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Comparison of ordinary fractions explanation and examples

Lecture



As well as natural numbers, ordinary fractions can be compared.

Consider two unequal fractions on the number axis. A smaller fraction will be located to the left, and a larger fraction to the right.

Comparison of ordinary fractions explanation and examples

Equal fractions correspond to the same point on the number axis.

The figure clearly shows that 1/5 <6/10. But it is not necessary to use the number axis to compare fractions .

Comparing Fractions with Same Denominators

Of the two fractions with the same denominators, the one with the numerator is greater.

Example. Compare 1/5 and 4/5.

In both fractions the same denominator is 5.

In the first fraction, the numerator is 1 and it is less than the numerator of the second fraction, which is 4.

Therefore, the first fraction (1/5) is less than the second (4/5).

Comparison of ordinary fractions explanation and examples

Comparing fractions with identical numerators

Of the two fractions with the same numerators, the one with the smaller denominator is greater.

Example. Compare 1/2 and 1/8. Answer:

Comparison of ordinary fractions explanation and examples

The rule above is easier to understand if you imagine that you have pieces of cake in your hands. In the first case, the cake was divided into 2 parts (the denominator of the fraction is 2), and you have half the cake in your hands, and in the second, the cake was divided into 8 parts, and you have a small piece of cake in your hands.

Comparison of ordinary fractions explanation and examples

Comparing Fractions with Different Denominators

To compare fractions with different denominators , you need to bring the fraction to a common denominator.

After reduction of fractions to a common denominator, fractions are compared by the rule of comparison of fractions with the same denominators.

Example. Compare 2/7 and 1/14.

  • We bring fractions to a common denominator. Comparison of ordinary fractions explanation and examples
  • Compare fractions with the same denominators. Comparison of ordinary fractions explanation and examples

Any improper fraction is greater than any improper fraction.

This is because the wrong fraction is always greater than or equal to 1, and the correct fraction is always less than 1.

Comparison of ordinary fractions explanation and examples

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Arithmetic

Terms: Arithmetic