Equivalent Fractions

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Equivalent Fractions · Grade 4 · Worksheet 3

1. Mason is making a batch of homemade lemonade for his family. The recipe calls for 7/12 of a cup of lemon juice. Mason only has a 1/12 cup measuring spoon. How many scoops of the 1/12 cup measuring spoon does Mason need to measure out the correct amount of lemon juice? Answer: 7 Solution: We need to find how many 1/12 cup scoops equal 7/12 cup. This is like asking: 7/12 = ?/12, where the numerator tells us how many scoops.
   Full step-by-step solution

   Step 1: We need to find how many 1/12 cup scoops equal 7/12 cup. Step 2: This is like asking: 7/12 = ?/12, where the numerator tells us how many scoops. Step 3: Since the denominators are already the same (12), the numerator 7 tells us how many parts of 1/12 are in 7/12. Step 4: So 7/12 = 7 × (1/12), meaning 7 scoops. Step 5: Mason needs 7 scoops of the 1/12 cup measuring spoon. The answer is 7.

2. Liam is making a fruit salad for his class party. He needs 3/4 of a cup of strawberries for each serving. If he wants to make 8 servings, how many cups of strawberries does Liam need in total? Answer: 6 Solution: Liam needs 3/4 of a cup of strawberries for each serving. He wants to make 8 servings. To find the total cups needed, multiply the amount per serving by the number of servings.
   Full step-by-step solution

   Liam needs 3/4 of a cup of strawberries for each serving. He wants to make 8 servings. To find the total cups needed, multiply the amount per serving by the number of servings. Step 1: Write the multiplication. Total cups = (3/4) * 8 Step 2: Write 8 as a fraction to make multiplication easier. 8 = 8/1 So, Total cups = (3/4) * (8/1) Step 3: Multiply the numerators and the denominators. Numerator: 3 * 8 = 24 Denominator: 4 * 1 = 4 So, Total cups = 24/4 Step 4: Simplify the fraction. 24 divided by 4 equals 6. So, Total cups = 6 Therefore, Liam needs 6 cups of strawberries in total.

3. Hana is designing a rectangular tile pattern for a wall. The wall is 120 cm tall and 100 cm wide. She wants to cover the wall with identical square tiles, using the largest possible square tiles so that no space is left over and no tiles need to be cut. What is the side length, in centimeters, of each square tile? Answer: 20 Solution: The wall dimensions are 120 cm tall and 100 cm wide. We need the largest square tile that fits evenly along both dimensions. This means finding the greatest common factor (GCF) of 120 and 100.
   Full step-by-step solution

   Step 1: The wall dimensions are 120 cm tall and 100 cm wide. We need the largest square tile that fits evenly along both dimensions. This means finding the greatest common factor (GCF) of 120 and 100. Step 2: List the factors of 120: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120. Step 3: List the factors of 100: 1, 2, 4, 5, 10, 20, 25, 50, 100. Step 4: The common factors are: 1, 2, 4, 5, 10, 20. Step 5: The greatest common factor is 20. Step 6: Therefore, the largest square tile that fits without gaps has a side length of 20 cm. Step 7: Check: Along the height, 120 ÷ 20 = 6 tiles. Along the width, 100 ÷ 20 = 5 tiles. Total tiles = 6 × 5 = 30 tiles, with no leftover space. The answer is 20.

4. A rectangular chocolate bar is divided into 8 equal rows and 6 equal columns. If you eat 4 complete rows of the chocolate bar, what fraction of the entire chocolate bar did you eat? Answer: 1/2 Solution: Find the total number of pieces in the chocolate bar 8 rows × 6 columns = 48 pieces Find how many pieces are in 4 rows 4 rows × 6 columns = 24 pieces 24 pieces eaten out of 48 total pieces = 24/48 24 ÷ 24 = 1 48 ÷ 24 = 2 24/48 = 1/2 The answer is 1/2.
   Full step-by-step solution

   Step 1: Find the total number of pieces in the chocolate bar 8 rows × 6 columns = 48 pieces Step 2: Find how many pieces are in 4 rows 4 rows × 6 columns = 24 pieces Step 3: Write the fraction of chocolate bar eaten 24 pieces eaten out of 48 total pieces = 24/48 Step 4: Simplify the fraction 24 ÷ 24 = 1 48 ÷ 24 = 2 24/48 = 1/2 The answer is 1/2.

5. Noah is baking cookies for a school bake sale. His recipe calls for 5/6 cup of brown sugar. Noah only has a 1/12 cup measuring spoon. How many scoops of the 1/12 cup measuring spoon will Noah need to measure out the correct amount of brown sugar? Answer: 10 Solution: We need to find how many 1/12 cup scoops equal 5/6 cup. This means we need to find an equivalent fraction for 5/6 with a denominator of 12. To change the denominator from 6 to 12, we multiply by 2 (since 6 x 2 = 12).
   Full step-by-step solution

   Step 1: We need to find how many 1/12 cup scoops equal 5/6 cup. This means we need to find an equivalent fraction for 5/6 with a denominator of 12. Step 2: To change the denominator from 6 to 12, we multiply by 2 (since 6 x 2 = 12). Step 3: Multiply the numerator by the same number: 5 x 2 = 10. Step 4: So 5/6 = 10/12. Step 5: Since 10/12 means 10 parts of 1/12 each, Noah needs 10 scoops of the 1/12 cup measuring spoon. The answer is 10.

6. Tane is creating a rectangular garden plot that is 150 inches long and 90 inches wide. He wants to divide the entire plot into the largest possible equal square sections by drawing rows and columns of string, with no leftover space. What is the side length, in inches, of each square section? Answer: 30 Solution: The rectangle is 150 inches long and 90 inches 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 rectangle is 150 inches long and 90 inches 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 inches. Step 7: Check: Along the length, 150 ÷ 30 = 5 squares. Along the width, 90 ÷ 30 = 3 squares. Total squares = 5 × 3 = 15 squares, with no leftover space. The answer is 30.