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Dividing Fractions

Introduction

Dividing two fractions can be made easier by multiplying one fraction by the reciprocal of the other.

Terms

Fraction - Fractions are used when using numbers to express parts of whole.
Divisor/Denominator - the ‘bottom’ number of a fraction. It is the total number of parts.
Dividend/Numerator - the ‘top’ number of a fraction. It is the number of parts being taken from the whole.
Reciprocal - this is the multiplicative inverse of a fraction. Simply, it is the fraction flipped upside down (so the numerator becomes the denominator and vice versa).

Lesson

To divide 12 rac{1}{2} by 34 rac{3}{4}, we take the reciprocal of the fraction doing the dividing – i.e. 34 rac{3}{4}. The inverse of 34 rac{3}{4} is 43 rac{4}{3}. Then we multiply the first fraction by the reciprocal of the second: 1243=46=23 rac{1}{2} * rac{4}{3} = rac{4}{6} = rac{2}{3}.

Here is another example:

23÷14=2341=83dfrac{2}{3} div dfrac{1}{4} = dfrac{2}{3} * dfrac{4}{1} = dfrac{8}{3}

Examples

Dividing Fractions (Example #1)

25÷15\dfrac{2}{5} \div \dfrac{1}{5}
Dividing fractions is the same as multiplying by the reciprocal
The reciprocal of the second fraction is 51\dfrac{5}{1}
25\dfrac{2}{5} / 15\dfrac{1}{5} = 25\dfrac{2}{5} * 51\dfrac{5}{1}
2551\dfrac{2}{5} * \dfrac{5}{1}
(25)(51)\dfrac{(2 * 5)}{(5 * 1)}
(251)(511)\dfrac{(2 * 5^1)}{(5^1 * 1)}
22

Dividing Fractions (Example #2)

34÷45\dfrac{3}{4} \div \dfrac{4}{5}
Dividing fractions is the same as multiplying by the reciprocal
The reciprocal of the second fraction is 54\dfrac{5}{4}
34\dfrac{3}{4} / 45\dfrac{4}{5} = 34\dfrac{3}{4} * 54\dfrac{5}{4}
3454\dfrac{3}{4} * \dfrac{5}{4}
(35)(44)\dfrac{(3 * 5)}{(4 * 4)}
1516\dfrac{15}{16}

Dividing Fractions (Example #3)

910÷45\dfrac{9}{10} \div \dfrac{4}{5}
Dividing fractions is the same as multiplying by the reciprocal
The reciprocal of the second fraction is 54\dfrac{5}{4}
910\dfrac{9}{10} / 45\dfrac{4}{5} = 910\dfrac{9}{10} * 54\dfrac{5}{4}
91054\dfrac{9}{10} * \dfrac{5}{4}
(95)(104)\dfrac{(9 * 5)}{(10 * 4)}
(951)(1024)\dfrac{(9 * 5^1)}{(10^2 * 4)}
1181\dfrac{1}{8}

Dividing Fractions (Example #4)

12÷14\dfrac{1}{2} \div \dfrac{1}{4}
Dividing fractions is the same as multiplying by the reciprocal
The reciprocal of the second fraction is 41\dfrac{4}{1}
12\dfrac{1}{2} / 14\dfrac{1}{4} = 12\dfrac{1}{2} * 41\dfrac{4}{1}
1241\dfrac{1}{2} * \dfrac{4}{1}
(14)(21)\dfrac{(1 * 4)}{(2 * 1)}
(1142)(2111)\dfrac{(1^1 * 4^2)}{(2^1 * 1^1)}
22

Dividing Fractions Worksheets (PDF)

Dividing Fractions Worksheet 1

Dividing Fractions Worksheet 2

Dividing Fractions Worksheet 3

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