Expressing Fraction in Lower/Higher Terms

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Expressing Fraction in Lower/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 $dfrac{15}{30}$ , we see that the common factors of 15 and 30 are 3, 5 and 15, of which 15 is the greatest. So dividing

$dfrac{30}{15} div dfrac{15}{15}$ gives us $dfrac{1}{2}$

Therefore, $dfrac{15}{30}$ can be reduced to $dfrac{1}{2}$ .

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 $dfrac{2}{3}$ 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

$dfrac{2}{3} * dfrac{4}{4} = dfrac{8}{12}$

Examples

Expressing Fraction in Higher Terms (Example #1)

\dfrac{2}{3}

with denominator of

36

To get an equivalent fraction with a denominator of

36

, we need to multiply the numerator and denominator by

12

\dfrac{2}{3} * \dfrac{12}{12} = \dfrac{24}{36}

Reducing Fractions (Example #1)

\dfrac{3}{9}

The largest number that divides

3\text{ and }9

3

, so the GCD =

3

\dfrac{3}{9}

can be reduced, since

3

is a factor of both

3

and

9

\dfrac{3}{9} \div \dfrac{3}{3} = \dfrac{1}{3}

The fraction is now in lowest terms

Expressing Fraction in Higher Terms (Example #2)

\dfrac{1}{2}