Topic Content:
- 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 1.3.1:
Find the value of each of the following mentally when x = 3
i. \( \scriptsize x + 10 \)
ii. \( \scriptsize x\: – \: 1 \)
iii. \( \scriptsize x \: \times \: 8 \)
iv. \( \scriptsize x \: \div \: 9 \)
v. \( \scriptsize x \: \times \: 3 + 1\)
Solution
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 1.3.2:
Find the value of each of the following mentally when y = 20
i. \( \scriptsize y + y + 2 \)
ii. \( \scriptsize (y \: – \: y ) \: + \: 5 \)
iii. \( \scriptsize (y \: – \: 10) \)
iv. \( \scriptsize y \: \div \: y \: + \: 25 \)
v. \( \scriptsize y \: – \: y \: + \: 8 \)
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 ii, we solved the brackets () first
For question iii, we solved the brackets () first
For question iv, we divided first before adding
For question v, we solved 20 + 8 first which is equal to 28. We then solved the subtraction 20 – 28 = -8.