Std 6 th Mathematics- 4. Operations on Fractions page 2

Question 1:

What fractions do the points A and B show on the number lines below?
1. 



2. 


3.

Answer 1:

1. $A=\frac{5}{6}\mathrm{and}B=\frac{10}{6}$

2. $A=\frac{3}{5}\mathrm{and}B=\frac{7}{5}$

3. $A=\frac{3}{7}\mathrm{and}B=\frac{10}{7}$

Question 2:

Show the following fractions on the number line.

(1) $\frac{3}{5},\frac{6}{5},2\frac{3}{5}$

(2) $\frac{3}{4},\frac{5}{4},2\frac{1}{4}$

Answer 2:

(1) $\frac{3}{5},\frac{6}{5},2\frac{3}{5}\mathrm{or}\frac{13}{5}$



(2) $\frac{3}{4},\frac{5}{4},2\frac{1}{4}\mathrm{or}\frac{9}{4}$

Question 1:

Multiply.

(i) $\frac{7}{5}\times \frac{1}{4}$

(ii) $\frac{6}{7}\times \frac{2}{5}$

(iii) $\frac{5}{9}\times \frac{4}{9}$

(iv) $\frac{4}{11}\times \frac{2}{7}$

(v) $\frac{1}{5}\times \frac{7}{2}$

(vi) $\frac{9}{7}\times \frac{7}{8}$

(vii) $\frac{5}{6}\times \frac{6}{5}$

(viii) $\frac{6}{17}\times \frac{3}{2}$

Answer 1:

(i)
$\frac{7}{5}\times \frac{1}{4}=\frac{7\times 1}{5\times 4}=\frac{7}{20}$

(ii)
$\frac{6}{7}\times \frac{2}{5}=\frac{6\times 2}{7\times 5}=\frac{12}{35}$

(iii)
$\frac{5}{9}\times \frac{4}{9}=\frac{5\times 4}{9\times 9}=\frac{20}{81}$

(iv)
$\frac{4}{11}\times \frac{2}{7}=\frac{4\times 2}{11\times 7}=\frac{8}{77}$

(v)
$\frac{1}{5}\times \frac{7}{2}=\frac{1\times 7}{5\times 2}=\frac{7}{10}$

(vi)
$\frac{9}{7}\times \frac{7}{8}=\frac{9}{7}\times \frac{7}{8}=\frac{9}{8}$

(vii)
$\frac{5}{6}\times \frac{6}{5}=\frac{5}{6}\times \frac{6}{5}=1$

(viii)
$\frac{6}{17}\times \frac{3}{2}=\frac{36}{17}\times \frac{3}{2}=\frac{3\times 3}{17}=\frac{9}{17}$

Question 2:

Ashokrao planted bananas on $\frac{2}{7}$ of his field of 21 acres. What is the area of the banana plantation?

Answer 2:

Ashokrao planted bananas on $\frac{2}{7}$ of his field of 21 acres.
The area of the banana plantation = $\frac{2}{7}\times 21$
$=\frac{2}{7}\times 213=6\mathrm{acres}$
Hence, the area of the banana plantation is 6 acres.

Question 3:

Of the total number of soldiers in our army, $\frac{4}{9}$ are posted on the northern border and one - third of them on the north - eastern border. If the number of soldiers in the north is 540000, how many are posted in the north - east?

Answer 3:

Let the total number of the soldiers be x.
Number of soldiers posted on the northern border = 540000
$\Rightarrow \frac{4}{9}x=540000\Rightarrow x=\frac{540000\times 9}{4}=1215000$
Now, the number of soldiers posted on the northern border = $\frac{1}{3}\times 1215000$
= 405000
Hence, 405000 soldiers are posted in the north - east.

Question 1:

Write the reciprocals of the following numbers.
(i) 7

(ii) $\frac{11}{3}$

(iii) $\frac{5}{13}$

(iv) 2

(v) $\frac{6}{7}$

Answer 1:

(i) The reciprocal of 7 is $\frac{1}{7}$.

(ii) The reciprocal of $\frac{11}{3}$ is $\frac{3}{11}$.

(iii) The reciprocal of $\frac{5}{13}$ is $\frac{13}{5}$.

(iv) The reciprocal of 2 is $\frac{1}{2}$.

(v) The reciprocal of $\frac{6}{7}$ is $\frac{7}{6}$.

Question 2:

Carry out the following divisions.
(i) $\frac{2}{3}÷\frac{1}{4}$

(ii) $\frac{5}{9}÷\frac{3}{2}$

(iii) $\frac{3}{7}÷\frac{5}{11}$

(iv) $\frac{11}{12}÷\frac{4}{7}$

Answer 2:

(i)
$\frac{2}{3}÷\frac{1}{4}=\frac{2}{3}\times \frac{4}{1}=\frac{2\times 4}{3\times 1}=\frac{8}{3}$

(ii)
$\frac{5}{9}÷\frac{3}{2}=\frac{5}{9}\times \frac{2}{3}=\frac{5\times 2}{9\times 3}=\frac{10}{27}$

(iii)
$\frac{3}{7}÷\frac{5}{11}=\frac{3}{7}\times \frac{11}{5}=\frac{3\times 11}{7\times 5}=\frac{33}{35}$

(iv)
 $\frac{11}{12}÷\frac{4}{7}=\frac{11}{12}\times \frac{7}{4}=\frac{11\times 7}{12\times 4}=\frac{77}{48}$

Question 3:

There were 420 students participating in the Swachh Bharat campaign. They cleaned $\frac{42}{75}$ part of the town, Sevagram. What part of Sevagram did each student clean if the work was equally shared by all?

Answer 3:

420 students cleaned $\frac{42}{75}$ part of the Sevagram town.
1 student cleaned the part of the Sevagram town equal to $\frac{42}{75}÷420$
$=\frac{42}{75}\times \frac{1}{420}=\frac{42}{75\times 420}=\frac{1}{75\times 10}=\frac{1}{750}$
Hence, each student cleaned $\frac{1}{750}$ part of the Sevagram town.