Equivalent Fractions

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Answer Key & Explanations

Equivalent Fractions · Grade 3 · Worksheet 1

1. A rectangular garden is divided into 4 equal sections. If 3 sections are planted with tomatoes, what fraction of the garden has tomatoes? Write your answer as a fraction. Answer: 3/4 Solution: The garden is divided into 4 equal sections. That means the whole garden is represented as 4/4 or 1 whole. Determine how many sections have tomatoes.
   Full step-by-step solution

   Step 1: Understand the problem. The garden is divided into 4 equal sections. That means the whole garden is represented as 4/4 or 1 whole. Step 2: Determine how many sections have tomatoes. The problem says 3 sections are planted with tomatoes. Step 3: Write the fraction of the garden with tomatoes. Since 3 out of 4 equal sections have tomatoes, the fraction is 3/4. Step 4: Check the answer. The garden is in 4 equal parts, and 3 of them have tomatoes, so 3/4 is correct. Final answer: 3/4

2. 2/4 = ?/8 Answer: 4 Solution: We start with the equation: 2/4 = ?/8 Notice that both sides are fractions. The left side is 2/4, which can be simplified. 2/4 simplifies to 1/2.
   Full step-by-step solution

   We start with the equation: 2/4 = ?/8 Step 1: Notice that both sides are fractions. The left side is 2/4, which can be simplified. 2/4 simplifies to 1/2. Step 2: So now we have: 1/2 = ?/8 Step 3: To find the missing number, observe that the denominators are 2 and 8. Since 8 is 4 times 2, we can multiply the numerator and denominator of 1/2 by 4 to make the denominator 8. Step 4: Multiply numerator and denominator: (1 × 4)/(2 × 4) = 4/8 Step 5: So the missing number is 4. Final answer: 4

3. Noah is painting a mural on a long wall at his school. The wall is divided into 12 equal sections. He paints 8 sections with blue sky and 4 sections with green grass. What fraction of the whole wall did Noah paint? Write your answer in simplest form. Answer: 1 Solution: The wall is divided into 12 equal sections. Noah paints 8 sections with blue sky and 4 sections with green grass. Total sections painted = 8 + 4 = 12 sections.
   Full step-by-step solution

   Step 1: The wall is divided into 12 equal sections. Step 2: Noah paints 8 sections with blue sky and 4 sections with green grass. Step 3: Total sections painted = 8 + 4 = 12 sections. Step 4: Fraction of wall painted = total sections painted / total sections = 12/12. Step 5: Simplify 12/12 = 1. The answer is 1.

4. A rectangular garden is divided into 16 equal square plots. The gardener plants tomatoes in 4 of the plots and carrots in 8 of the plots. What fraction of the garden is planted with vegetables? Write your answer in simplest form. Answer: 3/4 Solution: Find the total number of plots used for vegetables. Tomato plots: 4 Carrot plots: 8 Total vegetable plots = 4 + 8 = 12 Write the fraction of garden with vegetables.
   Full step-by-step solution

   Step 1: Find the total number of plots used for vegetables. Tomato plots: 4 Carrot plots: 8 Total vegetable plots = 4 + 8 = 12 Step 2: Write the fraction of garden with vegetables. Total plots in garden: 16 Fraction = vegetable plots / total plots = 12/16 Step 3: Simplify the fraction. Both 12 and 16 can be divided by 4. 12 ÷ 4 = 3 16 ÷ 4 = 4 So 12/16 = 3/4 The answer is 3/4.

5. Noah is painting a mural on a long wall. He divides the wall into 12 equal sections. He paints 8 sections with blue sky and 4 sections with green grass. What fraction of the whole wall did Noah paint? Write your answer in simplest form. Answer: 1 Solution: Noah painted 8 sections with blue sky and 4 sections with green grass. To find the total painted sections, add the blue and green sections: 8 + 4 = 12.
   Full step-by-step solution

   Step 1: Noah painted 8 sections with blue sky and 4 sections with green grass. Step 2: To find the total painted sections, add the blue and green sections: 8 + 4 = 12. Step 3: The wall was divided into 12 equal sections, so the whole wall is represented by 12/12. Step 4: The fraction of the wall that was painted is 12/12. Step 5: Simplify 12/12 by dividing both the numerator and denominator by 12: 12 ÷ 12 = 1 and 12 ÷ 12 = 1. Step 6: 12/12 simplifies to 1/1, which equals 1. The answer is 1.

6. Lily is baking cookies for her school bake sale. She has a large bag with 120 chocolate chips. If she wants to divide the chocolate chips equally among 8 batches of cookies, how many chocolate chips should she put in each batch? Answer: 15 Solution: To find how many chocolate chips go in each batch, we need to divide the total number of chocolate chips by the number of batches. Identify the total number of chocolate chips and the number of batches. Total chocolate chips = 120 Number of batches = 8 Set up the division problem.
   Full step-by-step solution

   To find how many chocolate chips go in each batch, we need to divide the total number of chocolate chips by the number of batches. Step 1: Identify the total number of chocolate chips and the number of batches. Total chocolate chips = 120 Number of batches = 8 Step 2: Set up the division problem. We need to calculate: 120 divided by 8. Step 3: Perform the division. Think of it as: How many times does 8 go into 120? We know that 8 times 15 equals 120 because: 8 * 10 = 80 8 * 5 = 40 Then, 80 + 40 = 120. So, 8 * 15 = 120. Step 4: State the result. Since 120 divided by 8 equals 15, this means each batch should get 15 chocolate chips. Answer: 15

7. Liam is baking cookies for his class party. He has a recipe that makes 24 cookies, but he needs to make 72 cookies total. Liam realizes that 72 is the same as 24 three times. What fraction of the total cookies does one batch of 24 cookies represent? Answer: 1/3 Solution: Liam needs 72 cookies in total. One batch makes 24 cookies. Figure out how many batches are needed.
   Full step-by-step solution

   Step 1: Understand the problem. Liam needs 72 cookies in total. One batch makes 24 cookies. Step 2: Figure out how many batches are needed. Since 72 ÷ 24 = 3, Liam needs 3 batches. Step 3: Determine what fraction one batch is of the total. One batch = 24 cookies. Total cookies = 72 cookies. So the fraction is: 24 / 72. Step 4: Simplify the fraction. Divide numerator and denominator by 24: 24 ÷ 24 = 1 72 ÷ 24 = 3 So 24/72 = 1/3. Step 5: Interpret the result. One batch of 24 cookies is 1/3 of the total 72 cookies. Final answer: 1/3

8. 3/4 = ?/12 Answer: 9 Solution: Look at the denominators. The first fraction has a denominator of 4, and the second fraction has a denominator of 12. Find what number you multiply 4 by to get 12.
   Full step-by-step solution

   Step 1: Look at the denominators. The first fraction has a denominator of 4, and the second fraction has a denominator of 12. Step 2: Find what number you multiply 4 by to get 12. 4 × 3 = 12. Step 3: Multiply the numerator by the same number. 3 × 3 = 9. Step 4: The equivalent fraction is 3/4 = 9/12. The answer is 9.

9. 4/6 = ?/12 Answer: 8 Solution: Look at the denominators. The first fraction has a denominator of 6, and the second fraction has a denominator of 12. Determine what number you multiply 6 by to get 12.
   Full step-by-step solution

   Step 1: Look at the denominators. The first fraction has a denominator of 6, and the second fraction has a denominator of 12. Step 2: Determine what number you multiply 6 by to get 12. 6 × 2 = 12. Step 3: Multiply the numerator of the first fraction by the same number (2). 4 × 2 = 8. Step 4: The equivalent fraction is 8/12. The answer is 8.