# How do you reduce 84/98 to its lowest terms?

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Jim G. Share
Dec 27, 2017

$\frac{6}{7}$

#### Explanation:

$\text{reduce the fraction by dividing the numerator/denominator}$
$\text{by the "color(blue)"highest common factor}$

$\text{in this case the highest common factor is 14}$

$\Rightarrow \frac{84}{98} = \frac{84 \div \textcolor{red}{14}}{98 \div \textcolor{red}{14}} = \frac{6}{7}$

$\text{this is often expressed using "color(blue)"cancelling}$

$\Rightarrow {\cancel{84}}^{6} / {\cancel{98}}^{7} = \frac{6}{7}$

$\text{if you do not see that 14 is the highest common factor}$

$\text{then begin by using smaller common factors}$

$\text{2 is a common factor of both numbers}$

$\Rightarrow {\cancel{84}}^{42} / {\cancel{98}}^{49} = \frac{42}{49}$

$\text{now repeat using the common factor of 7}$

$\Rightarrow {\cancel{42}}^{6} / {\cancel{49}}^{7} = \frac{6}{7} \leftarrow \textcolor{red}{\text{in simplest form}}$

$\text{A fraction is in "color(red)"simplest form"" when no other}$
$\text{factor but 1 divides into the numerator/denominator}$

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Dec 29, 2017

$\frac{6}{7}$

#### Explanation:

To reduce any fraction to it's lowest terms means to reduce it to a fraction which cannot be reduced further.

So, to find the lowest term for the fraction $\frac{84}{98}$, the following steps should be done:

Step1. Divide the numerator and denominator by a common factor which is $2$ (though it can be divided by $14$ as well if we take LCD of both numbers. But in case one forgets the concept of LCD, then also the question can be done stepwise)

which is, $\frac{{\cancel{84}}^{42}}{{\cancel{98}}_{49}}$ or, $\frac{42}{49}$

Step 2: Divide $\frac{42}{49}$ by a common factor again, which is $7$

So, ${\cancel{42}}^{6} / {\cancel{49}}_{7}$ = $\frac{6}{7}$

Remember, when no common factor other than $1$ is there for dividing the numerator and denominator, then that step will be the last step to find the lowest term.

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