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Equivalent Fractions

Introduction

Equivalent fractions are fractions that are equal. In order to determine if one fraction is equal or equivalent to another, both fractions must first be simplified if needed.

Terms

- Fractions are used when using numbers to express parts of whole.
- a fraction expressed in its lowest terms.

Lesson

To determine if a fraction is equivalent to another, we need to compare the two fractions in their simplest form. So if we are given 14 rac{1}{4} and 28 rac{2}{8}, we can see that 14 rac{1}{4} is in its simplest form, but 28 rac{2}{8} can be further reduced to 14 rac{1}{4} by dividing the top and bottom by 2.

28÷22=14dfrac{2}{8} div dfrac{2}{2} = dfrac{1}{4}

Therefore 14 rac{1}{4} and 28 rac{2}{8} are equivalent fractions.

Similarly, if we are given 510 rac{5}{10} and 2130 rac{21}{30}, we first simplify both fractions.

510÷55=12dfrac{5}{10} div dfrac{5}{5} = dfrac{1}{2}

2130÷33=710dfrac{21}{30} div dfrac{3}{3} = dfrac{7}{10}

We can now see that 510 rac{5}{10} is NOT equivalent to 2130 rac{21}{30}, because 12 rac{1}{2} is not equivalent to 710 rac{7}{10}

To find the equivalent of a fraction when we are given either the numerator or denominator is similar to expressing a fraction in higher terms. If we are told to solve the following problem:

310=15?dfrac{3}{10} = dfrac{15}{?}

we can determine that in order for the new numerator to equal 15, the original numerator must be multiplied by 5. So we multiply the denominator by 5 as well, and get the answer

310=1550dfrac{3}{10} = dfrac{15}{50}

Examples

Equivalent Fractions (Example #1)

85\dfrac{8}{5} and 1610\dfrac{16}{10}
First, write each fraction in lowest terms
The greatest common divisor of 88 and 55 is 1, so 85\dfrac{8}{5} is already in lowest terms
1610\dfrac{16}{10} can be reduced, since 22 is a factor of both 1616 and 1010:
1610÷22=85\dfrac{16}{10} \div \dfrac{2}{2} = \dfrac{8}{5}
The fraction is now in lowest terms
85\dfrac{8}{5} is equal to 1610\dfrac{16}{10}

Make Equivalent Fraction (Example #1)

65=3x\dfrac{\text{6}}{\text{5}} = \dfrac{\text{3}}{\text{x}}
We have to multiply the first numerator (6) by 0 to get the second numerator (3)
To make an equivalent fraction, we need to multiply the denominator by 0 as well

Equivalent Fractions (Example #2)

34\dfrac{3}{4} and 58\dfrac{5}{8}
First, write each fraction in lowest terms
The greatest common divisor of 33 and 44 is 1, so 34\dfrac{3}{4} is already in lowest terms
The greatest common divisor of 55 and 88 is 1, so 58\dfrac{5}{8} is already in lowest terms
34\dfrac{3}{4} is not equal to 58\dfrac{5}{8}

Make Equivalent Fraction (Example #2)

34=3x\dfrac{\text{3}}{\text{4}} = \dfrac{\text{3}}{\text{x}}
We have to multiply the first numerator (3) by 1 to get the second numerator (3)
To make an equivalent fraction, we need to multiply the denominator by 1 as well

Equivalent Fractions Worksheets (PDF)

Equivalent Fractions Worksheet 1

Equivalent Fractions Worksheet 2

Equivalent Fractions Worksheet 3

Make Equivalent Fractions Worksheet 1

Make Equivalent Fractions Worksheet 2

Make Equivalent Fractions Worksheet 3

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