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Equivalent Fractions

Grade 4 · Fractions · Worksheet 1

  1. 4/7 = __/56 Answer: ______________
  2. 4/7 = __/28 Answer: ______________
  3. 3/5 = __/20 Answer: ______________
  4. A recipe calls for 3/4 cup of flour. If you want to make 3 times the recipe, how many cups of flour do you need? Write your answer as a fraction. Answer: ______________
  5. A rectangular garden is divided into 4 equal sections. If 3 of these sections are planted with vegetables, what fraction of the garden is planted with vegetables? Write your answer in simplest form. Answer: ______________
  6. A rectangular field is 12 meters long and 8 meters wide. The farmer divides it into equal square plots by drawing lines every 2 meters along both the length and width. What fraction of the total field does one of these square plots represent?
    Answer: ______________
  7. 3/7 = __/84 Answer: ______________
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Answer Key & Explanations

Equivalent Fractions · Grade 4 · Worksheet 1

  1. 4/7 = __/56 Answer: 32 Solution: The original fraction is 4/7 and the new denominator is 56. Find what number you multiply the original denominator (7) by to get the new denominator (56). 7 × 8 = 56.
    Full step-by-step solution

    Step 1: The original fraction is 4/7 and the new denominator is 56. Step 2: Find what number you multiply the original denominator (7) by to get the new denominator (56). 7 × 8 = 56. Step 3: Multiply the original numerator (4) by the same number (8). 4 × 8 = 32. Step 4: The equivalent fraction is 32/56. The missing numerator is 32.

  2. 4/7 = __/28 Answer: 16 Solution: The original fraction is 4/7 and the new denominator is 28. Find what number you multiply the original denominator (7) by to get the new denominator (28). 7 × 4 = 28.
    Full step-by-step solution

    Step 1: The original fraction is 4/7 and the new denominator is 28. Step 2: Find what number you multiply the original denominator (7) by to get the new denominator (28). 7 × 4 = 28. Step 3: Multiply the original numerator (4) by the same number (4). 4 × 4 = 16. Step 4: The equivalent fraction is 16/28. The missing numerator is 16.

  3. 3/5 = __/20 Answer: 12 Solution: The original fraction is 3/5 and the new denominator is 20. Find what number you multiply the original denominator (5) by to get the new denominator (20). 5 × 4 = 20.
    Full step-by-step solution

    Step 1: The original fraction is 3/5 and the new denominator is 20. Step 2: Find what number you multiply the original denominator (5) by to get the new denominator (20). 5 × 4 = 20. Step 3: Multiply the original numerator (3) by the same number (4). 3 × 4 = 12. Step 4: The equivalent fraction is 12/20. The missing numerator is 12.

  4. A recipe calls for 3/4 cup of flour. If you want to make 3 times the recipe, how many cups of flour do you need? Write your answer as a fraction. Answer: 9/4 Solution: The recipe calls for 3/4 cup of flour. We want to make 3 times the recipe, so we need to multiply the amount of flour by 3. Write the multiplication.
    Full step-by-step solution

    Step 1: Understand the problem. The recipe calls for 3/4 cup of flour. We want to make 3 times the recipe, so we need to multiply the amount of flour by 3. Step 2: Write the multiplication. 3/4 cup × 3 Step 3: Rewrite 3 as a fraction. 3 is the same as 3/1, so: 3/4 × 3/1 Step 4: Multiply the fractions. Multiply the numerators: 3 × 3 = 9 Multiply the denominators: 4 × 1 = 4 So the result is 9/4. Step 5: Interpret the answer. 9/4 cups of flour is the amount needed for 3 times the recipe. Final answer: 9/4

  5. A rectangular garden is divided into 4 equal sections. If 3 of these sections are planted with vegetables, what fraction of the garden is planted with vegetables? Write your answer in simplest form. Answer: 3/4 Solution: The garden is divided into 4 equal sections. This means the whole garden is represented by 4 parts. Determine how many sections are planted with vegetables.
    Full step-by-step solution

    Step 1: Understand the problem. The garden is divided into 4 equal sections. This means the whole garden is represented by 4 parts. Step 2: Determine how many sections are planted with vegetables. The problem says 3 of these sections are planted with vegetables. Step 3: Write the fraction of the garden planted with vegetables. The fraction is the number of vegetable sections 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

  6. A rectangular field is 12 meters long and 8 meters wide. The farmer divides it into equal square plots by drawing lines every 2 meters along both the length and width. What fraction of the total field does one of these square plots represent? Answer: 1/24 Solution: Area = length × width = 12 m × 8 m = 96 square meters Determine how many squares fit along each dimension Along the length: 12 m ÷ 2 m = 6 squares Along the width: 8 m ÷ 2 m = 4 squares Total squares = 6 × 4 = 24 squares Each square represents 1 out of 24 total squares, so the fraction is 1/24…
    Full step-by-step solution

    Step 1: Find the total area of the rectangular field Area = length × width = 12 m × 8 m = 96 square meters Step 2: Determine how many squares fit along each dimension Along the length: 12 m ÷ 2 m = 6 squares Along the width: 8 m ÷ 2 m = 4 squares Step 3: Find the total number of squares Total squares = 6 × 4 = 24 squares Step 4: Calculate the fraction for one square Each square represents 1 out of 24 total squares, so the fraction is 1/24 The answer is 1/24.

  7. 3/7 = __/84 Answer: 36 Solution: The original fraction is 3/7 and the new denominator is 84. Find what number you multiply the original denominator (7) by to get the new denominator (84). 7 × 12 = 84.
    Full step-by-step solution

    Step 1: The original fraction is 3/7 and the new denominator is 84. Step 2: Find what number you multiply the original denominator (7) by to get the new denominator (84). 7 × 12 = 84. Step 3: Multiply the original numerator (3) by the same number (12). 3 × 12 = 36. Step 4: The equivalent fraction is 36/84. The missing numerator is 36.