NCERT Book Class 8 Mathematics (Part II) Chapter 1 Fractions in Disguise

FRACTIONS IN
1 DISGUISE

1.1 Fractions as Percentages
You might have heard statements like, “Mega Sale — up to 50% off!” or
“Hiya scored 83% in her board exams”.
Do you know what the symbol ʻ%ʼ means?
This symbol is read as per cent.
The word ‘per cent’ is derived from the Latin phrase ‘per centum’,
meaning ‘by the hundred’ or ‘out of hundred’.
So, 25 per cent (25%) means 25 out of every 100 — like 25 people out
of 100, 25 rupees out of 100 rupees, or 25 marks out of 100 marks.
If we say 50% of some quantity s, it means
1
50% = 50 × 100 × s (50 times the unit fraction of s)
50
= 100 × s = 12 s.
Thus, percentages are simply fractions where the denominator
is 100. Examples:
20% = 20 = 2 = 1 ,
100 10 5
33 .
33% = 100
We saw that percentages are just fractions. Given any fraction, can we
express it as a percentage? Yes, let us see how.

Expressing Fractions as Percentages
Example 1: Surya wants to use a deep orange colour to capture the
sunset. He mixes some red paint and yellow paint to make this colour.
3
The red paint makes up 4 of this mixture. What percentage of the colour
is made with red?
3
4 is 3 out of every 4. 3 6 30 75
4 = 8 = 40 = 100
That is, 6 out of every 8 (equivalent fraction).
That is, 30 out of every 40.
That is, 75 out of every 100.
This means 75%.