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How do you divide $\frac{3}{4} \div \frac{5}{4}$ $\frac { 3} { 4} \div \frac { 5} { 4}$ ?

3 Answers

Apr 6, 2017

$\frac{3}{4} \div \frac{5}{4} = \frac{3}{5}$ $3/4div5/4=color(green)(3/5)$

Explanation:

Dividing is the same as multiplying by the inverse.

So
$XXX \frac{3}{4} \div \frac{5}{4}$ $color(white)("XXX")3/4div5/4$
is the same as
$XXX \frac{3}{4} \times \frac{4}{5}$ $color(white)("XXX")3/4xx4/5$

$XXX = \frac{3}{5}$ $color(white)("XXX")=3/5$

David Drayer · Sena Dzirasa

Apr 7, 2017

Use the complex fraction method. A fraction is a division problem so set one fraction divided by the second fraction.

Explanation:

The complex fraction method makes sense of the rule of invert and multiply.

$\frac{3}{4} \div \frac{5}{4}$ $3/4-:5/4$ can be written as

$\frac{\frac{3}{4}}{\frac{5}{4}}$ $(3/4) / ( 5/4)$ This is a complex fraction

To simplify the fraction multiply both the numerator ( top fraction) and the denominator ( bottom fraction) by the inverse of the denominator .

The inverse of $\frac{5}{4} = \frac{4}{5}$ $5/4 = 4/5$ Now multiply both fractions by $\frac{4}{5}$ $4/5$

$\frac{(\frac{3}{4}) \times (\frac{4}{5})}{(\frac{5}{4}) \times (\frac{4}{5})}$ ${ ( 3/4) xx (4/5)} / {(5/4) xx ( 4/5)}$

$(\frac{5}{4}) \times (\frac{4}{5}) = 1$ $( 5/4) xx ( 4/5) = 1$ This causes the bottom fraction to disappear. This leaves only the top fraction which gives.

$(\frac{3}{4}) \times (\frac{4}{5}) = (\frac{12}{20})$ $( 3/4) xx ( 4/5) = ( 12/20)$ Now factor out the common factor of 4

$\frac{4 \times 3}{4 \times 5}$ $( 4 xx 3)/ (4 xx 5)$ This leaves

$\frac{3}{5}$ $3/5$

After the bottom fraction divides out it leaves the invert and multiply method. Using the complex fraction makes mathematical sense of the method and avoids reliance on memory.

Apr 8, 2017

If the denominators are the same just divide the numerators.

$3 \div 5 \to \frac{3}{5}$ $3-:5->3/5$

Explanation:

A fraction consists of $\frac{count}{size indicators of what you are counting}$ $("count")/("size indicators of what you are counting")$

Using the allocated names we have:

$\frac{count}{size indicator} \to \frac{numerator}{denominator}$ $("count")/("size indicator")->("numerator")/("denominator")$

Consider whole numbers. For example 6 and 3

These can, and may, be written as $\frac{6}{1} and \frac{3}{1}$ $6/1 and 3/1$ They are rational numbers. It is not normally done but never the less it is correct.

Now consider $6 \div 3 \to \frac{6}{1} \div \frac{3}{1}$ $6-:3->6/1-:3/1$

$You just divide the counts as the 'size indicators' are the same$ $color(blue)("You just divide the counts as the 'size indicators' are the same")$

$6 \div 3 \to \frac{6}{1} \div \frac{3}{1} \to \frac{6}{3} = 2$ $6-:3->6/1-:3/1->6/3=2$

$You have been applying this principle for a long time without even realizing that you were.$ $color(magenta)("You have been applying this principle for a long time without even realizing that you were.")$

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