5th Class Mathematics Arithmetic

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)\[S.I.=A-P\]