Question

Graph $\frac{25}{125}$ and $\frac{64}{128}$ as decimals on a number line. The larger proportion .

• A. is $\frac{64}{128}$
• B. is $\frac{25}{125}$
• C. can't be determined

Answer 1

The correct option is A is $\frac{64}{128}$

Let's convert the fractions into decimals before graphing them on a number line.

$\frac{25}{125}=\frac{25}{5\times 25}$

We cancel 25 from numerator and denominator.

$\frac{25}{5\times 25}=\frac{1}{5}$

To convert $\frac{1}{5}$ into a decimal number, we convert the denominator to 10 by multiplying 2 in numerator and denominator.

$\frac{1}{5}=\frac{1\times 2}{5\times 2}=\frac{2}{10}=0.2$

Now, let's convert $\frac{64}{128}$ into a decimal number.

$\frac{64}{128}=\frac{64}{2\times 64}=\frac{1}{2}=0.5$

Hence, the two proportions are reduced to 0.2 and 0.5.

As both are tenths hence, we can compare them.

$0.5>0.2$

Let's verify the same by plotting them on a number line.

As 0.2 and 0.5 are between 0 and 1, we divide the space into 10 equal intervals to plot the numbers.​​​​​​​


We observe here that 0.5 comes to the right of 0.2 on a number line.

$\therefore 0.5>0.2$ is indeed correct.

Hence, $\frac{64}{128}$ is larger that $\frac{25}{125}$.