Write a problem that uses a fraction greater than 1.
The Correct Answer and Explanation is:
Problem:
Sarah is baking cookies for a school fundraiser. The recipe calls for 2 1/4 cups of sugar, but she wants to make 3 times the amount of cookies the recipe yields. How much sugar will Sarah need to use?
Answer:
Sarah will need 6 3/4 cups of sugar.
Explanation:
To solve this problem, we need to multiply the amount of sugar required in the original recipe by 3, since Sarah wants to make 3 times the amount of cookies.
Step 1: Convert the mixed number into an improper fraction.
The amount of sugar in the recipe is 2 1/4 cups. A mixed number consists of a whole number and a fraction. To convert 2 1/4 into an improper fraction, we follow these steps:
- Multiply the whole number (2) by the denominator of the fraction (4).
[
2 \times 4 = 8
] - Add the numerator of the fraction (1) to this product:
[
8 + 1 = 9
]
So, 2 1/4 is equivalent to the improper fraction 9/4.
Step 2: Multiply the improper fraction by 3.
Now, we need to multiply 9/4 by 3 to find the total amount of sugar needed for the larger batch of cookies.
[
\frac{9}{4} \times 3 = \frac{9 \times 3}{4} = \frac{27}{4}
]
Thus, the result is 27/4 cups.
Step 3: Convert the improper fraction back to a mixed number.
To convert 27/4 back to a mixed number, divide 27 by 4. The quotient is 6, and the remainder is 3. This means:
[
27 \div 4 = 6 \text{ remainder } 3
]
Thus, 27/4 is equal to 6 3/4.
Therefore, Sarah will need 6 3/4 cups of sugar to make 3 times the original batch of cookies.
Conclusion:
By converting the mixed number to an improper fraction and then performing the multiplication, we determined that Sarah needs 6 3/4 cups of sugar. This method helps when multiplying mixed numbers in real-life scenarios like cooking.