# Fractions of Numbers Homework

Wednesday 12/17/08

### Figuring out the unit

Sometimes, I need to find out the unit given the value of some fraction of it. In order to solve this, I first draw a number line where the units are split up as required, but the units are not yet labeled. I then figure out the length of the spaces by dividing by the numerator. Finally, I use that to find the unit.

For example, I might want to find the full price of a pair of shoes given that it is on sale for \$36 and that is 4/5 of its regular price. I draw a number line where the units are divided into fifths, and label the mark that would be four fifths of a unit as "36". Since that is four spaces from zero, each space is 9 long. That, in turn, lets me figure out that the unit is 45.
1. Below, draw a number line to answer the question: If 40 is two thirds of some number, what is the number?

2. Below, draw a number line to answer the question: 3/5 × ? = 33

3. A coat costs \$24 when it is on sale for three quarters of the full price. What was the full price?

4. Below, draw a number line to answer the question: If 40 is five halves of some number, what is the number?

5. Below, draw a number line to answer the question: 8/3 × ? = 64

6. Gasoline now costs 7/4 of what it did a year ago. If it costs me \$42; to get a full tank of gas now, how much did it cost before?

7. Challenge: Draw two number lines to answer the question: If a sweater costs \$36 when it is on sale for four fifths of the full price, how much would it cost if it were on sale for two thirds of the full price?
(Hint: find the full price first)