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## JSS1: MATHEMATICS - 2ND TERM

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#### Quizzes

Lesson 1, Topic 3
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# Algebraic Processes

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### Substituting Numbers:

The value of an expression such as x + 8  can be found by replacing x with a given number. This is called substitution. For example:

For the expression x + 8

If  x = 8,  then  8 + 8  = 16

If x = 10, then 10 + 8  =  18

### Example 1

Find the value of each of the following mentally when  x = 3

i. $$\scriptsize x + 10 \\ \rightarrow \scriptsize 3 + 10 \\ = \scriptsize 13$$

ii. $$\scriptsize x\: – \: 1 \\ \rightarrow \scriptsize 3\: – \: 1 \\ = \scriptsize 2$$

iii. $$\scriptsize x \: \times \: 8 \\ \rightarrow \scriptsize 3 \: \times \: 8 \\ = \scriptsize 24$$

iv. $$\scriptsize x \: \div \: 9 \\ \rightarrow \scriptsize 3 \: \div\: 9 \\ = \frac{3}{9} \\ = \frac{1}{3}$$

v. $$\scriptsize x \: \times \: 3 + 1 \\ \rightarrow \scriptsize 3 \: \times \: 3 + 1 \\ = \scriptsize 10$$

### Example 2

Find the value of each of the following mentally when  y = 20

i. $$\scriptsize y + y + 2 \\ \rightarrow \scriptsize 20 + 20 + 2 \\ = \scriptsize 42$$

ii. $$\scriptsize (y \: – \: y ) \: + \: 5 \\ \rightarrow \scriptsize (20 \: – \: 20) \: + \: 5 \\ \scriptsize = 0 \: + \: 5 \\ \scriptsize = 5$$

iii. $$\scriptsize (y \: – \: 10) \: \times \: 8 \\ \rightarrow \scriptsize (20 \: – \: 10) \: \times \: 8 \\ = \scriptsize 10 \: \times \: 8 \\ \scriptsize = 80$$

iv. $$\scriptsize y \: \div \: y \: + \: 25 \\ \rightarrow \scriptsize 20 \: \div \: 20 \: + \: 25 \\ = \scriptsize 1 + 25 \\= \scriptsize 26$$

v. $$\scriptsize y \: – \: y \: + \: 8 \\ \rightarrow \scriptsize 20 \: – \: 20 \: + \: 8 \\ \scriptsize = 20 \: – \: 28 \\ \scriptsize = \; – 8$$

Remember BODMAS.

B = Brackets $$\scriptsize \left( \right)$$

O = Orders $$\scriptsize x^2 \: \: \sqrt{x}$$

D = Division $$\scriptsize \div$$

M = Multiplication $$\scriptsize \times$$

A = Addition $$\scriptsize +$$

S = Subtraction $$\scriptsize –$$

For question v. we solved 20 + 8 first which is equal to 28. We then solved the subtraction 20 – 28 = -8. For question ii. we solved the bracket first (20 – 20) = 0