Comparison Math Example 3

Follow the full solution, then compare it with the other examples linked below.

Example 3

easy

Insert

<

>

, or

=

between each pair: (a)

0.75

and

\dfrac{3}{4}

, (b)

\dfrac{2}{3}

and

\dfrac{3}{4}

Solution

1
(a) $\dfrac{3}{4} = 0.75$ , so $0.75 = \dfrac{3}{4}$ .
2
(b) Common denominator $12$ : $\dfrac{2}{3} = \dfrac{8}{12}$ , $\dfrac{3}{4} = \dfrac{9}{12}$ . Since $8 < 9$ : $\dfrac{2}{3} < \dfrac{3}{4}$ .

Answer

(a)

0.75 = \dfrac{3}{4}

; (b)

\dfrac{2}{3} < \dfrac{3}{4}

For (a), converting to the same form reveals equality. For (b), a common denominator makes numerator comparison direct. These two strategies cover most fraction comparison scenarios.

About Comparison

Determining how two quantities relate in terms of size or value, using the symbols $<$ , $>$ , or $=$ .

Learn more about Comparison →

More Comparison Examples

Example 1 easy

Compare [formula] and [formula]. Which is greater?

Example 2 medium

Place [formula], [formula], [formula], and [formula] in order from least to greatest.

Example 4 medium

Without a calculator, determine which is larger: [formula] or [formula].

← All Comparison Examples Comparison Concept

Related Concepts

More and Less Inequalities Ordering Numbers