Greater Than and Less Than: Comparing Decimals to Fractions

Remembering which inequality sign or symbol to use in a number comparison can be difficult, but we have an easy memory trick that can help!

See how the inequality symbol has a wide end and a narrow end?

The wide end opens to the greater value, and the narrow end points to the lesser value. If we describe the image below from left to right, it reads as all the Spider People are greater (or bigger) than just one Spider-Ham.

If we flip things around, we can still read it left to right, but now it reads as one Spider-Ham is less (or smaller) than all the Spider People.

When we’re comparing numbers, we compare place values from left to right. The number that has the first place value with a bigger digit is farther from 0 on the number line.

The number farthest to the right on the number line is the greater number.

$-1$

$-\frac{3}{4}$

$-0.5$

$-\frac{1}{4}$

$0$

$\frac{1}{4}$

$0.5$

$\frac{3}{4}$

$1$

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Remember that numbers farther to the right are greater by imagining a phone's signal bars - the bars get bigger and greater in strength as we go further to the right.

This also means that any positive number is greater than any negative number 💡.

Why is a bigger negative number less than a smaller negative number? 🤔

Remember, numbers get greater as we move to the right on the number line.

For negative numbers, you can think of “greater than” as meaning “which number is less negative (or more positive).”

$-0.8$

$-\frac{1}{2}$

$0$

$$-\frac{1}{2}>-0.8$$

Since $-\frac{1}{2}$ is farther to the right than $-0.8$, $-\frac{1}{2}$ is greater than $-0.8$.

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