Question

Where is ${\displaystyle \frac{2}{3}}$ on a number line?

Answer 1

Hint: Here, in the given question we need to represent ${\displaystyle \frac{2}{3}}$ on a number line. As we can see ${\displaystyle \frac{2}{3}}$ is a fraction number, we can represent it on the fraction number line and also on the normal number line. Let us represent ${\displaystyle \frac{2}{3}}$ on a fraction number line. Note that ${\displaystyle \frac{2}{3}}$ lies 0 and 1.

Complete step-by-step answer:
Steps to make a fraction number line of ${\displaystyle \frac{2}{3}}$
Step 1: Draw a number line with whole numbers.
Step 2: Look for the denominator of the fraction number ${\displaystyle \frac{2}{3}}$ we want to show on the number line. Here, the denominator is $3$.
Step 3: Mark as many points between each whole division as the numerator, i.e. divide each unit division into $3$ parts.
Step 4: Write the fractions with the denominator $3$.
Step 5: Write the numerators as $0,1,2,3,4,$ and so on.
Now, you can see ${\displaystyle \frac{2}{3}}$ on the number line, mark the point where it lies. Here, you can also see that one unit has three equal divisions.

As you can see ${\displaystyle \frac{2}{3}}$ lies between $0$ and $1$ on the fractional number line.

Note: There’s another method also to represent any fraction number on the number line. We can convert the fraction number into a decimal number and represent it on the normal number line. Let us represent ${\displaystyle \frac{2}{3}}$ on the normal number line. The fraction is converted into decimal by dividing the numerator with the denominator. In this case $2$ is divided by $3$ which gives the result as $0.67$. As we can see $0.67$ is less than $1$ and greater than $0$, therefore it will lie between $0$ and $1$.