Question

Graph $\frac{5}{25}$ and $\frac{8}{16}$ as decimals on a number line. The smaller proportion .

• A. is $\frac{5}{25}$
• B. is $\frac{8}{16}$
• C. can't be determined

Answer 1

The correct option is A is $\frac{5}{25}$

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

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

We cancel the 5 from numerator and denominator.

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

To convert $\frac{1}{5}$ to a decimal number, we convert the denominator into 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 $\frac{8}{16}$ into a decimal number.

$\frac{8}{16}=\frac{8}{2\times 8}=\frac{1}{2}=0.5$

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

As both are tenths hence, we can compare them.

$0.2<0.5$

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 0.2 comes to the left of 0.5 on a number line.

$\therefore 0.2<0.5$ is indeed correct.

Hence, $\frac{5}{25}$ is smaller that $\frac{8}{16}$.