Page 114 - Maths Skills - 8

112 Maths

INTRODUCTION
We need to compare various quantities in our daily life. For example, when you need to buy say, a jam bottle, you
compare to see which product is cheaper. If 500 g of jam available for ` 100 and 750 g is available for ` 120 then
the 750 g pack is cheaper.

Now let us consider another example. Ram earns ` 4500 and saves ` 500, Raju earns ` 7200 and saves ` 600.
Who save more relatively?

Aastha scored 17 out of 25 in a test, while Siddhie scored 28 marks out of 40 in a test. Whose performance
is better?
You can find out whether Ram and Raju saves more by taking ratios of their savings or by finding the percentage
of their savings. Similarly, you can compare the performance of Aastha and Siddhie in the test by taking the ratio
or finding the percentage.

PER CENT

Per cent is an abbreviation of the Latin word ‘per centum’ meaning hundredths or per hundred. It is denoted by
the symbol ‘%’. A fraction with denominator 100 is called a ‘per cent’.
Fact-o-meter
18 30 151
Thus, = 18%, = 30%, = 151%, etc 1
100 100 100 %=
100
Per cent as a Fraction

To express a per cent as a fraction, we drop the per cent sign ‘%’ and multiply the given number by 1
100
1 45 1 80
For example; 45% = 45 × = , 80% = 80 × = , etc.
100 100 100 100

Per cent as a Ratio
To express a per cent as a ratio, we first express it as a fraction as above and then reduce it to its simplest form.

1 25 1 1 60 3
For example; 25% = 25 × = = = 1 : 4, 60% = 60 × = = = 3 : 5, etc.
100 100 4 100 100 5
Per cent as a Decimal
When we express a per cent as a decimal, we first express it as a fraction as above and then shift the decimal point
two places (further, if a decimal already exists) to the left.

1 85 1 45 .
For example; 85% = 85 × = = 0.85, 4.5% = 4.5 × = = 0.045, etc.
100 100 100 100

PERCENTAGE INCREASE AND DECREASE
● To increase a quantity by some per cent, find the percentage of the quantity and add it to the original number.

Increase in original value
Increase % = × 100 %
Original value
Fact-o-meter
● To decrease a quantity by some per cent, find the percentage
of the quantity and subtract it to the original number. Percent Error= Error × 100%
Decrease in original value Actual Value
Decrease % = Original value × 100%

Let us learn through examples.