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(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(2)/(10)`

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

`(2)/(10)=(1)/(5)`

So the length of the blue yarn is:

`8(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*8(1)/(5)`

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

`6*8(1)/(5)=6*8+6*(1)/(5)`

This gives the following result:

`=48+(6)/(5)`

Which can be expressed as a mixed number:

`48(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}(1)/(5)+48(6)/(5)`

we add the whole numbers:

8+48=56

and the fractions:

1/5 + 6/5 =7/5

And the result is:

`56(7)/(5)`

But we can still simplify the result, because:

`(7)/(5)=1(2)/(5)`

So the final result is:

`56(7)/(5)=56+1(2)/(5)=57(2)/(5)`

Answer:

`57(2)/(5)\text{ yards}`