Question

4 1/2 yards of cloth are needed to make a woman’s dress. 2 2/7 yards of cloth are needed to make a girl’s dress. How much more cloth is needed to make a woman’s dress than a girl’s dress?

Answer 1

Answer:

$2\frac{3}{14}$ yards

Step-by-step explanation:

We have been given that 4 1/2 yards of cloth are needed to make a woman’s dress. 2 2/7 yards of cloth are needed to make a girl’s dress.

To find the yards of more cloth needed to make a woman’s dress than a girl’s dress, we will subtract cloth needed for girl's dress from the cloth needed for woman's dress.

$4\frac{1}{2}-2\frac{2}{7}$

Convert mixed fraction into improper fraction:

$4\frac{1}{2}\Rightarrow \frac{4\times 2+1}{2}=\frac{8+1}{2}=\frac{9}{2}$

$2\frac{2}{7}\Rightarrow \frac{2\times 7+2}{7}=\frac{14+2}{7}=\frac{16}{7}$

$4\frac{1}{2}-2\frac{2}{7}=\frac{9}{2}-\frac{16}{7}$

Make a common denominator:

$\frac{9*7}{2*7}-\frac{16*2}{7*2}$

$\frac{63}{14}-\frac{32}{14}$

$\frac{63-32}{14}$

$\frac{31}{14}$

$2\frac{3}{14}$

Therefore, $2\frac{3}{14}$ yards more cloth is needed to make a woman’s dress than a girl’s dress.