Equivalent Fractions

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Answer Key & Explanations

Equivalent Fractions · Grade 4 · Worksheet 2

1. Sophia is making a large pot of vegetable soup for her family. The recipe calls for 8/10 cup of diced carrots. Sophia only has a 1/5 cup measuring cup. How many scoops of the 1/5 cup measuring cup does Sophia need to measure out the correct amount of carrots? Answer: 4 Solution: We need to find how many 1/5 cup scoops equal 8/10 cup. This is the same as finding an equivalent fraction for 8/10 with a denominator of 5. To change the denominator from 10 to 5, we divide by 2: 10 divided by 2 = 5.
   Full step-by-step solution

   Step 1: We need to find how many 1/5 cup scoops equal 8/10 cup. This is the same as finding an equivalent fraction for 8/10 with a denominator of 5. Step 2: To change the denominator from 10 to 5, we divide by 2: 10 divided by 2 = 5. Step 3: Divide the numerator by the same number: 8 divided by 2 = 4. Step 4: So 8/10 = 4/5. Step 5: Since 4/5 means 4 parts of 1/5 each, Sophia needs 4 scoops of the 1/5 cup measuring cup. The answer is 4.

2. Liam is baking cookies and needs 3/4 cup of sugar. He only has a 1/8 cup measuring cup. How many scoops of the 1/8 cup does Liam need to measure out the correct amount of sugar? Answer: 6 Solution: We need to find how many 1/8 cup scoops make 3/4 cup. Write the problem as a division. We want: (3/4) ÷ (1/8) Remember that dividing by a fraction is the same as multiplying by its reciprocal.
   Full step-by-step solution

   We need to find how many 1/8 cup scoops make 3/4 cup. Step 1: Write the problem as a division. We want: (3/4) ÷ (1/8) Step 2: Remember that dividing by a fraction is the same as multiplying by its reciprocal. So, (3/4) ÷ (1/8) = (3/4) × (8/1) Step 3: Multiply the fractions. Multiply the numerators: 3 × 8 = 24 Multiply the denominators: 4 × 1 = 4 So we have 24/4. Step 4: Simplify 24/4. 24 divided by 4 is 6. Step 5: Interpret the result. This means Liam needs 6 scoops of the 1/8 cup to get 3/4 cup of sugar. Final answer: 6

3. A school is organizing a field trip and needs to divide 120 students equally among 5 buses. Each bus will have the same number of students. What fraction of the total students will be on each bus? Write your answer in simplest form. Answer: 1/5 Solution: Identify the total number of students: 120 Identify the number of buses: 5 To find the fraction of students on each bus, we put the number of buses (the number of equal groups) in the denominator and 1 (since we're looking at one bus) in the numerator The fraction is 1/5 Check if the fraction…
   Full step-by-step solution

   Step 1: Identify the total number of students: 120 Step 2: Identify the number of buses: 5 Step 3: To find the fraction of students on each bus, we put the number of buses (the number of equal groups) in the denominator and 1 (since we're looking at one bus) in the numerator Step 4: The fraction is 1/5 Step 5: Check if the fraction can be simplified: 1/5 is already in simplest form Each bus will carry 1/5 of the total students.

4. A farmer needs to divide 5/6 of an acre of land equally among 4 vegetable plots. What fraction of an acre will each plot receive? Answer: 5/24 Solution: The farmer has 5/6 of an acre to divide equally among 4 plots To divide a fraction by a whole number, we multiply the fraction by the reciprocal of the whole number The reciprocal of 4 is 1/4 Multiply 5/6 × 1/4 = (5 × 1)/(6 × 4) = 5/24 Each plot will receive 5/24 of an acre Check: 4 plots × 5/24…
   Full step-by-step solution

   Step 1: The farmer has 5/6 of an acre to divide equally among 4 plots Step 2: To divide a fraction by a whole number, we multiply the fraction by the reciprocal of the whole number Step 3: The reciprocal of 4 is 1/4 Step 4: Multiply 5/6 × 1/4 = (5 × 1)/(6 × 4) = 5/24 Step 5: Each plot will receive 5/24 of an acre Step 6: Check: 4 plots × 5/24 acre each = 20/24 = 5/6 acre total The answer is 5/24.

5. 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.

6. A school is organizing a field day and needs to divide 120 students equally into teams. If each team should have 3/4 of the students from a full team of 16, how many complete teams can be formed? Answer: 10 Solution: Find the number of students in each team. A full team has 16 students. Each team will have 3/4 of that.
   Full step-by-step solution

   Step 1: Find the number of students in each team. A full team has 16 students. Each team will have 3/4 of that. So, students per team = 3/4 × 16 = (3 × 16)/4 = 48/4 = 12 students. Step 2: Find how many teams of 12 students can be formed from 120 students. Number of teams = Total students ÷ Students per team = 120 ÷ 12 = 10. Step 3: Check if any students are left. 10 teams × 12 students = 120 students. No students are left. The school can form 10 complete teams.

7. 4/7 = __/63 Answer: 36 Solution: The original fraction is 4/7 and the new denominator is 63. Find what number you multiply the original denominator (7) by to get the new denominator (63). 7 × 9 = 63.
   Full step-by-step solution

   Step 1: The original fraction is 4/7 and the new denominator is 63. Step 2: Find what number you multiply the original denominator (7) by to get the new denominator (63). 7 × 9 = 63. Step 3: Multiply the original numerator (4) by the same number (9). 4 × 9 = 36. Step 4: The equivalent fraction is 36/63. The missing numerator is 36.

8. 4/5 = __/75 Answer: 60 Solution: The original fraction is 4/5 and the new denominator is 75. Find what number you multiply the original denominator (5) by to get the new denominator (75). 5 × 15 = 75.
   Full step-by-step solution

   Step 1: The original fraction is 4/5 and the new denominator is 75. Step 2: Find what number you multiply the original denominator (5) by to get the new denominator (75). 5 × 15 = 75. Step 3: Multiply the original numerator (4) by the same number (15). 4 × 15 = 60. Step 4: The equivalent fraction is 60/75. The missing numerator is 60.

9. Matiu is helping his family prepare coconut cream for a special feast. The recipe calls for 8/9 of a cup of coconut cream. Matiu only has a measuring cup that holds 1/9 of a cup. How many scoops of the small measuring cup will Matiu need to measure out the correct amount of coconut cream? Answer: 8 Solution: We need to find how many 1/9 cup scoops equal 8/9 cup. This is like asking: how many times does 1/9 fit into 8/9? Since both fractions have the same denominator (9), we can simply compare the numerators.
   Full step-by-step solution

   Step 1: We need to find how many 1/9 cup scoops equal 8/9 cup. This is like asking: how many times does 1/9 fit into 8/9? Step 2: Since both fractions have the same denominator (9), we can simply compare the numerators. 8/9 means 8 parts of 1/9 each. Step 3: So, 8/9 = 8 x (1/9). This means Matiu needs 8 scoops of the 1/9 cup measuring cup. Step 4: We can check by multiplying: 8 x (1/9) = 8/9. This matches the required amount. The answer is 8.