Question

Draw and explain how you can use a number line to rename a fraction greater then 1 as a mixed number

Answer 1

Solution:

Consider a Mixed fraction greater than 1, $1\frac{a}{b}$ where , b>a.

To represent it on the number line

1. Divide or mark b-1 points between 1 and 2.

2. So, if you have to mark , $1 \frac{a}{b}$, start writing on number line as $1 \frac{1}{b}$, $1 \frac{2}{b}$,$1 \frac{3}{b}$,..and finally mark $1 \frac{a}{b}$.

Now suppose you have to represent $1\frac{2}{5}$$=\frac{7}{5}$ on number line.

Following the procedure described above

1. Mark four points between 1 and 2.

2. The first point is $1\frac{1}{5}$ and second point is $1\frac{2}{5}$ . Last one is $1\frac{5}{5}=2$ .

Now, Suppose the fraction is $\frac{123}{15}$ and you have to write it in terms of mixed fraction

Use the Euclid Lemma to write it as mixed fraction

That is , a= b ×q +r, when natural number a is divided by b gives q as quotient and r as remainder,

123 = 15 × 8 + 3

$\frac{123}{15}=\frac{15 \times 8+3}{15}=\frac{15 \times 8}{15}+\frac{3}{15}=8\frac{3}{15}$

Answer 2

Consider the number $\frac{27}{13}$.

Since the numerator is greater than the denominator, this fraction is greater than 1.

Now, in the number line, find out how many 13's are there within 27.

The answer is 2.

Now, subtract 2 × 13 from 27.

27 - 26 = 1

Hence, the required mixed fraction is $2\frac{1}{13}$