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