Number families, reciprocals and ordering
Watch the whole lecture free
Make a free account to watch every lecture to the end: 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.
That was the teaching part. The rest of this lecture is free with an account: 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.
No password needed now: we email you a link to set one. Already have an account? Sign in, then come back to this page.
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
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.
Chapter 1: Number
- Number families, reciprocals and ordering 6 min
- The four operations and negative numbers 6 min
- Primes, factors and prime factor trees 6 min
- HCF and LCM 5 min
Also for IGCSE Maths 0580
Which topics come up most in IGCSE Maths 0580 past papers, counted from every paper since 2004.