If it takes 5/6 yards of fabric to make a dress, then how many yards will it take to make 8 dresses? a, 6 2/3 b, 5 1/2 c, 6 2/4 d,3 2/3
The Correct Answer and Explanation is:
So, the correct answer is (a) 6 2/3 yards.
Explanation:
This type of problem involves multiplication of a whole number by a fraction, a concept often used in real-life applications such as tailoring, cooking, or construction. Here, we are told that it takes five-sixths of a yard to make one dress. To determine the total fabric required for eight dresses, we multiply the fabric needed for one dress by the total number of dresses: Total fabric=8×56\text{Total fabric} = 8 \times \frac{5}{6}Total fabric=8×65
When multiplying a whole number by a fraction, multiply the whole number by the numerator (top number of the fraction) and divide by the denominator (bottom number): 8×56=8×56=4068 \times \frac{5}{6} = \frac{8 \times 5}{6} = \frac{40}{6}8×65=68×5=640
Now, we simplify 406\frac{40}{6}640. Both numbers are divisible by 2: 406=203\frac{40}{6} = \frac{20}{3}640=320
To express this as a mixed number, divide 20 by 3:
- 3 goes into 20 six times (since 3 × 6 = 18)
- The remainder is 2
So, 203=623\frac{20}{3} = 6 \frac{2}{3}320=632
Therefore, it would take 6 2/3 yards of fabric to make 8 dresses. Understanding how to work with fractions and whole numbers together is essential in solving problems that involve repeated quantities, such as this one.
