Equivalent Fractions

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Answer Key & Explanations

Equivalent Fractions · Grade 4 · Worksheet 1

1. Matiu is designing a rectangular banner that is 150 cm long and 90 cm wide. He wants to divide the entire banner into the largest possible equal square sections by drawing vertical and horizontal lines, with no leftover space. What is the side length, in centimeters, of each square section? Answer: 30 Solution: The banner is 150 cm long and 90 cm wide. To divide it into equal square sections with no leftover space, the side length of each square must divide evenly into both 150 and 90.
   Full step-by-step solution

   Step 1: The banner is 150 cm long and 90 cm wide. To divide it into equal square sections with no leftover space, the side length of each square must divide evenly into both 150 and 90. We need the greatest common factor (GCF) of 150 and 90. Step 2: List the factors of 150: 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 150. Step 3: List the factors of 90: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90. Step 4: The common factors are: 1, 2, 3, 5, 6, 10, 15, 30. Step 5: The greatest common factor is 30. Step 6: Therefore, the largest possible side length for each square section is 30 cm. Step 7: Check: Along the length, 150 divided by 30 equals 5 squares. Along the width, 90 divided by 30 equals 3 squares. Total squares = 5 times 3 = 15 squares, with no leftover space. The answer is 30.

2. 5/8 = __/96 Answer: 60 Solution: The original fraction is 5/8 and the new denominator is 96. Find what number you multiply the original denominator (8) by to get the new denominator (96). 8 × 12 = 96.
   Full step-by-step solution

   Step 1: The original fraction is 5/8 and the new denominator is 96. Step 2: Find what number you multiply the original denominator (8) by to get the new denominator (96). 8 × 12 = 96. Step 3: Multiply the original numerator (5) by the same number (12). 5 × 12 = 60. Step 4: The equivalent fraction is 60/96. The missing numerator is 60.

3. Charlotte is making a large batch of fruit punch for her birthday party. The recipe calls for 4/7 cup of orange juice for each serving. She wants to make 14 servings. How many cups of orange juice does Charlotte need in total? Write your answer as a fraction in simplest form. Answer: 8 Solution: Charlotte needs 4/7 cup of orange juice for each serving, and she wants to make 14 servings. So we need to multiply 4/7 by 14. Write 14 as a fraction: 14 = 14/1.
   Full step-by-step solution

   Step 1: Charlotte needs 4/7 cup of orange juice for each serving, and she wants to make 14 servings. So we need to multiply 4/7 by 14. Step 2: Write 14 as a fraction: 14 = 14/1. Step 3: Multiply the numerators: 4 × 14 = 56. The new numerator is 56. Step 4: Multiply the denominators: 7 × 1 = 7. The denominator stays 7. Step 5: The product is 56/7. Step 6: Simplify 56/7 by dividing both numerator and denominator by 7: 56 ÷ 7 = 8, and 7 ÷ 7 = 1. So 56/7 = 8/1 = 8. Charlotte needs 8 cups of orange juice.

4. A rectangular garden is divided into 4 equal sections. If 3 of these sections are planted with vegetables, what fraction of the garden has vegetables? Draw a rectangle divided into 4 equal parts and shade 3 of them to visualize. Answer: 3/4 Solution: The garden is a rectangle divided into 4 equal sections. This means the whole garden is made of 4 equal parts. Identify how many sections have vegetables.
   Full step-by-step solution

   Step 1: Understand the garden layout. The garden is a rectangle divided into 4 equal sections. This means the whole garden is made of 4 equal parts. Step 2: Identify how many sections have vegetables. The problem says 3 of these sections are planted with vegetables. Step 3: Determine the fraction. A fraction is formed by comparing the number of parts we are interested in (vegetable sections) to the total number of equal parts. So, the fraction is: (Number of vegetable sections) / (Total number of sections) = 3 / 4. Step 4: Visual confirmation (imagining the drawing). If you draw a rectangle and split it into 4 equal parts (like 4 smaller rectangles of the same size), and then shade 3 of them, you can see that most of the garden is shaded. This confirms that 3 out of 4 parts, or 3/4 of the whole, is covered with vegetables. Final Answer: 3/4

5. Kaia is making traditional woven baskets for a community market. She has a roll of ribbon that is 9/12 of a meter long. She needs to cut the ribbon into pieces that are each 1/6 of a meter long. How many pieces of ribbon can Kaia cut from the roll? Answer: 4 Solution: We need to find how many 1/6 meter pieces fit into 9/12 meter. This is like dividing 9/12 by 1/6. To compare, write 9/12 as an equivalent fraction with denominator 6.
   Full step-by-step solution

   Step 1: We need to find how many 1/6 meter pieces fit into 9/12 meter. This is like dividing 9/12 by 1/6. Step 2: To compare, write 9/12 as an equivalent fraction with denominator 6. Divide numerator and denominator by 2: 9 ÷ 2 = 4.5, but this doesn't work cleanly. Instead, write 1/6 as an equivalent fraction with denominator 12. Multiply numerator and denominator by 2: 1/6 = (1 × 2)/(6 × 2) = 2/12. Step 3: Now the problem is: how many times does 2/12 fit into 9/12? Divide the numerators: 9 ÷ 2 = 4.5, but pieces must be whole, so we check: 4 pieces of 2/12 use 8/12, leaving 1/12 leftover. Step 4: So Kaia can cut 4 whole pieces of ribbon, each 1/6 meter long. The answer is 4.

6. Tane is weaving a traditional flax basket. He has completed 3/5 of the basket. His grandmother says this is the same as 9/15 of the basket. Tane wants to check if she is correct by finding an equivalent fraction. What number should Tane multiply the numerator and denominator of 3/5 by to get 9/15? Answer: 3 Solution: We start with the fraction 3/5. We want to find the number that multiplies both the numerator and denominator to get 9/15. For the numerator: 3 x ?
   Full step-by-step solution

   Step 1: We start with the fraction 3/5. Step 2: We want to find the number that multiplies both the numerator and denominator to get 9/15. Step 3: For the numerator: 3 x ? = 9. Divide 9 by 3 to find the multiplier: 9 / 3 = 3. Step 4: Check the denominator: 5 x 3 = 15. This matches the denominator of the equivalent fraction. Step 5: Since multiplying both numerator and denominator by 3 gives 9/15, the number Tane should multiply by is 3. The answer is 3.