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Unit: Number System
Chapter: Fractions – Introduction & Types
Reference: – Introduction to Fractions, Numerator and Denominator, Fraction as Part of a Whole, Unit Fractions, Proper Fractions, Improper Fractions, Mixed Fractions, Like and Unlike Fractions, Equivalent Fractions
After studying this chapter, you should be able to understand:
- Introduction to Fractions & Their Meaning
- Numerator and Denominator
- Fraction as Part of a Whole
- Unit Fractions
- Proper and Improper Fractions
- Mixed Fractions & Conversions
- Like and Unlike Fractions
- Equivalent Fractions
Fractions, Introduction
What is a fraction?
A fraction is a part of a whole i.e. if something is broken into parts, a fraction shows how many parts we are left with out of all those parts.
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A fraction has two parts i.e. the numerator and the denominator.
It is expressed in the form:NumeratorDenominator
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(Denominator ≠ 0)
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Let us look at the shaded portion in the following figures-
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Here 34and35
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both are fractions. The coloured portion represents the part of a whole expressed as a fraction.
Examples-
- What fraction of a year is 5 months?
No. of months in a year = 12
Fraction of the year represented by 5 months =512
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- Write first 10 natural numbers. What fraction of these numbers are prime?
First 10 natural numbers = 1, 2, 3, 4, 5, 6, 7, 8, 9 and 10
Prime numbers among these = 2, 3, 5 and 7
So, the fraction =410
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Fractions on a number line
We have learnt to represent whole numbers on a number line. We can also represent fractions on the number line since every fraction has got a corresponding point on the number line.
Examples-
- Represent 12
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on the number line.
- 12
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is greater than 0 but is less than 1. It represents 1 part after dividing a whole into 2 parts.
- So, we divide the space between 0 and 1 into two equal parts and show one of the parts as the fraction 12
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- Represent 35
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on the number line.
- 35
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is greater than 0 but is less than 1. It represents 3 parts after dividing a whole into 5 parts.
- So, first we divide the space between 0 and 1 into five equal parts.
- Then we show the first part as 15,
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second part as 25
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, third part as 35
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and fourth part as 45
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.
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- Represent 335
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on the number line.
- 335
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is greater than 3 but is less than 4. It represents 3 whole and 3 parts after dividing a whole into 5 parts.
- So, first we divide the space between 3 and 4 into five equal parts.
- Then we show the first part as 315,
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second part as 325
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, third part as 335
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and fourth part as 345
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.
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