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Fractions Equal Parts

Grade 3 · Fractions · Worksheet 1

  1. Hana shades 2/3 of a rectangle that is divided into 12 equal parts. How many parts does she shade? Answer: ______________
  2. What fraction of the circle is shaded? Answer: ______________
  3. A rectangular vegetable garden is divided into 16 equal square plots. The gardener plants tomatoes in 5 plots, carrots in 4 plots, and lettuce in 3 plots. The remaining plots are left empty. What fraction of the garden is planted with vegetables? Answer: ______________
  4. Mason shades 2/7 of a rectangle. What fraction of the rectangle is NOT shaded? Answer: ______________
  5. What fraction of the rectangle is shaded? The rectangle is divided into 9 equal parts, and 4 parts are shaded. Answer: ______________
  6. Shade 2/7 of the rectangle. Answer: ______________
  7. 1/4 + 2/4 = ? Answer: ______________
  8. A rectangular garden is divided into 15 equal square sections. The gardener plants flowers in 8 sections and vegetables in 4 sections. The remaining sections are left for herbs. What fraction of the garden is planted with flowers? Answer: ______________
  9. Liam is helping his teacher set up chairs for the school concert. He needs to arrange 72 chairs into 8 equal rows. How many chairs should Liam put in each row? Answer: ______________
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Answer Key & Explanations

Fractions Equal Parts · Grade 3 · Worksheet 1

  1. Hana shades 2/3 of a rectangle that is divided into 12 equal parts. How many parts does she shade? Answer: 8 Solution: The rectangle is divided into 12 equal parts. The fraction 2/3 means 2 out of every 3 equal parts are shaded. To find how many parts that is, divide the total number of parts (12) by the denominator (3): 12 ÷ 3 = 4.
    Full step-by-step solution

    Step 1: The rectangle is divided into 12 equal parts. The fraction 2/3 means 2 out of every 3 equal parts are shaded. Step 2: To find how many parts that is, divide the total number of parts (12) by the denominator (3): 12 ÷ 3 = 4. This tells us each 'third' has 4 parts. Step 3: Since the numerator is 2, we take 2 groups of 4: 2 × 4 = 8. Step 4: Hana shades 8 parts of the rectangle. The answer is 8.

  2. What fraction of the circle is shaded? Answer: 5/12 Solution: Look at the circle. It is divided into 12 equal parts. Count the shaded parts.
    Full step-by-step solution

    Step 1: Look at the circle. It is divided into 12 equal parts. Step 2: Count the shaded parts. There are 5 shaded parts. Step 3: Write the fraction: shaded parts / total parts = 5/12. Step 4: The fraction 5/12 is already in simplest form because 5 and 12 have no common factors other than 1. The answer is 5/12.

  3. A rectangular vegetable garden is divided into 16 equal square plots. The gardener plants tomatoes in 5 plots, carrots in 4 plots, and lettuce in 3 plots. The remaining plots are left empty. What fraction of the garden is planted with vegetables? Answer: 3/4 Solution: Tomatoes: 5 plots Carrots: 4 plots Lettuce: 3 plots Total vegetable plots = 5 + 4 + 3 = 12 plots Total garden plots = 16 Vegetable fraction = 12/16 12/16 = (12 ÷ 4)/(16 ÷ 4) = 3/4 The answer is 3/4.
    Full step-by-step solution

    Step 1: Find the total number of vegetable plots Tomatoes: 5 plots Carrots: 4 plots Lettuce: 3 plots Total vegetable plots = 5 + 4 + 3 = 12 plots Step 2: Write the fraction of vegetable plots Total garden plots = 16 Vegetable fraction = 12/16 Step 3: Simplify the fraction 12/16 = (12 ÷ 4)/(16 ÷ 4) = 3/4 The answer is 3/4.

  4. Mason shades 2/7 of a rectangle. What fraction of the rectangle is NOT shaded? Answer: 5/7 Solution: The rectangle is divided into 7 equal parts. The whole rectangle is 7/7. Mason shades 2/7 of the rectangle.
    Full step-by-step solution

    Step 1: The rectangle is divided into 7 equal parts. The whole rectangle is 7/7. Step 2: Mason shades 2/7 of the rectangle. Step 3: To find the unshaded part, subtract the shaded part from the whole: 7/7 - 2/7 = (7 - 2)/7 = 5/7. Step 4: So, 5/7 of the rectangle is not shaded. The answer is 5/7.

  5. What fraction of the rectangle is shaded? The rectangle is divided into 9 equal parts, and 4 parts are shaded. Answer: 4/9 Solution: Look at the rectangle. It is divided into 9 equal parts. This means the denominator is 9.
    Full step-by-step solution

    Step 1: Look at the rectangle. It is divided into 9 equal parts. So the whole is divided into 9 equal pieces. This means the denominator is 9. Step 2: Count the shaded parts. There are 4 parts that are shaded. So the numerator is 4. Step 3: Write the fraction: numerator over denominator = 4/9. The answer is 4/9.

  6. Shade 2/7 of the rectangle. Answer: 2/7 Solution: The rectangle is divided into 7 equal parts. This means the whole is split into 7 pieces, so each piece is 1/7 of the whole. We need to shade 2/7 of the rectangle.
    Full step-by-step solution

    Step 1: The rectangle is divided into 7 equal parts. This means the whole is split into 7 pieces, so each piece is 1/7 of the whole. Step 2: We need to shade 2/7 of the rectangle. This means we need to shade 2 out of the 7 equal parts. Step 3: Count 2 parts and shade them in. The shaded area represents the fraction 2/7. The answer is 2/7.

  7. 1/4 + 2/4 = ? Answer: 3/4 Solution: Identify the problem. We are adding two fractions: 1/4 and 2/4. Check if the denominators are the same.
    Full step-by-step solution

    Step 1: Identify the problem. We are adding two fractions: 1/4 and 2/4. Step 2: Check if the denominators are the same. Both fractions have the same denominator, which is 4. When denominators are the same, we can add the fractions directly. Step 3: Add the numerators. Keep the common denominator (4) and add the numerators (1 + 2). So, 1/4 + 2/4 = (1 + 2)/4 Step 4: Perform the addition in the numerator. 1 + 2 = 3 This gives us 3/4. Step 5: Check if the fraction can be simplified. The fraction 3/4 is already in its simplest form because 3 and 4 have no common factors other than 1. Therefore, the final answer is 3/4.

  8. A rectangular garden is divided into 15 equal square sections. The gardener plants flowers in 8 sections and vegetables in 4 sections. The remaining sections are left for herbs. What fraction of the garden is planted with flowers? Answer: 8/15 Solution: The garden is divided into 15 equal sections, so the whole garden is represented by 15/15. Flowers are planted in 8 sections, so the fraction for flowers is 8 out of 15 total sections. Write this as a fraction: 8/15.
    Full step-by-step solution

    Step 1: The garden is divided into 15 equal sections, so the whole garden is represented by 15/15. Step 2: Flowers are planted in 8 sections, so the fraction for flowers is 8 out of 15 total sections. Step 3: Write this as a fraction: 8/15. The answer is 8/15.

  9. Liam is helping his teacher set up chairs for the school concert. He needs to arrange 72 chairs into 8 equal rows. How many chairs should Liam put in each row? Answer: 9 Solution: We are told that Liam has 72 chairs and must arrange them into 8 equal rows. To find how many chairs go in each row, we need to divide the total chairs by the number of rows. Write the division problem.
    Full step-by-step solution

    We are told that Liam has 72 chairs and must arrange them into 8 equal rows. To find how many chairs go in each row, we need to divide the total chairs by the number of rows. Step 1: Write the division problem. Total chairs = 72 Number of rows = 8 So, chairs per row = 72 ÷ 8. Step 2: Think about what 72 ÷ 8 means. We are splitting 72 into 8 equal groups. We can also think: 8 times what number equals 72? Step 3: Recall the multiplication fact for 8. 8 × 9 = 72. Since 8 × 9 = 72, then 72 ÷ 8 = 9. Step 4: Conclusion. Liam should put 9 chairs in each row. Final answer: 9