Farid is baking muffins. The recipe calls for (3)/(4) cup of sugar for a full batch. farid is making (1)/(2) of a batch. write an expression for the amount of sugar farid needs to make to make (1)/(2)of a batch of muffins.
The correct answer and explanation is:
To determine how much sugar Farid needs for 12\frac{1}{2} of a batch of muffins, we can calculate: Sugar needed=34×12\text{Sugar needed} = \frac{3}{4} \times \frac{1}{2}
Step-by-Step Calculation:
- Multiply the numerators: 3×1=33 \times 1 = 3.
- Multiply the denominators: 4×2=84 \times 2 = 8.
Thus, the expression simplifies to: 34×12=38\frac{3}{4} \times \frac{1}{2} = \frac{3}{8}
Farid needs 38\frac{3}{8} cup of sugar.
Explanation (300 words):
This problem involves fractional multiplication to adjust the amount of sugar required based on the portion of the recipe being used. Farid’s muffin recipe calls for 34\frac{3}{4} cup of sugar for a full batch. However, since Farid is making only 12\frac{1}{2} of a batch, he needs to proportionally reduce the amount of sugar.
To find the correct amount, we multiply the amount of sugar for a full batch (34\frac{3}{4}) by the fraction of the batch Farid is making (12\frac{1}{2}). When multiplying fractions, you multiply the numerators (the top numbers) to find the new numerator and multiply the denominators (the bottom numbers) to find the new denominator.
In this case:
- The numerator 33 represents the sugar needed for the full batch, and 11 represents the portion of the batch Farid is making.
- The denominator 44 corresponds to the full batch’s measurement, and 22 adjusts for the halving of the batch.
The product, 38\frac{3}{8}, indicates that Farid needs 33 parts out of 88, or three-eighths of a cup of sugar. This method works because fractions are inherently ratios that scale quantities proportionally.
In practical terms, Farid will measure 38\frac{3}{8} of a cup of sugar, ensuring his muffins have the correct sweetness while avoiding overuse or waste of ingredients. This proportional reasoning can be applied to other recipes or adjustments, demonstrating the utility of fraction multiplication in everyday scenarios.