Problem solving rational number

Question

Matt spent 3/10 of his allowance on projects, 2/5 on snacks, and 2/3 of the remainder on books.

1.What fraction of his allowance was spent on books? 

2.If he saved the rest, what fraction of his allowance did he save?

Answer 1

Hello,

With word problems, we always want to start with what we know.

3/10 on projects

2/5 on snacks

Then the question asks about the remainder, but we don't know that until we find out how much he spent. That's easy, they told us he spent:

3/10 + 2/5

To add these fractions, we need to get a common denominator. So, let's multiply 2/5 by 2 to get common denominators and we have:

3/10 + 4/10 <- now we have a common denominator (10)

What's 3/10 + 4/10? Well, that just 3 + 4 tenths. 3 + 4 =7 so we know he spent 7/10 of his allowance.

Now for the remainder.

If he spent 7/10, how much is left? You can probably do it in your head, but let's show it for completeness:

10/10 (all allowance) - 7/10 spent = 3/10 is the remainder

What's next? Well, the told us he spent 2/3 of the remainder on books.

How much is 2/3 of the remainder? Easy, it's 2/3 x 3/10. When you see the word "of" used in fractions like this, you know you need to multiply. "2/3 of 3/10" means "2/3 X 3/10".

So,

2/3 of 3/10 = 2/3 x 3/10 = 6/30

Simplifying 6/30, we have:

3/15

That's the answer to the first question. He spent 3/15 of his allowance on books.

Now question #2 is easy because we know everything we need to answer it.

"What fraction did he save?"

Just add up how much he spent and subtract that from 1.

He spent 7/10 on projects and snacks (they told us)

He spent 3/15 on books (we just calculated that)

How much is left over?

Total spent: 7/10 + 3/15 = 21/30 + 6/30 = 27/30

Left over for savings: 1 - 27/30, or 30/30 - 27/30 = 3/30, which simplifies to

1/10

He saved 1/10 of his allowance.

Hope that helps!