Question

Steven is knitting a scarf and a hat He needs 3/4 of a bundle of yarn to make a scarf He needs half that to make a hat How much yarn does he need to make a hat? How do you know?

Answer 1

The correct answer is:

3/8 of a bundle.

Step-by-step explanation:

He needs 3/4 of a bundle to make a scarf. Since it takes 1/2 of that to make a hat,

3/4(1/2) = (3*1)/(4*2) = 3/8 of a bundle is what is needed to make a hat.

Answer 2

Hey. Let me help you on this one.

If we take a closer look at the problem, Steven wants to make two different clothing pieces - a hat and a scarf using the same type of yarn bundle (amount requires doesn't matter). Each piece requires a different amount of yarn. For example, a hat needs 3/4 of the bundle, while a scarf is supposed to be knitted with a half of the yarn.

Let's start off by converting everything to a fraction with the same denominator - number below numerator.

Hat -
`(3)/(4)`
Scarf - one half, or
`(1)/(2)`

As we can see, our denominators are different. Let's multiply
`(1)/(2)` by 2 in order for us to raise the denominator to four, since two times two is four.

We must not forget to multiply the numerator by two as well - whatever is multiplied in a fraction, it's to be multiplied in both parts.


`(1)/(2) *2= (2)/(4)`

Awesome. Now, that we know both values needed for the clothing pieces, let's add them together.


`(3)/(4) + (2)/(4) = (5)/(4)`

When adding fractions, we don't touch denominators. Remember this golden rule!

Five fourths can also be transformed into one whole number, and one fourth.
`1 (1)/(4)`.

That's it! We solved this problem. I am attaching a helpful picture for you to study this material.

Answer: 1 1/4 of yarn bundles are needed.