Math 6H ( Period 5)

Equivalent Ratios in the Real World 1-6

There are 2 ways to determine if 2 ratios are equivalent:

1. Restate them both as unit rates. If they’re the same unit rates, they’re equivalent.

2. Use equivalent fractions if finding the unit rate is difficult (let’s say you need to go several decimal places in the division and don’t have a calculator)

Example using both methods:

You know that one store will charge you $2 for 10 photo prints and another has a sign offering 30 prints for $6.

Are these 2 stores charging EQUIVALENT AMOUNTS?

First way: Unit Rates

The unit rates are the same:

You can either find the prints per dollar or the unit price per print.

Both will show that the stores are equivalent.

Prints per dollar:

10 prints/$2 = 5 prints/$1 and 30 prints/$6 = 5 prints/$1 as well

Unit price:

$2/10 prints = $.20/print and $6/30 prints = $.20/print as well

Second way: Equivalent Fractions

The equivalent fraction approach asks you to see if you can find a common factor that the numerator and denominator were both either multiplied by or divided by to get to each other:

Can I get from 10/2 to 30/6 by multiplied both the numerator and denominator by the same number?

Yes I can!

I can multiply by 3 (scale forward by 3)

When I do this, it’s helpful to show a curved arrow with the x 3 on each arrow:

So by using equivalent fractions, the 2 stores are offering the same deal.