Positive and negative numbers on the number line · lesson

Opposites

💡 Opposites are the same distance from zero on different sides.

Every number has an opposite. It sits the same distance from 0, but on the other side.

The opposite of a negative number is positive. The opposite of a positive number is negative.

🧠 Let's work it out

What is the opposite of −18?

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💡 Absolute value is distance from zero, so it is never negative.

The absolute value of a number is how far it is from 0. We write it with bars, like |−22|.

Distance is never negative. So |−22| = 22 and |22| = 22.

🧠 Let's work it out

Find |−7| + |4|.

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💡 Below zero, under sea level, or owing money all mean a negative number.

Zero is often a starting point. Sea level is 0 feet. A bank balance of 0 means you have nothing and owe nothing.

Words like below, under, owe, loss, and drop point to a negative number.

🧠 Let's work it out

A fish swims 35 feet below sea level. What is its elevation?

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💡 On a number line, the number farther right is always greater.

On a number line, numbers grow as you move right. So −2 is greater than −8, because −2 is farther right.

With negatives, the number closer to 0 is greater. That works for decimals too.

The least number in a list is the one farthest left.

🧠 Let's work it out

Which is greater, −6.3 or −6.7?

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💡 Count the steps between numbers to find distance, and move left for less or right for more.

To find the distance between a negative and a positive number, add their distances from 0.

Moving left makes a number smaller. Moving right makes it bigger.

The point halfway between two numbers is half the distance from either end.

🧠 Let's work it out

How far apart are −4 and 6?

−4 is 4 from 0, and 6 is 6 from 0.
They are on opposite sides of 0, so add: 4 + 6 = 10.
Another example, halfway between −11 and 1: the distance is 12, and half of it is 6.
Start at −11 and move 6 right: −11 + 6 = −5.

What do you think comes next?