All sections

Integers, Rational Numbers and Real Numbers

Chapter 2 Study Notes

Start Practice
Section 2 of 8
Contents▾
Why Negative Numbers Matter2.1Negative Numbers and Ordering2.2Addition and Subtraction of Integers2.3Multiplication and Division of Integers2.4Combined Operations (BODMAS)2.5Operations on Fractions and Decimals with Negatives2.6Rational and Irrational NumbersChapter Summary

2.1Negative Numbers and Ordering

Numbers greater than 00 are called positive numbers. Numbers less than 00 are called negative numbers. We read −80-80 as "negative 80".

Integers
{…,−3,−2,−1,0,1,2,3,…}\{\ldots, -3, -2, -1, 0, 1, 2, 3, \ldots\}

On a number line, positive numbers sit to the right of 00 and negative numbers to the left, and a number further right is always greater. Write this with >>, <<, ≥\geq and ≤\leq.

-6-5-4-3-2-101234smaller to the left, larger to the right
Every number has one place on the line. Further left is always smaller, so −5<−3<−1<0<1<3-5 < -3 < -1 < 0 < 1 < 3, whatever the digits look like.

Now you try

A question on this, marked as you go, with the working shown. No account needed.

Try this question →

Ordering temperatures

The overnight temperatures in three cities were: Moscow −18 ∘C-18\,^{\circ}\text{C}, Oslo −7 ∘C-7\,^{\circ}\text{C}, Helsinki −12 ∘C-12\,^{\circ}\text{C}. Arrange these from coldest to warmest.

Show solution▾
On a number line: −18-18 is furthest left, then −12-12, then −7-7.
-20-18-16-14-12-10-8-6-4-18-12-7Moscow, Helsinki, Oslo: coldest is furthest left
Coldest to warmest: Moscow (−18 ∘C-18\,^{\circ}\text{C}), Helsinki (−12 ∘C-12\,^{\circ}\text{C}), Oslo (−7 ∘C-7\,^{\circ}\text{C}).
−18<−12<−7-18 < -12 < -7

Practise this

Questions on Integers, Rational Numbers and Real Numbers, marked as you go, with the working shown.

Practise Integers, Rational Numbers and Real Numbers