Steply
Foundations · 25 problems, easy to harder
The steps for Calculate $2.40 for 4 ounces or $3.30 for 6 ounces. Every solution names its steps, so you always know what comes next.
Question: simplify the ratio 12 to 18.
Simplify means: smaller numbers, the same ratio.
12 and 18 can both be divided by 6.
We divide every part by 6.
The ratio stays the same.
12 divided by 6 is 2.
18 divided by 6 is 3.
Nothing else divides all of them.
So the simplest ratio is 2 to 3.
Question: simplify the ratio 6 to 9 to 15.
Simplify means: smaller numbers, the same ratio.
6, 9 and 15 can all be divided by 3.
We divide every part by 3.
The ratio stays the same.
6 divided by 3 is 2.
9 divided by 3 is 3.
15 divided by 3 is 5.
Nothing else divides all of them.
So the simplest ratio is 2 to 3 to 5.
Question: which is the better buy, A: $2.40 for 4 ounces, or B: $3.30 for 6 ounces?
The amounts are different, so we can't just look at the prices.
We find the price for 1 ounce in each deal.
We write each deal as a fraction.
The money goes on top.
The ounces go on the bottom.
We want 1 ounce on the bottom.
In A, we divide the top and the bottom by 4.
In B, we divide them by 6.
2.4 divided by 4 is 0.6.
3.3 divided by 6 is 0.55.
So A is 60 cents per ounce.
B is 55 cents per ounce.
55 cents is less than 60 cents.
Deal B costs less for each ounce.
So deal B is the better buy.
Let's look back.
First: write both as fractions.
Then: divide to get 1 at the bottom.
Last: compare.
Try each one, then open the answer. Stuck? Open the problem to watch every step.