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Mathematics/Prealgebra/Dividing_fractions.md
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@ -43,7 +43,8 @@ Note that we omit the numerator but that technically the answer would be $\frac{
We combine the foregoing (that it is easier to divide by fractional amounts using multiplication) with the concept of a [reciprocol](Reciprocals.md) to arrive at a definitive method for dividing two fractions.
It boils down to: _invert and multiply_:
If $\frac{a}{b}$ and $\frac{c}{d}$ are fractions then: $$\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \cdot \frac{d}{c}$$
If $\frac{a}{b}$ and $\frac{c}{d}$ are fractions then:
$$\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \cdot \frac{d}{c}$$
We invert the divisor (the second factor) and change the operator from division to multiplication.

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Mathematics/Prealgebra/Mixed_and_improper_fractions.md
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@ -63,7 +63,7 @@ $$
## Multiplying and dividing by mixed fractions
Now that we know how to convert mixed fractions into improper fractions, it is straight forward to multiply and divide with them. We convert the mixed fraction into an improper fraction and then divide and multiply as we would with a proper fraction.
### Demonstration
### Demonstration of multiplication
Calculate $-2\frac{1}{12} \cdot 2 \frac{4}{5}$:
@ -107,5 +107,9 @@ Calculate $-2\frac{1}{12} \cdot 2 \frac{4}{5}$:
\end{split}
$$
## Demonstration of division
Again we convert the mixed fraction into an improper fraction and then follow the requisite rule, in the case of division this is to [invert and multiply]('./../Dividing_fractions.md#formal-specification-of-how-to-divide-fractions').
Calculate
## Adding and subtracting mixed fractions