Fractions Equal Parts

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Answer Key & Explanations

Fractions Equal Parts · Grade 3 · Worksheet 2

1. Maria is making a quilt for her grandmother. She has a rectangular piece of fabric that is 72 inches long. She needs to cut it into 8 equal strips to make the quilt border. How many inches long will each strip be? Answer: 9 Solution: Maria has 72 inches of fabric total. She needs to divide it into 8 equal strips. To find the length of each strip, divide the total length by the number of strips: 72 ÷ 8 72 ÷ 8 = 9 Each strip will be 9 inches long.
   Full step-by-step solution

   Step 1: Maria has 72 inches of fabric total. Step 2: She needs to divide it into 8 equal strips. Step 3: To find the length of each strip, divide the total length by the number of strips: 72 ÷ 8 Step 4: 72 ÷ 8 = 9 Each strip will be 9 inches long.

2. A rectangular garden is divided into 8 equal sections. 3 sections are planted with carrots and 2 sections are planted with tomatoes. What fraction of the garden is planted with vegetables? Answer: 5/8 Solution: The garden is divided into 8 equal sections. Carrots take 3 sections, tomatoes take 2 sections. We want the fraction of the garden planted with vegetables.
   Full step-by-step solution

   Step 1: Understand the problem. The garden is divided into 8 equal sections. Carrots take 3 sections, tomatoes take 2 sections. We want the fraction of the garden planted with vegetables. Step 2: Find the total number of sections with vegetables. Sections with carrots = 3 Sections with tomatoes = 2 Total vegetable sections = 3 + 2 = 5 Step 3: Write the fraction of the garden that is vegetables. The garden has 8 equal sections in total, so the fraction is: (Total vegetable sections) / (Total sections) = 5 / 8 Step 4: Conclusion. The fraction of the garden planted with vegetables is 5/8.

3. Shade 7/8 of the rectangle. Answer: 7/8 Solution: The rectangle is divided into 8 equal parts. This means the whole is divided into 8 equal pieces. The fraction 7/8 means we need to shade 7 out of the 8 equal parts.
   Full step-by-step solution

   Step 1: The rectangle is divided into 8 equal parts. This means the whole is divided into 8 equal pieces. Step 2: The fraction 7/8 means we need to shade 7 out of the 8 equal parts. Step 3: Count 7 of the 8 parts and shade them in. Step 4: The shaded parts represent the fraction 7/8. The answer is 7/8.

4. A rectangular chocolate bar is divided into 12 equal squares. If you break off and eat 5 squares, what fraction of the whole chocolate bar remains? Answer: 7/12 Solution: The chocolate bar has 12 equal squares, so the whole bar represents 12/12. You eat 5 squares, so 5 squares are removed. To find how many squares remain: 12 - 5 = 7 squares.
   Full step-by-step solution

   Step 1: The chocolate bar has 12 equal squares, so the whole bar represents 12/12. Step 2: You eat 5 squares, so 5 squares are removed. Step 3: To find how many squares remain: 12 - 5 = 7 squares. Step 4: The fraction that remains is 7 out of 12 total squares, which is 7/12. The answer is 7/12.

5. What fraction of the rectangle is shaded? The rectangle is divided into 11 equal parts, and 4 parts are shaded. Answer: 4/11 Solution: Identify the total number of equal parts in the rectangle. The rectangle is divided into 11 equal parts, so the denominator is 11. Count the number of shaded parts.
   Full step-by-step solution

   Step 1: Identify the total number of equal parts in the rectangle. The rectangle is divided into 11 equal parts, so the denominator is 11. Step 2: Count the number of shaded parts. There are 4 shaded parts, so the numerator is 4. Step 3: Write the fraction as numerator over denominator: 4/11. Step 4: Check if the fraction can be simplified. 4 and 11 have no common factors other than 1, so 4/11 is already in simplest form. The answer is 4/11.

6. Maria is baking cookies for her school bake sale. She has a large rectangular pan of brownies that she cuts into 12 equal pieces. If she sells 7 pieces at the bake sale, what fraction of the whole pan of brownies did she sell? Answer: 7/12 Solution: The whole pan of brownies was cut into 12 equal pieces. This means the denominator (the bottom number of the fraction) is 12. Maria sold 7 of these pieces.
   Full step-by-step solution

   Step 1: The whole pan of brownies was cut into 12 equal pieces. This means the denominator (the bottom number of the fraction) is 12. Step 2: Maria sold 7 of these pieces. This means the numerator (the top number of the fraction) is 7. Step 3: The fraction of the whole pan that was sold is the number of pieces sold over the total number of pieces, which is 7/12. The answer is 7/12.

7. Shade 8/9 of the rectangle. Answer: 8/9 Solution: The rectangle is divided into 9 equal parts. The denominator (bottom number) of the fraction is 9, which matches the total number of parts. The numerator (top number) is 8.
   Full step-by-step solution

   Step 1: The rectangle is divided into 9 equal parts. The denominator (bottom number) of the fraction is 9, which matches the total number of parts. Step 2: The numerator (top number) is 8. This means we need to shade 8 out of the 9 equal parts. Step 3: Count 8 parts of the rectangle and shade them in. The remaining 1 part is left unshaded. Step 4: The shaded fraction is 8/9. The answer is 8/9.

8. Isabella shades 2/7 of a rectangle that is divided into 42 equal parts. How many parts does she shade? Answer: 12 Solution: The fraction 2/7 means 2 out of 7 equal parts of the whole rectangle. But the rectangle is divided into 42 equal parts, not 7.
   Full step-by-step solution

   Step 1: The fraction 2/7 means 2 out of 7 equal parts of the whole rectangle. But the rectangle is divided into 42 equal parts, not 7. Step 2: To find how many parts are in one seventh, divide the total number of parts (42) by the denominator (7): 42 ÷ 7 = 6. So each seventh of the rectangle has 6 parts. Step 3: Since Isabella shades 2/7, multiply the number of parts in one seventh (6) by the numerator (2): 6 × 2 = 12. Step 4: Isabella shades 12 parts. The answer is 12.

9. Noah shades 7/9 of a rectangle divided into 9 equal parts. What fraction of the rectangle is NOT shaded? Answer: 2/9 Solution: The rectangle is divided into 9 equal parts. The whole is 9/9. Noah shades 7/9 of the rectangle.
   Full step-by-step solution

   Step 1: The rectangle is divided into 9 equal parts. The whole is 9/9. Step 2: Noah shades 7/9 of the rectangle. Step 3: To find the unshaded part, subtract the shaded fraction from the whole: 9/9 - 7/9. Step 4: Subtract the numerators: 9 - 7 = 2. Keep the denominator the same: 9. Step 5: The unshaded fraction is 2/9. The answer is 2/9.