# 5th Class Mathematics Arithmetic

Arithmetic

Category : 5th Class

ARITHMETIC

FUNDAMENTALS

•                   In this chapter, we shall study comparing quantities like ratio and proportion, profit and loss, discount simple interest, distance speed and time.

Ratio and Proportion

•                  Ratio is a method of comparing two quantities of the same kind by division.
•                  When two ratios are equal, they are said to be in proportion.
•                  If two ratios are to be equal or are in proportion, their product of means should be equal to the product of extremes.

Example: If a: b: c: d then the statement ad = be, holds good.

If a: b and b: c are in proportion such that ${{b}^{2}}$=

Ac than b is called the mean proportional of a: b and b: c

•                  Multiplying or dividing terms of the ratio by the same number gives equivalent ratios.

Elementary Questions

Q.        If$5:6=a:18$, then$a=?$?

Sol.      $\frac{5}{6}-\frac{a}{18}=5\times 18=a\times 6$

$\Rightarrow a=\frac{5\times 15}{6}=15$

Elementary Question:

Q.        $\frac{37}{25}$can also be written as,

(a)$\frac{147}{99}$                              (b)$\frac{149}{101}$                             (c)$\frac{148}{100}$                                    (d)$\frac{152}{97}$

Sol.      $\frac{37}{25}=\frac{37\times 4}{25\times 4}=\frac{148}{100}$

Percentage

•                  Another way of comparing quantities is percentage. The word percent means per hundred. Thus 12% means 12 parts out of 100 parts
•                  Fractions can be converted into percentages and vice= versa.

Example:$\frac{2}{5}=\frac{2}{5}\times 100%=40%$

(ii)$25%=\frac{25}{100}=+\frac{1}{4}$

•                  Decimals can be converted into percentages and vice-versa.

Example:

(i)$0.36=0.36\times 100%$

(ii) $43%=\frac{43}{100}=0.43$

Simple Internet

•                   When we deposit money in banks, bank give interest on money. Interest may be simple interest (called S.I.)

A= Amount

B= Principle

R= Rate

T= Time

$S.I.=\frac{P\times R\times T}{100}$

(Simple Interest)$S.I.=A-P$

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