# What is 1/2 -: 3/4?

Mar 11, 2018

$\textcolor{b l u e}{\frac{2}{3}}$

#### Explanation:

Note that a/b÷c/d=a/b×d/c

So, 1/2÷3/4 = 1/2×4/3

1/cancel2×cancel4^2/3

$\frac{2}{3} \approx 0.66$

In decimal $0. \overline{6}$

Mar 11, 2018

$\frac{2}{3}$

#### Explanation:

$= \frac{1}{2} / \frac{3}{4}$

$= \frac{1}{2} \cdot \frac{4}{3}$

$= 1 \cdot \frac{2}{3}$

$= \frac{2}{3}$.

Mar 11, 2018

$\frac{2}{3}$

#### Explanation:

Because you use KFC... Keep Flip Change.

You keep the first fraction the same

$\frac{1}{4}$

then you flip the other fraction

1/4 ÷ 4/3

Finally, you change the symbol to a times

$\frac{1}{4} \times \frac{4}{3}$

You then multiply the fraction getting

$\frac{4}{6}$

Simplified makes

$\frac{2}{3}$

Mar 12, 2018

A fraction is actually a division problem so to divide two fractions set it up as a division problem or complex fraction. This makes the most sense.

$\frac{1}{2} / \frac{3}{4} = \frac{\frac{1}{2}}{\frac{3}{4}}$

Now multiply both the top fraction and the bottom fraction by the inverse of the bottom fraction. This makes sense because multiply by $\frac{\frac{4}{3}}{\frac{4}{3}} = 1$ multiplying by one doesn't anything

Also multiplying by the inverse equals one

$\left(\frac{3}{4}\right) \times \left(\frac{4}{3}\right) = \frac{12}{12} = 1$

$\frac{\frac{1}{2} \times \frac{4}{3}}{\frac{3}{4} \times \frac{4}{3}} = \frac{\frac{1}{2} \times \frac{4}{3}}{1}$ Which leaves.

$\frac{1}{2} \times \frac{4}{3} = \frac{4}{6}$ Divide both top and bottom by 2

$\frac{\frac{4}{2}}{\frac{6}{2}} = \frac{2}{3}$

Dividing a fraction by a fraction makes sense and is easier to remember, even thought it takes longer.

Mar 12, 2018

$\frac{2}{3}$

#### Explanation:

Here is another approach to understand WHY the method of Multiply and Flip works to divide by a fraction, rather than just HOW to do it.

The fraction $\frac{3}{4}$ means 'three' quarters.

Quarters are obtained when a whole number is divided into four equal pieces, each is a quarter.

To find the number of quarters there are, multiply a number by $4$

In $1$ there will be $1 \times 4 = 4$ quarters
In $2$ there will be $2 \times 4 = 8$ quarters
In $3$ there will be $3 \times 4 = 12$ quarters

In $11$ there will be $11 \times 4 = 44$ quarters

In $\frac{1}{2}$ there will be $\frac{1}{2} \times 4 = 2$ quarters

However, when dividing by $\frac{3}{4}$ we are actually asking "How many groups of $\frac{3}{4}$ can be obtained ?"
(or how many times can $\frac{3}{4}$ be subtracted?)

That means, once you have the total number of quarters, divide them into groups of three's - each group will be 'Three' quarters.

You do this by dividing the total number of quarters by $3$

In $1$ there will be $1 \times 4 = 4$ quarters
$4 \div 3 = 1 \frac{1}{3}$, so there are $1 \frac{1}{3}$ groups of $\frac{3}{4}$
Hence $\frac{3}{4}$ divides into 1, a total of $1 \frac{1}{3}$ times

(ie. once with a bit left over.)
.

In $2$ there will be $2 \times 4 = 8$ quarters

$8 \div 3 = 2 \frac{2}{3}$ so there are $2 \frac{2}{3}$ groups of $\frac{3}{4}$
Hence $\frac{3}{4}$ divides into $2$, a total of $2 \frac{2}{3}$ times.

In $9$ there will be $9 \times 4 = 36$ quarters.

$36 \div 3 = 12$, so there are $12$ groups of $\frac{3}{4}$ in $9$
.

In each case we are multiplying by $4$ and dividing by $3$.

$\frac{4}{3}$ is the reciprocal of $\frac{3}{4}$

Hence the simple rule of Multiply and flip.

$\frac{1}{2} \div \frac{3}{4}$

$= \textcolor{b l u e}{\frac{1}{2} \times 4} \div 3 \text{ } \leftarrow$ change into quarters

$= 2 \textcolor{red}{\div 3} \text{ } \leftarrow$ divide into groups of $3$

$= \frac{2}{3}$
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Something like $6 \div \frac{3}{4}$ can be shown very nicely practically by taking $6$ squares, cutting them into quarters and then then making groups of $\frac{3}{4}$ ... there will be exactly $8$. which nicely demonstrates:

$6 \div \frac{3}{4}$

$= 6 \times 4 \div 3$

$= 6 \times \frac{4}{3}$

$= 8$

$\frac{3}{4}$ fits into $6$ a total of $8$ times.
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