Question

a piece of blue yarn is 8 2/10 yards long. a piece of pink yarn is 6 times as long as the blue. what is the total length of the blue and pink yarn?

Answer 1

The blue yarn is

$8\frac{2}{10}\text{ yars long}$

And the pink yarn is 6 times as long.

Step 1. Simplify the number given for the yards of blue yarn.

We have a mixed number:

$8\frac{2}{10}$

But to simplify the operations, we can simplify 2/10 by dividing both numbers by 2:

$\frac{2}{10}=\frac{1}{5}$

So the length of the blue yarn is:

$8\frac{1}{5}\text{ yards}$

Step 2. Find the length of the pink yarn.

The pink yarn is 6 times as long as the blue one. Thus, to find the length of the pink yarn, we multiply the length of the blue yarn by 6:

$6\times8\frac{1}{5}$

We can expand this operation by multiplying 6 times 8, and 6 times 1/5:

$6\times8\frac{1}{5}=6\times8+6\times\frac{1}{5}$

This gives the following result:

$=48+\frac{6}{5}$

Which can be expressed as a mixed number:

$48\frac{6}{5}\text{ yards}$

That is the length of the pink yarn.

Step 3. Now we need to find the total length:

$\text{Total length = length blue + length pink}$

So we have that:

$\text{total length=8}\frac{1}{5}+48\frac{6}{5}$

we add the whole numbers:

8+48=56

and the fractions:

1/5 + 6/5 =7/5

And the result is:

$56\frac{7}{5}$

But we can still simplify the result, because:

$\frac{7}{5}=1\frac{2}{5}$

So the final result is:

$56\frac{7}{5}=56+1\frac{2}{5}=57\frac{2}{5}$

Answer:

$57\frac{2}{5}\text{ yards}$