Contents
In this post, we’ll look at which fractions are equal and how to compare two fractions with the same numerator/denominator or with different denominators.
Equal fractions
Two fractions are equal if their numerators and denominators are respectively equal (proportionately equal).
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are equal, because the numerator and denominator of the first fraction are half the numerator and denominator of the second fraction.
Equal fractions correspond to:
- the same point on the number axis;
- the same decimal fraction, which is calculated by dividing the numerator by the denominator. In our case 4 / 5 = 8 / 10 = 0,8.
Comparison of simple fractions
With the same denominators
Of two fractions with the same denominator, the larger is the one with the larger numerator.
>
, because 5> 3.
with the same numerators
Of two fractions with the same numerator, the larger one is the one with the smaller denominator.
>
, because 4 <11.
With different denominators
In order to be able to compare fractions with different denominators, you first need them, after which they can already be compared with the same denominator.
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.
In this case, we need to represent the first fraction with a denominator 16 by multiplying the numerator and denominator by a number 2.
=
=
.
Now we have two fractions with the same denominators, which we can compare according to the corresponding rule discussed above.
>
, because 6> 2.
Other rules for comparing fractions
1. Any proper fraction is less than 1.
<1.
2. Any improper fraction is greater than 1.
>1, because
=2
> 1.
3. Any improper fraction is always greater than the correct one, which follows from rules 1 and 2 above.
>
.