# Which is bigger? 6/9 or 4/6

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Jan 15, 2018

They are the same.

#### Explanation:

If we simplify the fractions we find that they are both equal to $\frac{2}{3}$. To simplify a fraction you just need to divide the numerator and the denominator by the same number. This works because you are essentially dividing the number by 1, meaning that the value is not changed.

For $\frac{6}{9}$, we can see that both the numerator and the denominator are divisible by 3.

$\frac{6 \div 3}{9 \div 3} = \frac{2}{3}$

We can do the same for $\frac{4}{6}$, except instead of dividing by $\frac{3}{3}$ we can divide by $\frac{2}{2}$, because both 4 and 6 are divisible by 2.

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

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Jan 14, 2018

See explanation.

#### Explanation:

To compare 2 fractions we have to find their (lowest) common denominator (i.e. the number both denominators can be changed to by multiplying or dividing numerator and denominator by the same number)

Here the fractions are $\frac{6}{9}$ and $\frac{4}{6}$the first fraction can be reduced by $3$:

## $\frac{6}{9} = \frac{2 \cdot \cancel{3}}{3 \cdot \cancel{3}} = \frac{2}{3}$

The second fraction can be reduced by $2$:

## $\frac{4}{6} = \frac{2 \cdot \cancel{2}}{3 \cdot \cancel{2}} = \frac{2}{3}$

Both numbers are reduced to the same fraction $\frac{2}{3}$, so they are equal:

## $\frac{6}{9} = \frac{4}{6} = \frac{2}{3}$

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