Math Skills: Fractions

Lesson 8: Lesson Eight--Applications and Final Test

Section Two: More Applications

Some of these can be done in your head, but most require a piece of paper or calculator--however, given smaller numbers, they also could all be done in your head.

Supposing Carla makes $52.80 in 8 hours. How much does she make in 20 hours? (This is Lesson 17 exercise, problem 3, p. 120 in Cambridge GED)

Remember to set it up dollars/hours = dollars/hours.

What is missing in the second proportion is dollars, so set it up:

$52.80/8 = x/20. Multiplying the two outside terms together, then the two inside terms together, we get 8x = $1056, and dividing by 8 we get $132.00

The ratio of the number of problems Shirley got right to the number she got wrong is 7:2. There were 36 problems on the test. How many problems did she get right?

Review Lesson 18, Example 1 before doing this problem.

The easiest was however to figure this out is to figure out how the proportion will be set up. To figure out number of questions correct out of 36 total, you have to set it up correct/total = correct/total.

This means the first proportion must take into account the "total" of the ratio 7:2, which means you add 7 + 2 = 9, to get 7/9 = x/36. (You do this to find the part of the ratio that corresponds to the total).

Then, multiplying outside terms together, then inside terms together, you get:

9x = 252, so x = 28. She got 28 questions correct out of 36.

This problem was in Cambridge on p. 121, Lesson 18 exercise, problem # 1.

Some problems require you to know that: "of" means multiply; "per" means divide.

Supposing Denise drove 209 miles on 9 1/2 gallons of gasoline. What is her average distance she drove on one gallon? (in other words, what's her miles per gallon or mpg?)

Since it's "miles PER gallon", this is a division problem. 209 divided by 9 1/2 is actually (converting 9 1/2 to 19/2) 209/1 divided by 19/2 = 209/1 x 2/19 = 418/19 = 22, so she gets 22 miles per gallon. You can also set this up as a proportion.

This was Lesson 20 exercise, problem 2, p. 124 of Cambridge.

One application consumers are likely to need to know is how to figure out the sale price, or the original price of a sale item. Usually you'd need to know how to manipulate percents for this, but remember that all percents can be expressed as fractions. For instance an item "25% off" means "1/4 off" as well.

Let's do problem 3, p. 124, Lesson 20 exercise.

Joe bought a jacket originally selling for $72 for 1/4 off of the original price. Find the sale price of the jacket.

You are actually finding 1/4 "of" $72, and since "of" means multiply, it's 1/4 x 72 (or 1/4 x 72/1), and 1/4 x 72 = 18. But $18 is NOT the answer! Since the jacket is reduced by $18, you subtract the original price, $72, minus the price reduction, $18, so $72 - $18 = $54. The sale price is $54!

If you are given the sale price and want to find the original price, know by what percent or fraction the item was reduced, then ADD that reduction price to the sale price to get the original price.

One last problem, relating to salary and taxes. Carlos's employer deducts 1/5 of his gross salary for taxes and 1/10 of the gross salary for a savings fund. If the gross salary is $2400 per month, how much is deducted for taxes (in other words, ignore the 1/10 for savings fund)?

This is another "of" problem. You want to find 1/5 "of" $2400. So 1/5 x 2400/1 = 2400/5 = $480 deducted for taxes each month.

On to the test!

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