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# How to Learn Arithmetic Reasoning

Arithmetic Reasoning is a part of mathematics which deals with the number sequence, mathematical operators, ratio and proportion, percentage, power and roots, sets and probability. The application of arithmetic reasoning is found in our day to day life activity like calculating the total amount of expenditure, a percentage of monthly income, to find the area of a land,etc...The common arithmetic operators we use in problem are +,-,*,/, =.

Arithmetic Reasoning Formula:

SI = $\frac{(PTR)}{100}$

Speed = $\frac{(distance\ traveled)}{(time\ taken)}$

The ratio a to b is written as a: b

average of numbers or mean = $\frac{(sum\ of\ all\ the\ numbers)}{( number\ of\ terms)}$

Arithmetic Reasoning Problems:

1. Solve for a
2a + 10 = 20

Solution: To find the value of a  first add -10 to both side of the equation.
2a + 10 - 10 = 20 - 10
2a = 10
Divide both side of the equation by 2

$\frac{2a}{2}$ = $\frac{10}{2}$

a = 5

2. Convert the decimal number 0.575 to fraction

Solution: Multiply and divide the decimal number by 1000 to get the number in fraction form.

0.575 x $\frac{1000}{1000}$ = $\frac{585}{1000}$

Reduce the fraction to it’s simplest form.

$\frac{575}{1000}$ = $\frac{23}{40}$

3. Simplify 5 + [3 - {2 * 4} + 8 - 2]

Solution: The given expression is solved by making use of BODMAS rule.
The terms inside the brackets are simplified first.
= 5 + [3 - {8} + 8 - 2]
Do the addition and subtraction from left to right.
= 5 + [3 - 8 + 8 - 2]
= 5 + [3 - 2]
= 5 + [1]
= 6

4. Subtract the given Integer Number:

$\frac{3}{5}$ - $\frac{4}{7}$

Solution: A rational number can be subtracted from the other number by adding its negative to the given first rotational number.

= $\frac{3}{5}$ + (- $\frac{4}{7}$)

To add the terms first convert the number with equivalent rational numbers with a common denominator and then do the                     addition.
The L.C.M of the denominator is 5 and 7 is 35.
covert the rational number to its equivalent number by making use of the L.C.M

$\frac{3}{5}$ = $\frac{3*7}{5*7}$ = $\frac{21}{35}$

$\frac{4}{7}$ = $\frac{4*5}{7*5}$ = $\frac{20}{35}$

Multiply of a negative term by a positive term results in negative

= $\frac{21}{35}$ - $\frac{20}{35}$

= $\frac{1}{35}$