Equivalent Fractions

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Answer Key & Explanations

Equivalent Fractions · Grade 3 · Worksheet 2

1. Noah draws a rectangle on a grid and divides it into 10 equal vertical strips. He shades 6 of the strips blue. Then he draws a second, identical rectangle and divides it into some equal parts. He wants to shade the same fraction of the second rectangle. If the second rectangle is divided into 5 equal parts, how many parts should he shade? Answer: 3 Solution: In the first rectangle, 6 out of 10 parts are shaded. That is the fraction 6/10. The second rectangle is divided into 5 equal parts.
   Full step-by-step solution

   Step 1: In the first rectangle, 6 out of 10 parts are shaded. That is the fraction 6/10. Step 2: The second rectangle is divided into 5 equal parts. We need to find how many of those 5 parts to shade so that the shaded fraction equals 6/10. Step 3: We are looking for a fraction equivalent to 6/10 with a denominator of 5. Think: 10 divided by 2 equals 5. To keep the fraction equal, divide the numerator by the same number: 6 divided by 2 equals 3. Step 4: So 6/10 = 3/5. Noah should shade 3 parts out of 5. The answer is 3.

2. 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 in simplest form. Answer: 3/4 Solution: The garden is divided into 4 equal sections. That means the whole garden is represented by 4 parts. 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 by 4 parts. 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. The fraction is the number of sections with tomatoes over the total number of sections: 3/4 Step 4: Check if the fraction is in simplest form. 3 and 4 have no common factors other than 1, so 3/4 is already in simplest form. Final answer: 3/4

3. Noah is painting a mural on the school 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. Add the painted sections: 8 + 4 = 12 sections. The wall has 12 equal sections total.
   Full step-by-step solution

   Step 1: Noah painted 8 sections with blue sky and 4 sections with green grass. Step 2: Add the painted sections: 8 + 4 = 12 sections. Step 3: The wall has 12 equal sections total. Step 4: The fraction of wall painted is 12/12. Step 5: Simplify 12/12 = 1. The answer is 1.

4. Sophia is organizing her art supplies. She has a rectangular tray divided into 9 equal compartments. She puts paintbrushes in 6 of the compartments. She says that she has filled 2/3 of the tray. Is Sophia correct? Explain by finding an equivalent fraction. Answer: Yes, Sophia is correct because 6/9 = 2/3. Solution: The tray is divided into 9 equal compartments. Sophia uses 6 compartments, so the fraction filled is 6/9. To check if 6/9 equals 2/3, think about dividing the same tray into 3 equal parts instead of 9.
   Full step-by-step solution

   Step 1: The tray is divided into 9 equal compartments. Sophia uses 6 compartments, so the fraction filled is 6/9. Step 2: To check if 6/9 equals 2/3, think about dividing the same tray into 3 equal parts instead of 9. Each third would contain 3 compartments (because 9 divided by 3 is 3). Step 3: Sophia filled 6 compartments. Since each third has 3 compartments, 6 compartments make 2 full thirds (because 6 divided by 3 is 2). Step 4: So 2/3 of the tray is the same as 6/9. Therefore, 6/9 = 2/3. The answer is: Yes, Sophia is correct because 6/9 = 2/3.

5. 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.

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. Lily is baking cookies for her school bake sale. She has a large bag containing 240 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: 30 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 = 240 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 = 240 Number of batches = 8 Step 2: Set up the division problem. We need to calculate: 240 divided by 8. Step 3: Perform the division. Think of it as: How many times does 8 go into 240? We know that 8 times 3 is 24. Since 240 is 10 times larger than 24, we can multiply that result by 10. So, 8 times 30 is 240. Step 4: State the final answer. This means Lily should put 30 chocolate chips in each batch. Answer: 30

8. 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