Question

Question 1(c) :

Show $\frac{2}{6},\frac{4}{6},\frac{8}{6}$ and $\frac{6}{6}$ on the number line. Put appropriate signs between the fractions given:

$\frac{5}{6}\square \frac{2}{6},\frac{3}{6}\square 0,\frac{1}{6}\square \frac{6}{6},\frac{8}{6}\square \frac{5}{6}$

Answer 1

The given fractions are $\frac{2}{6},\frac{4}{6},\frac{8}{6}$ and $\frac{6}{6}$.

The denominator of all the fractions is 6. All the fractions above are less than or equal to 1 except $\frac{8}{6}$, which is less than 2.

So, on the number line, we divide the line segment between 0 and 1, 1 and 2 into 6 equal parts.

The fractions $\frac{2}{6},\frac{4}{6},\frac{8}{6}$ and $\frac{6}{6}$ are shown on the number line below.

Now, the given fractions are like fractions because they have the same denominator.

When we compare like fractions, the fraction whose numerator is greater has greater value.

Now, 5 > 2, 3 > 0, 1 < 6 and 8 > 5. So, the sign between the fractions $\frac{5}{6}\square \frac{2}{6},\frac{3}{6}\square 0,\frac{1}{6}\square \frac{6}{6},\frac{8}{6}\square \frac{5}{6}$ will also be the same.

The appropriate sign between the fractions are given below.

$\frac{5}{6}\begin{array}{c}>\end{array}\frac{2}{6}\frac{1}{6}\begin{array}{c}<\end{array}\frac{6}{6}\frac{3}{6}\begin{array}{c}>\end{array}\frac{0}{6}\frac{8}{6}\begin{array}{c}>\end{array}\frac{5}{6}$