Addition of Fractions

Q.

Multiply the following fractions: $\frac{3}{2}\times 5\frac{1}{3}$

Q. A man says, “I am thinking of a number. When I divide it by 3 and then add 5, my answer is twice the number I thought of”. Find the number.

Q. A farmer divides his herd of $‘n^{\prime }$ cows among his four sons so that the first son gets one-half the herd, the second son gets one-fourth, the third son gets one-fifth, and the fourth son gets $7$ cows, then $‘n^{\prime }$ is:

1. $140$
2. $280$
3. $180$
4. $240$

Q.

work out the following:

$\frac{5}{7}-\frac{4}{9}$

Q. Add the following rational numbers:​

(i) $\frac{3}{4}\text{and}\frac{-5}{8}$.

Q.

Simplify the following:

$3-1\frac{1}{6}-\frac{7}{15}$

Q. For the state budget in 2022, an additional $5 million was allocated for education, keeping the budget unchanged. If the education budget grew by 5% of its value in 2021, calculate the total value of the state budget.


Annual Budget (2022) \begin{tabular}{|ll} \hline \( 34 \% \) & Education \\ \( 23 \% \) & Agriculture \\ Infrastructure \\ \( 22 \% \) & Healthcare \end{tabular}

Q.

Q. The additive inverse of $\frac{-34}{-57}$ is

1. $\frac{-34}{-57}$
2. $\frac{34}{57}$
3. $\frac{-34}{57}$
4. $0$

Q. Solve
$108÷36$ of $\frac{1}{3}+\frac{2}{5}\times 3\frac{3}{4}$

Q. Verify associativity of addition of rational numbers i.e.,
$(x+y)+z=x+(y+z)$
iii) $x=\frac{-7}{11},y=\frac{2}{-5},z=\frac{-3}{22}$

Q. Which of the following fractions is greater than $\frac{3}{4}$ and less than $\frac{5}{6}$ ?

1. $\frac{2}{3}$
2. $\frac{1}{2}$
3. $\frac{4}{5}$
4. $\frac{9}{10}$

Q. The calue of $m$ for which ${\left[{\left\{{\left(\frac{1}{7^2}\right)}^{-2}\right\}}^{-\frac{1}{3}}\right]}^{\frac{1}{4}}=7^m$, is

1. $\frac{1}{4}$
2. $-\frac{1}{3}$
3. 2
4. -3

Q.

Work out the following:

$3\frac{5}{6}$$-$$2\frac{7}{15}$

Q. Solve
$\frac{1}{4}$ to $\frac{3}{4}$

Q. Which of the following illustrates the inverse property for addition?
a. $\frac{1}{8}-\frac{1}{8}=0$
b. $\frac{1}{8}+\frac{1}{8}=\frac{1}{4}$
c. $\frac{1}{8}+0=\frac{1}{4}$
d. $\frac{1}{8}-0=\frac{1}{8}$
$\left[1\right]$

Q. solve:

Q.

$1\frac{3}{25}+\frac{7}{20}-\frac{2}{5}$

Q. What is the value of the quotient if a non-zero rational number is divided by its additive inverse?

1. $1$
2. $-1$
3. $0$
4. $2$

Q. $(x^2{)}^{\frac{1}{2}}\times x^3=$________.

Q. Evaluate :
$(3\frac{5}{12}+1\frac{2}{3})÷(3\frac{5}{12}-1\frac{2}{3})$

Q. Sita can finish typing a $100-\text{page document}$ in $9$ hours, Mita in $6$ hours and Rita in $12$ hours. How long will they take to type a $100-\text{page document}$ if they work together $?$