Pre Algebra Period 2 (Tuesday)

Chapter 5-2 FRACTIONS = DECIMALS

How to change a fraction to a decimal
1. Divide (ALWAYS WORKS!)
EXAMPLE: 3/4 =
3 divided by 4 =
0.75

If the quotient starts repeating, then put a bar over the number(s) that repeat.

OR

2. Use equivalent fractions (SOMETIMES WORKS!)

Works if the denominator can be easily made into a power of 10
SAME EXAMPLE: 3/4
but this time you will multiply by 25/25 to get
75/100 = 0.75

3. MEMORY! Some equivalencies you should just know!
EXAMPLE: 1/2 = 0.5

IF IT'S A MIXED NUMBER, JUST ADD THE WHOLE NUMBER AT THE END!
EXAMPLE: 8 3/4
For the fraction: 3 divided by 4 = .75
Add the whole number:
8.75

IF THE MIXED NUMBER OR FRACTION IS NEGATIVE, SO IS THE DECIMAL!


Changing decimals to fractions.

CHANGING TERMINATING DECIMALS TO FRACTIONS:
EASY!!!
I learned this catchy phrase READ IT WRITE IT REDUCE!!
But we no longer say "reduce". We now say "simplify"

EXAMPLE:
Change .24 to a fraction
1) READ IT: 24 hundredths
2) WRITE IT: 24/100
3) SIMPLIFY: 24/100 = 6/25

EXAMPLE with whole number:
Change 7.24 to a fraction
The 7 is the whole number in the mixed number so you just put the 7 at the end
1) READ IT: 24 hundredths
2) WRITE IT: 24/100
3) SIMPLIFY: 24/100 = 6/25
4) (Now is the time to put the whole number back!!) 7 6/25


HOW TO CHANGE REPEATING DECIMALS TO FRACTIONS:
Repeating decimals (we'll use algebra!)
This involves algebra and takes some work, so MEMORIZE THE FOLLOWING:
1/3 = .333 . . . and 2/3 = .666. . .
Also showed the 1/9 family pattern which is the numerator with a bar
Another great time-saving pattern - 1/11 family: Multiply the numerator by 9 and put a bar over it

To get an exact answer when doing math operations with repeating decimals,
make all repeating decimals into their fraction equivalents and do the operations with fractions!

To change repeating decimals to fractions, follow these steps:
Let n = the repeating decimal
Multiply both sides by a power of 10 equal to the number of places that repeat under the bar
Subtract n on the left side and the repeating decimal equal to n on the right side
Solve as a one-step equation
Multiply both numerator and denominator by a power of 10 if necessary
to get the decimal out of the numerator.
Simplify

EXAMPLE: Restate .41666 . . . into a fraction
The repeating portion is .6 or one place so multiply both sides by 10
n = .41666 . . .

10n = 4.1666 . . .
- n = -.4166 . . .

9n = 3.75 so divide both sides by 9 to get

9n/9 = 3.75/9

n = 375/900

n = 5/12