Decimal-Fraction Equivalence

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Answer Key & Explanations

Decimal-Fraction Equivalence · Grade 4 · Worksheet 3

1. 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.

2. A rectangular vegetable garden is divided into 100 equal square sections. The gardener plants tomatoes in 28 squares, peppers in 15 squares, and carrots in 12 squares. What decimal represents the portion of the garden that remains unplanted? Answer: 0.45 Solution: Find the total number of planted squares: 28 + 15 + 12 = 55 squares Since there are 100 total squares, the planted portion is 55/100 Convert 55/100 to a decimal: 55/100 = 0.55 The unplanted portion is the whole garden minus the planted portion: 1.00 - 0.55 = 0.45 Therefore, 0.45 of the garden…
   Full step-by-step solution

   Step 1: Find the total number of planted squares: 28 + 15 + 12 = 55 squares Step 2: Since there are 100 total squares, the planted portion is 55/100 Step 3: Convert 55/100 to a decimal: 55/100 = 0.55 Step 4: The unplanted portion is the whole garden minus the planted portion: 1.00 - 0.55 = 0.45 Step 5: Therefore, 0.45 of the garden remains unplanted.

3. 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.

4. 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

5. 0.25 = ?/4 Answer: 1 Solution: We know 0.25 represents one quarter Since 1/4 means one quarter, and 0.25 also means one quarter Therefore, 0.25 = 1/4 This means the numerator is 1 The answer is 1
   Full step-by-step solution

   Step 1: We know 0.25 represents one quarter Step 2: Since 1/4 means one quarter, and 0.25 also means one quarter Step 3: Therefore, 0.25 = 1/4 Step 4: This means the numerator is 1 Step 5: The answer is 1

6. Emma is making lemonade for a school fundraiser. The recipe calls for 0.25 liters of lemon juice per pitcher. If she needs to make 12 pitchers of lemonade, how many liters of lemon juice does she need in total? Answer: 3 Solution: Identify the amount needed per pitcher: 0.25 liters Identify the number of pitchers: 12 Multiply the amount per pitcher by the number of pitchers: 0.25 × 12 Convert 0.25 to fraction form: 0.25 = 1/4 Multiply 1/4 × 12 = 12/4 Simplify 12/4 = 3 Emma needs 3 liters of lemon juice in total.
   Full step-by-step solution

   Step 1: Identify the amount needed per pitcher: 0.25 liters Step 2: Identify the number of pitchers: 12 Step 3: Multiply the amount per pitcher by the number of pitchers: 0.25 × 12 Step 4: Convert 0.25 to fraction form: 0.25 = 1/4 Step 5: Multiply 1/4 × 12 = 12/4 Step 6: Simplify 12/4 = 3 Emma needs 3 liters of lemon juice in total.

7. A farmer harvested 0.75 of his corn field. What fraction of the field did he harvest? Answer: 3/4 Solution: The farmer harvested 0.75 of his corn field. We need to write 0.75 as a fraction. Write the decimal as a fraction with denominator 1.
   Full step-by-step solution

   Step 1: Understand the problem. The farmer harvested 0.75 of his corn field. We need to write 0.75 as a fraction. Step 2: Write the decimal as a fraction with denominator 1. 0.75 = 0.75 / 1 Step 3: Multiply numerator and denominator by 100 to remove the decimal. 0.75 / 1 = (0.75 × 100) / (1 × 100) = 75 / 100 Step 4: Simplify the fraction 75/100. Find the greatest common divisor (GCD) of 75 and 100. The GCD is 25. Step 5: Divide numerator and denominator by 25. 75 ÷ 25 = 3 100 ÷ 25 = 4 So, 75/100 = 3/4 Step 6: Conclusion. The farmer harvested 3/4 of the field. Final answer: 3/4

8. 0.4 + 0.35 = ? Answer: 0.75 Solution: Write the problem vertically with decimals aligned: 0.40 + 0.35 Add the hundredths place: 0 + 5 = 5 Add the tenths place: 4 + 3 = 7 The result is 0.75 The answer is 0.75.
   Full step-by-step solution

   Step 1: Write the problem vertically with decimals aligned: 0.40 + 0.35 Step 2: Add the hundredths place: 0 + 5 = 5 Step 3: Add the tenths place: 4 + 3 = 7 Step 4: Bring down the decimal point Step 5: The result is 0.75 The answer is 0.75.

9. A rectangular garden is divided into 100 equal squares. If 35 squares are planted with carrots, what decimal represents the portion of the garden that has carrots? Answer: 0.35 Solution: The garden is divided into 100 equal squares. 35 of these squares are planted with carrots. We want the portion (fraction) of the garden with carrots, written as a decimal.
   Full step-by-step solution

   Step 1: Understand the problem. The garden is divided into 100 equal squares. 35 of these squares are planted with carrots. We want the portion (fraction) of the garden with carrots, written as a decimal. Step 2: Write the fraction of the garden with carrots. Number of carrot squares = 35 Total squares = 100 So the fraction is 35/100. Step 3: Convert the fraction to a decimal. 35 divided by 100 means moving the decimal point in 35 two places to the left. 35 is the same as 35.0 Moving the decimal two places left gives 0.35. Step 4: Interpret the result. 0.35 means 35 hundredths, which matches the fraction 35/100. Final Answer: 0.35