Explore Arithmetic operations

# Comparing numbers

From a young age, we understand the concept of quantity. There are two baskets in front of you. One has $$3$$ lollipops and the other has $$6$$ lollipops. Which one would 4-year old you choose? Well, obviously the basket with $$6$$ lollipops. Why? Because we compared the numbers $$3$$ and $$6$$ and concluded that $$6$$ is greater than $$3$$.

But how would we compare fractions or decimals? Let’s find out.

## What does it mean to compare numbers?

A comparison of numbers is an estimation of whether the given numbers are equal, one number is greater than the other, or one number is less than the other number.

$$a=b~~ \text{or}~~a>b~~ \text{or}~~a<b~$$

The signs can be combined, meaning that we can see if the numbers are greater than or equal to, or the opposite – less than or equal to, which is denoted by:

$$a\ge b, a\le b$$

### Why is comparing numbers so useful?

Comparing numbers is something we do every day. Let’s say, for example, you’re standing in a garden, comparing the heights of two trees. One is $$6$$ ft tall and the other is $$7$$ ft tall, so which symbol do you think should replace the question mark in the following:

$$6 \quad?\quad 7$$

## How to compare numbers

Now that we know what it means to compare numbers and why it’s so useful, it’s time to see it in action! Let’s walk through a problem together.

### Example 1

Compare the numbers:

$$587 > 23$$

Here, we have to determine whether the first number is greater than the second number. Notice that both numbers are positive, so we need to see which number is greater.

The first number consists of three digits and the second one consists of two digits, hence the first number is greater than the second number, which makes this statement true.

$$\text{True}$$

### Example 2

Compare the numbers:

$$24=23$$

Here, we have to determine whether the first number is equal to the second number. Obviously, $$24$$ is not equal to $$23$$, which makes this statement false.

$$\text{False}$$

That wasn’t so bad, right? Now that we’ve walked through detailed examples, let’s review the overall process so you can learn how to use it with any problem:

## Study summary

1. If needed, simplify the numbers on both sides of the equality or inequality.
2. Next, compare the numbers.

## Do it yourself!

Practicing math concepts like this one is a great way to prepare yourself for the math journey to come! So, when you’re ready, we’ve got some practice problems for you!

Compare the numbers:

1. $$\frac{8}{2}=4$$
2. $$\frac{9}{4} < 3$$
3. $$\sqrt{7} = 7$$
4. $$4.25 > \frac{17}{4}$$

Solutions:

1. $$\text{True}$$
2. $$\text{True}$$
3. $$\text{False}$$
4. $$\text{False}$$

If you’re still struggling with the solving process, that’s totally okay! Stumbling a few times is good for the learning process. If you get too stuck or lost, scan the problem using your Photomath app and we’ll walk you through it!

Here’s a sneak peek of what you’ll see:

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