Question

Which rational number expression is larger?
a. 2.75
b. 22/8
c. the numbers are equal

Answer 1

Convert 22/8 to decimal

Answer 2

\(22 \div 8 = 2.75\)

Therefore, the are equal.

Answer 3

In questions like this, make sure to have both of the numbers in the same format. It will be easier for comparing which one is greater or lesser.

Answer 4

(just another method but calc's is easier)

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You can also convert 2.75 to a mixed number and then improper fraction:\[2.75\rightarrow2\frac{3}{4}\]To convert, multiply the 2 by the 4, because \(2\rightarrow2\times\frac{1}{4}\), then add 3 because it's the remainder;\[\frac{(2\times4)+3}{4}\]This gets you the following:\[\frac{8+3}{4}=\frac{11}{4}\]Now, you need the fractions to have an equal denominator, so multiply the bottom by 2 to get 8. And since the top and bottom both need to be balanced:\[\frac{11}{4}\times\frac{2}{2}=\frac{11\times2}{4\times2}=\frac{22}{8}\]So yes, they are both equal.