Decimal-Fraction Equivalence

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Decimal-Fraction Equivalence · Grade 4 · Worksheet 3

1. Noah shades 61 squares in a 10 by 10 grid. What decimal represents the fraction of the grid that is not shaded? Answer: 0.39 Solution: The grid is 10 by 10, so total squares = 10 × 10 = 100 squares. Shaded squares = 61. Unshaded squares = 100 − 61 = 39 squares.
   Full step-by-step solution

   Step 1: The grid is 10 by 10, so total squares = 10 × 10 = 100 squares. Step 2: Shaded squares = 61. Unshaded squares = 100 − 61 = 39 squares. Step 3: The fraction of unshaded squares is 39/100. Step 4: To write 39/100 as a decimal, the numerator 39 goes in the hundredths place: 0.39. The answer is 0.39.

2. 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.

3. Lily is measuring ribbon for her craft project. She has a piece that is 0.75 meters long. Her friend Emma says this is the same as three-fourths of a meter. Is Emma correct? Answer: B. yes Solution: Lily has a ribbon 0.75 meters long. Emma says 0.75 meters is the same as three-fourths of a meter. We need to check if Emma is correct.
   Full step-by-step solution

   Step 1: Understand the problem. Lily has a ribbon 0.75 meters long. Emma says 0.75 meters is the same as three-fourths of a meter. We need to check if Emma is correct. Step 2: Recall the meaning of three-fourths of a meter. Three-fourths means 3 divided by 4, which is written as 3/4. Step 3: Convert the fraction 3/4 into a decimal. To do this, divide 3 by 4: 3 ÷ 4 = 0.75 Step 4: Compare the two values. Lily's ribbon length = 0.75 meters Three-fourths of a meter = 3/4 = 0.75 meters Both are equal. Step 5: Conclusion. Since 0.75 meters is exactly the same as three-fourths of a meter, Emma is correct. Answer: yes

4. Tane is training for a cross-country race. He ran 0.9 kilometers on Monday and 9/10 of a kilometer on Tuesday. Are the distances he ran on Monday and Tuesday equivalent? Explain your reasoning. Answer: Yes Solution: Write 0.9 as a fraction. The digit 9 is in the tenths place, so 0.9 = 9/10. The distance on Tuesday is 9/10 of a kilometer.
   Full step-by-step solution

   Step 1: Write 0.9 as a fraction. The digit 9 is in the tenths place, so 0.9 = 9/10. Step 2: The distance on Tuesday is 9/10 of a kilometer. Step 3: Compare 9/10 (Monday) and 9/10 (Tuesday). They are the same. Therefore, 0.9 and 9/10 are equivalent. The answer is yes.

5. Hana is helping her aunt measure ingredients for a large batch of fruit punch. The recipe calls for 0.6 liters of orange juice. Hana's aunt says they need 6/10 of a liter. Are these two amounts the same? Explain how you know. Answer: Yes, they are the same. Solution: Write 0.6 as a fraction. The digit 6 is in the tenths place, so 0.6 = 6/10. Compare 6/10 to the amount Hana's aunt mentioned, which is also 6/10.
   Full step-by-step solution

   Step 1: Write 0.6 as a fraction. The digit 6 is in the tenths place, so 0.6 = 6/10. Step 2: Compare 6/10 to the amount Hana's aunt mentioned, which is also 6/10. Step 3: Since both amounts are exactly 6/10 of a liter, they are the same. Answer: Yes, 0.6 and 6/10 are equivalent amounts.

6. Emma is making lemonade for a school picnic. 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 to find total liters needed: 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 to find total liters needed: 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. 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

8. A rectangular garden is divided into 10 equal sections along its length. If 3 sections are planted with carrots, what decimal represents the fraction of the garden that has carrots? Answer: 0.3 Solution: The garden is divided into 10 equal sections. 3 sections are planted with carrots. Write the fraction of the garden with carrots.
   Full step-by-step solution

   Step 1: Understand the problem. The garden is divided into 10 equal sections. 3 sections are planted with carrots. Step 2: Write the fraction of the garden with carrots. That is 3 sections out of 10 total sections, so the fraction is 3/10. Step 3: Convert the fraction to a decimal. The fraction 3/10 means 3 divided by 10. Step 4: Perform the division. 3 divided by 10 is 0.3. Step 5: Conclusion. The decimal that represents the fraction of the garden with carrots is 0.3.