Video: Ordering Rational Numbers

Order these numbers from least to greatest: −4/5, 3/10, −1/2, 19/20.


Video Transcript

Order these numbers from least to greatest: negative four-fifths, three-tenths, negative one-half, and nineteen twentieths.

We can see from the list that two of our fractions are negative. The other two fractions are positive. And these will be greater than the two negative fractions. In order to compare any fractions, we need to ensure the denominators are the same. Alternatively, we could turn all four fractions into decimals. The lowest common multiple of five, 10, two, and 20 is 20. So, this will be our lowest common denominator. We need to convert each of the fractions into something over 20.

Five multiplied by four is equal to 20. And whatever we do to the denominator, we must do to the numerator. Therefore, we must also multiply this by four. The fraction negative four-fifths is the same as or equivalent to negative 16 over 20 or negative sixteen twentieths. 10 multiplied by two is equal to 20. And three multiplied by two is equal to six. Therefore, three-tenths is the same as six twentieths.

We can multiply the numerator and denominator of the third fraction by 10, giving us negative ten twentieths. As the fourth fraction was already over 20, this remains as nineteen twentieths. The denominators of all four fractions are now the same. And we can compare them by looking at the numerators.

The smallest value out of negative 16, six, negative 10, and 19 is negative 16. The second smallest is negative 10. Next, we have six. And finally, the largest number is 19. This means that the numbers in order from least to greatest are negative four-fifths, negative one-half, three-tenths, and nineteen twentieths.

As mentioned at the start, we could’ve converted the fractions into decimals first. Negative four-fifths is the same as negative 0.8. Three-tenths is the same as 0.3. Negative one-half is the same as negative 0.5. And nineteen twentieths is the same as 0.95. Putting these decimals in order, we have negative 0.8, negative 0.5, 0.3, and 0.95. Rewriting them as fractions, we have the same order from least to greatest.

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