Number families, reciprocals and ordering
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The teaching part (1 min) is free to watch. A free account opens the whole lecture: 8 practice questions, 1 real past-paper question with the answer explained, the mistakes that lose marks, the full-marks tip, a one-card summary and a quick quiz.
What this lecture covers
- Which family is it?
- The number families
- Roots: rational or not?
Read the transcript of the teaching part
Last time
Before we start: last time, in Primes, factors and prime factor trees, you learned these points. Here they are again on one card. Keep them in mind, because today builds on them.
Which family is it?
Is zero a natural number? Is the square root of twenty a fraction? Cambridge loves these little questions, and they are easy marks once you know the families. Every number you meet belongs to a family. Today we sort them, flip them upside down, and put them in order.
The number families
Natural numbers are the counting numbers: one, two, three, and so on. Zero is not included. Integers are whole numbers, and they include zero and the negatives. Rational numbers can be written as a fraction of two integers. That includes decimals that stop or repeat. Irrational numbers cannot be written as a fraction. Their decimals go on for ever with no pattern, like pi.
Roots: rational or not?
A square root is rational only when the number under it is a perfect square. The square root of forty-nine is exactly seven, so it is rational, and natural too. But twenty is not a square number, so the square root of twenty is irrational. A calculator shows only a rounded version. It never ends, so never call it rational.
How often it comes up
How often Cambridge has asked each part, counted by ExamYard from every past paper in its question bank: Ordering numbers · Types of number.
The whole chapter: Numbers and the Four Operations.
Chapter 1: Number
- Number families, reciprocals and ordering 6 min
- The four operations and negative numbers 5 min
- Primes, factors and prime factor trees 5 min
Also for O Level Maths 4024
Which topics come up most in O Level Maths 4024 past papers, counted from every paper since 2004.