Pre Algebra (Period 2 & 4)

Fractions & Decimals 5-2 (cont'd)

Ordering or comparing fractions:(last method)

4: Make them into decimals because DECIMALS = FRACTION posers!

(or decimals are just fraction wannabes!)
Today, we will change fractions to decimals and decimals to fractions.

How to change a fraction to a decimal
1.
Divide (ALWAYS WORKS!)

EXAMPLE: 3/4 = 3 divided by 4 = .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: but this time you will multiply by 25/25 to get 75/100 = .75



3. MEMORY! Some equivalencies you should just know!
EXAMPLE: 1/2 = .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 TERMINATING DECIMALS TO FRACTIONS:
EASY!!!
Read it, Write it, 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) 7 6/25



HOW TO CHANGE REPEATING DECIMALS TO FRACTIONS-
FIrst know some by heart.. easier..
1/3 = .333333 = .3 with a vinculum over the 3... that's a bar.

1/9 family

Notice that you use the number found in the numerator, add a decimal point in front of it and add a bar above it.

1/11 family is a little different. You multiply the numerator by 9 ( making sure 1/11 has a two digit number after the decimal... and put a bar over the two digits.

To get exact answer when doing math operations with repeating decimals--> you must make decimals into their fraction equivalents and do operations with fractions

1/7 family really special!!!

Take a look and see if you remember the pattern we talked about in class today!!

To change repeating decimals to fractions follow these steps:
1) let n = the repeating decimal
2) multiply both sides by a power of 10 equal to the number of places under the vinculum (the bar)
3) rewrite n = the repeating decimal under #2
4) subtract n on the left side and the repeating decimal on the right
5) solve as a 1-step equation
6) multiply the numerator and the denominator by a power of 10 if necessary to get the decmial out of the numerator
7) simplify

We used

= 4.66666....

let n = .4166666...
multiply by a power of 10 in this case by 10¹ or just 10
10n =4.166666....
-1n = 0.416666....
9n = 3.75

then divide both sides by 9

9n/9 = 3.75/9

n = 3.75/9

need to multiply the numerator and the denominator by 100
375/900

simplifies to 5/12