PRE Algebra Types of Fractions, Finding Common Denominators

Reduce Fractions, Convert Improper Fractions

Fractions have a numerator and a denominator:
1/5 - in this fraction 1 is the numerator and 5 is the denominator

Types of Fractions

Improper Fractions
6/6
7/6
The numerator is equal to or greater than the denominator

Proper Fractions
The numerator is less than the denominator
2/3
3/6

Fraction with a Number is a Mixed Fraction
2 1/3
Two is the number 1/3 is the fraction

In Algebra it is common to reduce fractions

To reduce a fraction: find the largest number that divides equally into the numerator and denominator

3/12 find the number that divides equally into both the 3 and the 12.
3 divides equally into both
3 ÷ 3 = 1
12 ÷ 3 = 4
Reduce the fraction
Answer is 1/4

There are also Rules for Divisibility that are used to reduce fractions

Practice Reduce Fraction To Lowest Terms

15/20
10/40
20/36
35/60


ANSWERS

15/20 = 3/4 5 divides equally into both numerator and denominator
10/40 = 1/4 10 divides equally into both numerator and denominator
20/36 = 5/9 4 divides equally into both numerator and denominator
35/60 = 7/12 5 divides equally into both numerator and denominator

Fractions can be changed to Higher Terms

1/5 to higher term of 15

5 is the denominator; we multiply this by 3 to get 15 in the denominator.
We multiply the numerator by the 3 also;

1/5 to higher term of 15 = 3/15
Multiply the denominator and numerator by the same number when changing to higher terms

Practice Changing to Higher Terms Fractions

1/5 to 25
1/4 to 48
2/3 to 30
1/6 to 36


ANSWERS

1/5 5 multiplied by 5 = 25, so we multiply both the denominator and numerator by 5
1/4 12 multiplied by 4 = 48, so we multiply both the denominator and numerator by 12
2/3 10 multiplied by 3 = 30, so we multiply both the denominator and numerator by 10
1/6 6 multiplied by 6 = 36, so we multiply both the denominator and numerator by 6

First, multiply the number by the denominator to get your Higher Term, then multiply that same number by the numerator.

Improper Fractions To A Mixed Number

Improper fractions can be changed to a mixed number:

13/4 is a improper fraction

To change to a mixed number, divide the denominator into the numerator, and place the remainder as a fraction.
4 divided into 13 = 3 (4x3 = 12) with 1 remainder,(12 from 13 is 1) answer is 3 1/4

Practice Changing Improper Fractions to Mixed Numbers

9/4
7/2
21/4


ANSWERS

9/4 = 2 1/4 - 4 divides into 9, two times with a remainder of 1, write the remainder as a fraction, answer is 2 1/4
7/2 = 3 1/2 - 2 divides into 7, three times with a remainder of 1, write the remainder as a fraction, answer is 3 1/2
21/4 = 5 1/4 - 4 divides into 21, 5 times, with a remainder of 1, write the remainder as a fraction, answer is 5 1/4

Improper Fractions To Mixed Number with Whole Numbers

Sometimes when changing a improper fraction to a mixed number there is no remainder, therefore, it is a whole number.

30/6 = 5
40/10 = 4
60/3 = 20

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