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Year 7 Interactive Maths - Second Edition


Fractions

A number like a/b, where a and b are integers, is called a fraction.

5/6 is an example of a fraction where 5 is the numerator and 6 is the denominator.


Proper Fraction

If the numerator is smaller than the denominator, then the fraction is said to be a proper fraction.

3/4 is an example of a proper fraction.


Note:

Proper fractions are smaller than 1.


Improper Fraction

If the numerator is greater than the denominator, then the fraction is said to be an improper fraction.

4/3 is an example of an improper fraction.


Note: 

Improper fractions are greater than 1.


Equivalent Fractions

A graphic illustration of equivalent fractions.

The shaded portions are equal.

Equivalent fractions are equal fractions.

We notice that:

The value of a fraction remains the same after multiplying the numerator and denominator by the same number.


In general:

The numerator of a fraction and denominator of a fraction can be multiplied by the same number without altering the value of the fraction.


The value of a fraction remains the same after dividing the numerator and denominator by the same number.


In general:

The numerator of a fraction and denominator of a fraction can be divided by the same number without altering the value of the fraction.

The fractions 4/8 and 1/2 are equivalent.



Example 1

Simplify 56/63.

Solution:

We find, by trial and error, that 7 divides into both the numerator and denominator.

8/9 is a fraction in simplest form.


Setting out:

Usually, we set out the solution as follows:

56/63 = 8/9


Note:
Expressing a fraction in simplest form involves cancelling any factors common to the numerator and denominator.

Key Terms

fraction, numerator, denominator, proper fraction, improper fraction, equivalent fractions, simplest form, cancelling


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