answer: 2 1/3 Solution: We need to find how many 1/3 sections fit into 7/9. This is a division problem: 7/9 ÷ 1/3. To divide fractions, multiply by the reciprocal of the second fraction.
   Full step-by-step solution

   Step 1: We need to find how many 1/3 sections fit into 7/9. This is a division problem: 7/9 ÷ 1/3. Step 2: To divide fractions, multiply by the reciprocal of the second fraction. The reciprocal of 1/3 is 3/1. Step 3: So, 7/9 ÷ 1/3 = 7/9 × 3/1. Step 4: Multiply the numerators: 7 × 3 = 21. Step 5: Multiply the denominators: 9 × 1 = 9. Step 6: This gives 21/9. Step 7: Simplify by dividing numerator and denominator by 3: 21 ÷ 3 = 7, and 9 ÷ 3 = 3. Step 8: So, 21/9 = 7/3. Step 9: Convert the improper fraction to a mixed number: 7/3 = 2 1/3. The answer is 2 1/3 parts.

6. Kaia has 8 liters of juice. Kaia pours the juice equally into 4 bottles. How many liters of juice are in each bottle? Answer: 2 Solution: Divide the total juice by the number of bottles: 8 ÷ 4. 8 ÷ 4 = 2 liter per bottle.
   Full step-by-step solution

   Step 1: Divide the total juice by the number of bottles: 8 ÷ 4. Step 2: 8 ÷ 4 = 2 liter per bottle.

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.