# Find Missing Numbers Using Inverse Operations in an Algebraic Expression

In this worksheet, students will express an odd number as an algebraic expression and then determine if the missing number is odd or even.

Key stage:  KS 2

Curriculum topic:   Algebra

Curriculum subtopic:   Express Problems Algebraically

Difficulty level:

#### Worksheet Overview

In this activity, we will learn how to express an odd number as 'double a number plus one' and then identify whether the result is an odd or even number.

Example
Write this odd number as 'double a number plus one'. Then say whether the answer is odd or even.

209  =  2 x   ______   + 1

To solve this, we need to start with the answer of 209 and do the opposite (inverse) to it.

The inverse of adding 1 is subtracting 1.

The inverse of multiplying by 2 (doubling) is to divide by 2 (halving)

So, we do 209 - 1 = 208

208 ÷ 2 = 104

209  =  2  x 104 + 1, which is the same as 'double 104 plus one'.

The number 104 is an even number, since it is divisible by 2.

Does that make sense?

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