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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 1530dfrac{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

3015÷1515dfrac{30}{15} div dfrac{15}{15} gives us 12dfrac{1}{2}

Therefore, 1530dfrac{15}{30} can be reduced to 12dfrac{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 23dfrac{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

2344=812dfrac{2}{3} * dfrac{4}{4} = dfrac{8}{12}

Examples

Expressing Fraction in Higher Terms (Example #1)

23\dfrac{2}{3} with denominator of 3636
To get an equivalent fraction with a denominator of 3636, we need to multiply the numerator and denominator by 1212
231212=2436\dfrac{2}{3} * \dfrac{12}{12} = \dfrac{24}{36}

Reducing Fractions (Example #1)

39\dfrac{3}{9}
The largest number that divides 3 and 93\text{ and }9 is 33, so the GCD = 33
39\dfrac{3}{9} can be reduced, since 33 is a factor of both 33 and 99:
39÷33=13\dfrac{3}{9} \div \dfrac{3}{3} = \dfrac{1}{3}
The fraction is now in lowest terms

Expressing Fraction in Higher Terms (Example #2)

12\dfrac{1}{2} with denominator of 1212
To get an equivalent fraction with a denominator of 1212, we need to multiply the numerator and denominator by 66
1266=612\dfrac{1}{2} * \dfrac{6}{6} = \dfrac{6}{12}

Reducing Fractions (Example #1)

39\dfrac{3}{9}
The largest number that divides 3 and 93\text{ and }9 is 33, so the GCD = 33
39\dfrac{3}{9} can be reduced, since 33 is a factor of both 33 and 99:
39÷33=13\dfrac{3}{9} \div \dfrac{3}{3} = \dfrac{1}{3}
The fraction is now in lowest terms

Expressing Fraction in Lower/Higher Terms Worksheets (PDF)

Expressing Fractions in Lower or Higher Terms Worksheet 1

Expressing Fractions in Lower or Higher Terms Worksheet 2

Expressing Fractions in Lower or Higher Terms Worksheet 3