Multiplication and Division of Rational Numbers

Q.

Fill in the blanks:

$\left(\frac{-3}{7}\right)÷\left(\frac{-7}{3}\right)=\_\_\_\_\_\_\_.$

Q.

If the thickness of a pile of $12$ cardboard sheets is $45\mathrm{mm}$, then the thickness of a pile of $240$ sheets is _______ $\mathrm{cm}$.

Q. For every non-zero rational number $\frac{a}{b}$ there exists a rational $\frac{c}{d}$ such that $\frac{a}{b}\times \frac{c}{d}=1$, then the rational number $\frac{c}{d}$ is known as ___.

1. Multiplicative identity
2. Additive identity
3. Additive inverse
4. Multiplicative inverse

Q. A man earned $Rs.80$. He spent $Rs.13\frac{3}{5}$ on food, $25\frac{1}{2}$ on shopping and $Rs.4\frac{2}{5}$ on groceries. How much did he save.

Q.

Find the solution of the given problem:

$(-7)+(+8)$

Q. The siblings have a bucket containing 3$\frac{3}{7}$ L of water. They pour water into different flower pots. Find the number of flower pots if 1$\frac{1}{7}$ L of water is poured into each pot?

1. 2
2. 3
3. 4
4. 7

Q. How long will it take Ray to cover 30 miles if he is going at a speed of 5 mph?

1. 3 hr
2. 5 hr
3. 6 hr
4. 8 hr

Q. A shopkeeper purchased $300$ bulbs of Rs. $10$ each. $10$ bulbs were fused and thrown away. The remaining were sold at Rs. $12$ each. Find gain or loss $\%$.

1. Loss $=16\%$
2. Gain $=16\%$
3. Loss $=12\%$
4. Gain $=12\%$

Q.

Divide: $\frac{3}{5}÷2$

Q.

Find the solution of the given problem:

$(+12)+(-7)$

Q. A cyclist covers $126km$ in $6$ hours.What distance will he cover in $5$ hours ?

Q. Prove that :
$\frac{9!}{6!\times 3!}+\frac{9!}{5!\times 4!}=\frac{10!}{4!\times 6!}$

Q.

Find the product:
$\frac{9}{10}\times \frac{15}{7}$

1. $\frac{25}{14}$

2. $\frac{28}{14}$

3. $1\frac{11}{14}$

4. $1\frac{13}{14}$

Q. The siblings have a bucket containing 3$\frac{3}{7}$ L of water. They pour water into different flower pots. Find the number of flower pots if 1$\frac{1}{7}$ L of water is poured into each pot?

1. 2
2. 3
3. 4
4. 7

Q. If we multiply a fraction by itself and divide the product by its reciprocal the fraction thus
obtained is $18\frac{26}{27}$. The original fraction is

1. $2\frac{2}{3}$
2. $1\frac{1}{2}$
3. $\frac{8}{27}$
4. None of these

Q.

The area of a rectangular garden is 256 square meters. List all possible whole number dimensions that the garden can have. [2 MARKS]

Q.

If the distance covered by a car in 4 hours is 240 km then the distance covered by the car in 1.5 hours is _____.

1. 30 km

2. 60 km

3. 90 km

4. 180 km

Q. Add the following fractions:
(i) $\frac{1}{3}+\frac{2}{4}+\frac{3}{4}$
(ii) $3\frac{1}{3}+2\frac{2}{3}$

Q. If the distance covered by a car in 4 hours is 240 km then the distance covered by the car in 1.5 hours is _____.

1. 180 km
2. 30 km
3. 90 km
4. 60 km