How can you prove that a number is even in math?

I know 12 is even, but how can I prove it?

In this lesson you will learn how to prove that a number is even by representing it as the sum of

two equal addends.

Let’s Review

All even numbers can be evenly split into groups of two and two equal groups.

8 9 10761 2 3 4 5

EOEOEOEOEO

Let’s Review

In addition equations the addends are added together and the sum is the total.

6 + 6 = 12

Addend Addend Sum

A Common Misunderstanding

Thinking that addends have to be even to have an even sum.

6 + 6 12

= ✓✓7 + 7 =14

Core Lesson

If a number can make even groups of two it will always make two equal groups.

2 + 2 + 2 + 2 + 2 + 2

6 + 6

=

Core Lesson

6 + 6 = 126 = 6

12Even

Core Lesson

Any even number can be shown as the sum of two equal addends.

18

19

2017

16

11 12 13 14 15

EOEOEOEOEO

6 + 6

Core Lesson

7 + 7 = 14

Core Lesson

18

19

2017

16

11 12 13 14 15

EOEOEOEOEO

6 + 6 7 + 7

Core Lesson

8 + 8 = 16

Core Lesson

18

19

2017

16

11 12 13 14 15

EOEOEOEOEO

6 + 67 + 7

8 + 8 9 + 9

10 + 10

In this lesson you have learned how to prove a number is even by representing it as the sum of

two equal addends.