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## Expressing Fraction In Lower Or Higher Terms

#### Introduction

Expressing fractions in lower terms is as simple as dividing the numerator and denominator by their greatest common factor. This is also known as reducing or simplifying the fraction. Similarly, expressing a fraction in higher terms simply means to multiply the numerator and denominator by the same number.

#### Terms

Fraction - Fractions are used when using numbers to express parts of whole.
Denominator - the ‘bottom’ number of a fraction. It is the total number of parts.
Numerator - the ‘top’ number of a fraction. It is the number of parts being taken from the whole.
Simplified Fraction -
Greatest Common Factor - A greatest common factor (or GCF) is the highest factor that is the same between two or more numbers.

## Lesson

Reducing a fraction – in order to reduce a fraction to its lowest terms, we must find the greatest common factor for the numerator and denominator. If we are given , we see that the common factors of 15 and 30 are 3, 5 and 15, of which 15 is the greatest. So dividing

gives us

Therefore, can be reduced to .

Expressing a Fraction in Higher Terms – in order to express a fraction in higher terms, we must determine what the numerator (or denominator) should be multiplied by to get the given number, and then multiply the denominator (or numerator) by the same number. For example, if we are told to express with a denominator of 12, we know that in order for the denominator to equal 12, we have to multiply the original denominator by 4. So we multiply the numerator by 4 as well to get

## Examples

#### Expressing Fraction in Higher Terms (Example #1)

Express as an equivalent fraction
with denominator of
To get an equivalent fraction with a denominator of , we need to multiply the numerator and denominator by

#### Reducing Fractions (Example #1)

Reduce the fraction to lowest terms
The largest number that divides is , so the GCD =
can be reduced, since is a factor of both and :
The fraction is now in lowest terms

#### Expressing Fraction in Higher Terms (Example #2)

Express as an equivalent fraction
with denominator of
To get an equivalent fraction with a denominator of , we need to multiply the numerator and denominator by

#### Reducing Fractions (Example #1)

Reduce the fraction to lowest terms
The largest number that divides is , so the GCD =
can be reduced, since is a factor of both and :
The fraction is now in lowest terms
More Examples