Multiplication and Division of Rational Numbers

Q.

Divide the sum of $\frac{13}{5}$ and $\frac{-12}{7}$ by the product of $\frac{-31}{7}$ and $\frac{1}{-2}$

Q.

In a school, $\frac{5}{8}$ of the students are boys. If there are 240 girls, find the number of boys in the school.

Q.

Rita had Rs 300. She spent $\frac{1}{3}$ of her money on notebooks and $\frac{1}{4}$ of the remainder on stationery items. How much money is left with her ?

Q.

At a cricket test match $\frac{2}{7}$ of the spectators were in a covered place while 15000 were in open. Find the total number of spectators.

Q.

A cord of length $71\frac{1}{2}m$ has been cut into 26 pieces of equal length. What is the length of each piece ?

Q.

The area of a room is $65\frac{1}{4}{m}^2$.If its breadth is $5\frac{7}{16}m$, what is its length?

Q.

The product of two fractions is $9\frac{3}{5}$. If one of the fractions is $9\frac{3}{7}$, find the other.

Q.

Amit earns $Rs16000$ per month. He spends $\frac{1}{4}$ of his income on food; $\frac{3}{10}$ of the remainder on house rent and $\frac{5}{21}$ of the remainder on the education of children. How much money is still left with him?

Q.

Find the cost of $3\frac{2}{5}$ metres of cloth at Rs $36\frac{3}{4}$ per metre.

Q.

By what rational number should we multiply $\frac{-15}{56}$ to get $\frac{-5}{7}$ ?

Q.

After reading $\frac{7}{9}$ of a book, 40 pages are left. How many pages are there in the book ?

Q.

By what rational number should $\frac{-8}{39}$ be multiplies to obtain $\frac{1}{26}$ ?

Q. Question 118
A $117\frac{1}{3}m$ long rope is cut into equal pieces measuring $7\frac{1}{3}m$ each. How many such small pieces are these?

Q.

Find the area of a rectangular park which is $36\frac{3}{5}m\text{long and}16\frac{2}{3}m$ broad.

Q. Question 114
The cost of $\frac{19}{4}m$ of wire is $Rs.\frac{171}{2}$. Find the cost of one meter of the wire.

Q.

Find pythagorean triplet with the smallest number as 10

Q. Question 129
By what number should we multiply $\frac{-8}{13}$ so that the product may be 24?

Q.

$5\frac{1}{2}m$ long rope is cut into $12$ equal pieces. What is the length of each piece?

Q.

The cost of $3\frac{1}{2}$ metres of cloth is Rs $57\frac{3}{4}$. What is the cost of one metre of cloth ?

Q.

Write the multiplicative inverse of each of the following rational numbers. $7$, $-11$, $\frac{2}{5}$, $-\frac{7}{15}$ .

Q. Question 115
A train travels $\frac{1445}{2}$ km in $\frac{17}{2}$h. Find the speed of the train in km/h.

Q.

$\text{The product of two rational numbers is -2.}\text{If one of them is}\frac{4}{7},\text{find the other.}$

Q.

One litre of petrol costs Rs $46\frac{3}{4}$. What is the cost of 35 litres of petrol ?

Q. Question 127
The product of two rational numbers is $\frac{-14}{27}$. If one of the numbers be $\frac{7}{9}$, find the other.

Q.

Find the area of a square plot of land whose each side measures $8\frac{1}{2}$ metres.

Q. Question 128
By what numbers should we multiply $\frac{-15}{20}$ so that the product may be $\frac{-5}{7}$?

Q.

The product of two rational numbers is 15. If one of the numbers is -10, find the other.

Q.

Divide the sum of $\frac{5}{8}$ and $\frac{-11}{12}$ by the difference of $\frac{3}{7}$ and $\frac{5}{14}$.

Q. Question 130
The product of two rational numbers is - 7. If one of the number is - 5, find the other?

Q.

A car is moving at an average speed of $40\frac{2}{5}$ km/hr. How much distance will it cover km/hr. How much distance will it cover in $7\frac{1}{2}$ hours ?