Decimal-Fraction Equivalence

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Answer Key & Explanations

Decimal-Fraction Equivalence · Grade 4 · Worksheet 2

1. A rectangular garden measures 12.5 meters long and 8.4 meters wide. What is the total area of the garden in square meters? Answer: 105 Solution: To find the area of a rectangle, we multiply its length by its width. Write down the given measurements. Length = 12.5 meters Width = 8.4 meters Write the area formula.
   Full step-by-step solution

   To find the area of a rectangle, we multiply its length by its width. Step 1: Write down the given measurements. Length = 12.5 meters Width = 8.4 meters Step 2: Write the area formula. Area = Length × Width Step 3: Substitute the given numbers into the formula. Area = 12.5 × 8.4 Step 4: Perform the multiplication. First, multiply the numbers as if they were whole numbers, ignoring the decimal points. 125 × 84 = ? Calculate 125 × 80 = 10,000 Calculate 125 × 4 = 500 Add them together: 10,000 + 500 = 10,500 So, 125 × 84 = 10,500 Step 5: Now, we must place the decimal point correctly. In our original numbers, 12.5 has one digit after the decimal, and 8.4 also has one digit after the decimal. This is a total of two digits after the decimal. Therefore, our final answer must have two digits after the decimal point. We take our result from the whole number multiplication, 10500, and put a decimal point so that two digits are on its right. This gives us 105.00 Step 6: Write the final answer. 105.00 is the same as 105. So, the total area of the garden is 105 square meters.

2. Emma is making lemonade for a school fair. The recipe calls for 0.25 liters of lemon juice per batch. If Emma wants to make 12 batches of lemonade, how many liters of lemon juice does she need in total? Answer: 3 Solution: Identify the amount needed for one batch: 0.25 liters Convert 0.25 to a fraction: 0.25 = 25/100 = 1/4 Multiply the amount per batch by the number of batches: 1/4 × 12 Calculate: 1/4 × 12 = 12/4 = 3 Emma needs 3 liters of lemon juice in total.
   Full step-by-step solution

   Step 1: Identify the amount needed for one batch: 0.25 liters Step 2: Convert 0.25 to a fraction: 0.25 = 25/100 = 1/4 Step 3: Multiply the amount per batch by the number of batches: 1/4 × 12 Step 4: Calculate: 1/4 × 12 = 12/4 = 3 Emma needs 3 liters of lemon juice in total.

3. 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 mark the board at 5/4 of a meter from one end. Are these two measurements the same length? Answer: B. yes Solution: Convert the decimal measurement to a fraction. 1.25 meters means 1 and 25/100 meters. Simplify 25/100 by dividing numerator and denominator by 25: 25 ÷ 25 = 1, 100 ÷ 25 = 4, so 25/100 = 1/4.
   Full step-by-step solution

   Step 1: Convert the decimal measurement to a fraction. 1.25 meters means 1 and 25/100 meters. Step 2: Simplify 25/100 by dividing numerator and denominator by 25: 25 ÷ 25 = 1, 100 ÷ 25 = 4, so 25/100 = 1/4. Step 3: This means 1.25 = 1 + 1/4 = 4/4 + 1/4 = 5/4. Step 4: Compare 5/4 meters (from the conversion) with 5/4 meters (from the instructions). Step 5: Since both measurements are 5/4 of a meter, they are the same length. The answer is yes.

4. 0.4 = ?/10 Answer: 4 Solution: The decimal 0.4 means 4 tenths To write this as a fraction with denominator 10, we need to find the numerator 0.4 = 4/10 Therefore, the missing numerator is 4 The answer is 4.
   Full step-by-step solution

   Step 1: The decimal 0.4 means 4 tenths Step 2: To write this as a fraction with denominator 10, we need to find the numerator Step 3: 0.4 = 4/10 Step 4: Therefore, the missing numerator is 4 The answer is 4.

5. 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

6. Emma is baking cookies for her school bake sale. The recipe calls for 0.25 cups of chocolate chips for one batch. If she wants to make 8 batches of cookies, how many cups of chocolate chips does she need in total? Express your answer as a decimal. Answer: 2.00 Solution: Identify what we know - one batch needs 0.25 cups of chocolate chips Emma is making 8 batches, so we need to multiply: 0.25 × 8 Multiply the numbers: 0.25 × 8 = 2.00 The answer is 2.00 cups of chocolate chips
   Full step-by-step solution

   Step 1: Identify what we know - one batch needs 0.25 cups of chocolate chips Step 2: Emma is making 8 batches, so we need to multiply: 0.25 × 8 Step 3: Multiply the numbers: 0.25 × 8 = 2.00 Step 4: The answer is 2.00 cups of chocolate chips

7. Liam is measuring ribbon for a craft project. He has a piece that is 0.75 meters long. His friend Emma says this is the same as 3/4 of a meter. Is Emma correct? Explain your answer. Answer: Yes, 0.75 is equivalent to 3/4 Solution: We need to check if 0.75 meters is the same as 3/4 of a meter. Recall that a fraction can be converted to a decimal by dividing the numerator by the denominator. Here, the fraction is 3/4.
   Full step-by-step solution

   Step 1: Understand the problem. We need to check if 0.75 meters is the same as 3/4 of a meter. Step 2: Recall that a fraction can be converted to a decimal by dividing the numerator by the denominator. Here, the fraction is 3/4. Step 3: Perform the division: 3 divided by 4 = 0.75. Step 4: Compare the results. 0.75 from the division matches the given length of 0.75 meters. Step 5: Conclusion. Since 3/4 = 0.75, Emma is correct.