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Basic 2 · Mathematics · Number Operations

Order in Adding and the Number Zero

In this topic you will learn that changing the order of numbers in addition gives the same answer. You will also learn about zero.

By the end of these notes you should be able to:

  • Add numbers in any order
  • Add three numbers in two ways
  • Add and subtract zero

What you already know

  • Adding and subtracting to 100

Copy everything that has a blue line on its left into your notebook. The other parts are for reading.

Strand
Number
Sub-strand
Number Operations
Indicator
B2.1.2.1.1 – Use conceptual understanding of addition and subtraction to add and subtract numbers to, 100

Introduction

35 + 54 and 54 + 35 look different. But they give the same answer. Let us find out why.

1. Order Does Not Matter in Adding

35 + 54 = 89 and 54 + 35 = 89.

When we add, the order of the numbers does not change the sum.

Example

Add 18 + 12 + 3 in two ways.

  1. (18 + 12) + 3 = 30 + 3 = 33
  2. 18 + (12 + 3) = 18 + 15 = 33

Answer: Both ways give 33.

Tip: Add the numbers that make 10 or 20 first. 18 + 12 = 30 is easy.

2. The Number Zero

Zero: The number that means nothing, written 0.

  • Adding zero: 47 + 0 = 47
  • Subtracting zero: 47 – 0 = 47
  • Taking a number from itself: 47 – 47 = 0
An empty basket labelled 0 next to a basket of 5 mangoes
Figure 1: Zero means nothing Draw an empty plate and write 0.Illustration: Sirbus

Common mistake: Subtraction order matters! 9 – 4 is not the same as 4 – 9.

New words

order
The way things follow each other.
zero
The number for nothing, 0.
sum
The answer when we add.
same
Not different.

Summary

  • Changing the order in addition gives the same sum.
  • Adding or taking away zero does not change a number.
  • A number minus itself is zero.

Class activity: Order Swap

  1. Pick two number cards.
  2. Add them in one order, then swap them and add again.
  3. Check that the sums are the same.

You need: Bottle tops, Bundles of sticks, Exercise books

Exercises

Answer in your exercise book first, then check your answers.

  1. 1. 26 + 0 = ?

    • A. 0
    • B. 26
    • C. 27
    • D. 260
    Show answer
    Answer: 26Adding zero does not change the number.

  2. 2. Which is the same as 43 + 25?

    • A. 25 + 43
    • B. 43 – 25
    • C. 25 – 43
    • D. 43 + 52
    Show answer
    Answer: 25 + 43Order does not change the sum.

  3. 3. 15 + 9 = 9 + 15

    • A. True
    • B. False
    Show answer
    Answer: TrueBoth make 24.

  4. 4. 8 – 3 = 3 – 8

    • A. True
    • B. False
    Show answer
    Answer: FalseOrder matters in subtraction.

  5. 5. 64 – 64 = ______

    Show answer
    Answer: 0A number minus itself is zero.

  6. 6. Add 7 + 13 + 6 by first adding the two numbers that make 20.

    Show answer
    Answer: 7 + 13 = 20; 20 + 6 = 26Making 20 first is easier.

Homework

  1. Add three numbers from your house (e.g. people, chairs, cups) in two different orders.