Decimal-Fraction Equivalence

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Answer Key & Explanations

Decimal-Fraction Equivalence · Grade 4 · Worksheet 2

1. Emma is baking cookies for a school bake sale. Her recipe calls for 0.25 cups of chocolate chips for one batch. If she wants to make 3 batches of cookies, how many cups of chocolate chips does she need in total? Express your answer as a decimal. Answer: 0.75 Solution: Identify what is needed for one batch: 0.25 cups Determine how many batches Emma is making: 3 batches Multiply the amount per batch by the number of batches: 0.25 × 3 Calculate: 0.25 × 3 = 0.75 Emma needs 0.75 cups of chocolate chips in total.
   Full step-by-step solution

   Step 1: Identify what is needed for one batch: 0.25 cups Step 2: Determine how many batches Emma is making: 3 batches Step 3: Multiply the amount per batch by the number of batches: 0.25 × 3 Step 4: Calculate: 0.25 × 3 = 0.75 Emma needs 0.75 cups of chocolate chips in total.

2. 0.75 = ?/100 Answer: 75 Solution: We are given: 0.75 = ?/100 Understand the problem. The equation says: 0.75 equals some number divided by 100. That means: 0.75 = ?
   Full step-by-step solution

   We are given: 0.75 = ?/100 Step 1: Understand the problem. The equation says: 0.75 equals some number divided by 100. That means: 0.75 = ? / 100 Step 2: To find the unknown number, multiply both sides of the equation by 100. This is because if ? / 100 = 0.75, then ? = 0.75 × 100. Step 3: Perform the multiplication. 0.75 × 100 = 75.0 Step 4: Write the result. So, ? = 75 Step 5: Check the answer. 75 / 100 = 0.75, which matches the original equation. Therefore, the correct answer is 75.

3. Maria is making lemonade for a school event. 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 for one pitcher: 0.25 liters Identify the total number of pitchers: 12 Multiply the amount per pitcher by the number of pitchers: 0.25 × 12 Calculate the multiplication: 0.25 × 12 = 3 Maria needs 3 liters of lemon juice in total.
   Full step-by-step solution

   Step 1: Identify the amount needed for one pitcher: 0.25 liters Step 2: Identify the total number of pitchers: 12 Step 3: Multiply the amount per pitcher by the number of pitchers: 0.25 × 12 Step 4: Calculate the multiplication: 0.25 × 12 = 3 Maria needs 3 liters of lemon juice in total.

4. 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

5. A rectangular park is divided into a 10 by 10 grid of equal squares. The city plants flowers in 36 of these squares. What decimal represents the fraction of the park that has flowers? Answer: 0.36 Solution: Find the total number of squares in the grid. The grid is 10 by 10, so multiply 10 × 10 = 100 squares. The number of squares with flowers is 36.
   Full step-by-step solution

   Step 1: Find the total number of squares in the grid. The grid is 10 by 10, so multiply 10 × 10 = 100 squares. Step 2: The number of squares with flowers is 36. So the fraction of the park with flowers is 36/100. Step 3: To write 36/100 as a decimal, remember that the denominator 100 means two decimal places. So 36/100 = 0.36. The answer is 0.36.

6. Noah is helping his grandmother measure ingredients for a special pancake recipe. The recipe calls for 0.8 cups of milk. Noah's grandmother says they need 8/10 of a cup of milk. Are these two amounts equivalent? Explain your answer by writing the decimal as a fraction in tenths. Answer: Yes, they are equivalent because 0.8 = 8/10. Solution: Look at the decimal 0.8. The 8 is in the tenths place, which means 8 tenths. Step 2: Write 0.8 as a fraction with a denominator of 10: 0.8 = 8/10.
   Full step-by-step solution

   Step 1: Look at the decimal 0.8. The 8 is in the tenths place, which means 8 tenths. Step 2: Write 0.8 as a fraction with a denominator of 10: 0.8 = 8/10. Step 3: The recipe also calls for 8/10 of a cup of milk. Step 4: Since 0.8 = 8/10, they are the same amount. The answer is: Yes, they are equivalent because 0.8 = 8/10.

7. Liam is measuring ribbon for a craft project. He needs 0.75 meters of blue ribbon and 3/4 meter of red ribbon. Are these two lengths equivalent? Answer: B. yes Solution: We need to check if 0.75 meters of blue ribbon is the same length as 3/4 meter of red ribbon. Convert the fraction 3/4 into a decimal. To do this, divide 3 by 4: 3 ÷ 4 = 0.75 Compare the two lengths.
   Full step-by-step solution

   Step 1: Understand the problem. We need to check if 0.75 meters of blue ribbon is the same length as 3/4 meter of red ribbon. Step 2: Convert the fraction 3/4 into a decimal. To do this, divide 3 by 4: 3 ÷ 4 = 0.75 Step 3: Compare the two lengths. Blue ribbon: 0.75 meters Red ribbon: 3/4 meter = 0.75 meters Step 4: Conclusion. Since both lengths are 0.75 meters, they are equivalent. Final answer: yes

8. Emma is measuring fabric for her sewing project. She needs 0.6 meters of blue fabric and 3/5 of a meter of green fabric. Are these two lengths equivalent? Answer: B. yes Solution: Convert the decimal 0.6 to a fraction. Since 0.6 is six tenths, it can be written as 6/10. Simplify the fraction 6/10 by dividing the numerator and denominator by their greatest common factor, which is 2.
   Full step-by-step solution

   Step 1: Convert the decimal 0.6 to a fraction. Since 0.6 is six tenths, it can be written as 6/10. Step 2: Simplify the fraction 6/10 by dividing the numerator and denominator by their greatest common factor, which is 2. 6 ÷ 2 = 3 and 10 ÷ 2 = 5, so 6/10 simplifies to 3/5. Step 3: Compare the simplified fraction (3/5) to the other fabric length (3/5). They are the same. Therefore, 0.6 meters is equal to 3/5 of a meter. The answer is yes.