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
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