Decimal-Fraction Equivalence

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Answer Key & Explanations

Decimal-Fraction Equivalence · Grade 4 · Worksheet 1

1. A rectangular field is divided into a 10 by 10 grid of equal squares. The farmer plants corn in 47 of these squares. What decimal represents the portion of the field planted with corn? Answer: 0.47 Solution: Find the total number of squares in the grid. Since it's a 10 by 10 grid, there are 10 × 10 = 100 total squares. Determine the fraction of squares planted with corn.
   Full step-by-step solution

   Step 1: Find the total number of squares in the grid. Since it's a 10 by 10 grid, there are 10 × 10 = 100 total squares. Step 2: Determine the fraction of squares planted with corn. This is 47 out of 100, or 47/100. Step 3: Convert the fraction to a decimal. Since the denominator is 100, the decimal is 0.47. The answer is 0.47.

2. Noah is building a wooden frame for a school project. He needs a piece of wood that is 0.25 meters long, but his ruler only shows centimeters. How many centimeters long does the piece of wood need to be? Answer: 25 Solution: We know that 1 meter is equal to 100 centimeters. Noah needs 0.25 meters of wood. To find the length in centimeters, multiply the number of meters by the number of centimeters in one meter: 0.25 * 100.
   Full step-by-step solution

   Step 1: We know that 1 meter is equal to 100 centimeters. Step 2: Noah needs 0.25 meters of wood. Step 3: To find the length in centimeters, multiply the number of meters by the number of centimeters in one meter: 0.25 * 100. Step 4: 0.25 * 100 = 25. The piece of wood needs to be 25 centimeters long.

3. A rectangular field is divided into 100 equal squares. The farmer plants corn in 28 squares and beans in 35 squares. What decimal represents the portion of the field that is planted with either corn or beans? Answer: 0.63 Solution: Find the total number of squares planted with corn or beans: 28 + 35 = 63 The field has 100 equal squares total, so the fraction planted is 63/100 Convert the fraction to a decimal: 63/100 = 0.63 The answer is 0.63.
   Full step-by-step solution

   Step 1: Find the total number of squares planted with corn or beans: 28 + 35 = 63 Step 2: The field has 100 equal squares total, so the fraction planted is 63/100 Step 3: Convert the fraction to a decimal: 63/100 = 0.63 The answer is 0.63.

4. Lily is baking cookies and needs 0.75 cups of sugar for one batch. If she wants to make 4 batches of cookies, how many cups of sugar does she need in total? Answer: 3 Solution: Lily needs 0.75 cups of sugar for one batch of cookies. She wants to make 4 batches. We need to find the total sugar required.
   Full step-by-step solution

   Step 1: Understand the problem. Lily needs 0.75 cups of sugar for one batch of cookies. She wants to make 4 batches. We need to find the total sugar required. Step 2: Set up the calculation. Total sugar = (sugar per batch) × (number of batches) Total sugar = 0.75 × 4 Step 3: Multiply. 0.75 is the same as 3/4. So 0.75 × 4 = (3/4) × 4 Step 4: Simplify. (3/4) × 4 = 3 × (4/4) = 3 × 1 = 3 Step 5: Conclusion. Lily needs 3 cups of sugar in total for 4 batches. Answer: 3

5. Noah is helping his dad build a bookshelf. They need to cut a wooden board that is 1.25 meters long. The instructions say to use a board that is 5/4 meters. Are these two measurements equivalent? Answer: B. yes Solution: Convert the fraction 5/4 to a decimal Divide 5 by 4: 5 ÷ 4 = 1.25 Compare the decimal values: 1.25 meters (given) equals 1.25 meters (from 5/4) Since both measurements are 1.25 meters, they are equivalent The answer is yes.
   Full step-by-step solution

   Step 1: Convert the fraction 5/4 to a decimal Step 2: Divide 5 by 4: 5 ÷ 4 = 1.25 Step 3: Compare the decimal values: 1.25 meters (given) equals 1.25 meters (from 5/4) Step 4: Since both measurements are 1.25 meters, they are equivalent The answer is yes.

6. A rectangular garden is divided into 100 equal squares. If 28 squares are planted with tomatoes and 15 squares are planted with peppers, what decimal represents the portion of the garden that has vegetables? Answer: 0.43 Solution: Find the total number of squares planted with vegetables Tomatoes: 28 squares Peppers: 15 squares Total vegetable squares = 28 + 15 = 43 squares The garden has 100 equal squares Fraction with vegetables = 43/100 43/100 = 0.43 The answer is 0.43.
   Full step-by-step solution

   Step 1: Find the total number of squares planted with vegetables Tomatoes: 28 squares Peppers: 15 squares Total vegetable squares = 28 + 15 = 43 squares Step 2: Write this as a fraction of the whole garden The garden has 100 equal squares Fraction with vegetables = 43/100 Step 3: Convert the fraction to decimal form 43/100 = 0.43 The answer is 0.43.

7. 0.6 = ?/10 Answer: 6 Solution: The decimal 0.6 means 6 tenths In fraction form, tenths are written with denominator 10 So 0.6 = 6/10 The numerator is 6 The answer is 6.
   Full step-by-step solution

   Step 1: The decimal 0.6 means 6 tenths Step 2: In fraction form, tenths are written with denominator 10 Step 3: So 0.6 = 6/10 Step 4: The numerator is 6 The answer is 6.

8. 0.75 = ?/4 Answer: 3 Solution: We are given: 0.75 = ?/4 Understand the equation. The problem says 0.75 equals some number divided by 4. So we can write: 0.75 = x / 4, where x is the unknown number.
   Full step-by-step solution

   We are given: 0.75 = ?/4 Step 1: Understand the equation. The problem says 0.75 equals some number divided by 4. So we can write: 0.75 = x / 4, where x is the unknown number. Step 2: Eliminate the fraction. To solve for x, multiply both sides of the equation by 4: 0.75 * 4 = (x / 4) * 4 Step 3: Simplify. On the right side, (x / 4) * 4 = x. On the left side, 0.75 * 4 = 3. So we have: 3 = x Step 4: Conclusion. Therefore, the unknown number is 3. Final check: 3/4 = 0.75, which matches the given 0.75. Answer: 3

9. Liam is measuring ribbon for a craft project. He has a piece that is 0.75 meters long. He needs to know what fraction of a meter this is to compare it with another piece that is 3/4 of a meter. What fraction is equivalent to 0.75? Answer: 3/4 Solution: Write the decimal as a fraction with denominator 1. 0.75 = 0.75 / 1 Multiply the numerator and denominator by 100 to eliminate the decimal places.
   Full step-by-step solution

   Step 1: Write the decimal as a fraction with denominator 1. 0.75 = 0.75 / 1 Step 2: Multiply the numerator and denominator by 100 to eliminate the decimal places. (0.75 × 100) / (1 × 100) = 75 / 100 Step 3: Simplify the fraction by finding the greatest common divisor (GCD) of 75 and 100. The GCD of 75 and 100 is 25. Step 4: Divide both the numerator and denominator by the GCD. 75 ÷ 25 = 3 100 ÷ 25 = 4 Step 5: Write the simplified fraction. The simplified fraction is 3/4. Conclusion: 0.75 is equivalent to 3/4.