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Chapter Overview
Learning Goals
Learning Goals
Maths
Types of numbers
Number calculations
Fractions, decimals and percentages
Algebraic manipulation
Formulae and equations
Straight line graphs
Other graphs
Ratio
Proportion
Rates of change
Shapes
Properties of shapes
Lines and angles
Drawing shapes
Trigonometry
Probability
Maths
Summary
Substitution means replacing the variable with a number. Substitution helps find the value of simple expressions and formulae. You should be able to substitute positive or negative numbers. Take care when substituting in for more than one variable or with powers.
$+ \times + = +$ |
$+ \times - = -$ |
$- \times + = -$ |
$- \times - = +$ |
Substitute the value into the expression and then calculate the answer.
Find the value of $6n+7$ when $n=8$.
$\begin {aligned}6n+7 &= 6 \times 8 + 7 \\ &=\underline {55} \\\end {aligned}$
Find the value of $6n+7$ when $n=-2$.
$\begin {aligned}6n+7 &= 6 \times -2 + 7 \\ &= \underline{-5} \\\end {aligned}$
Find the value of $\frac {ab} c$ when $a=15, b=4, c=3$.
$\begin {aligned}\frac {ab} c &= \frac {15 \times 4} 3 \\ &= \underline{20} \\\end {aligned}$
The volume of the cuboid is given by $V = Lwh$. Find the volume when $L=5, w=2, h=3$.
$\begin {aligned}V &= L \times w \times h \\& = 5 \times 2 \times 3 \\&= \underline{30} \end {aligned}$
Substitution means replacing the variable with a number. Substitution helps find the value of simple expressions and formulae. You should be able to substitute positive or negative numbers. Take care when substituting in for more than one variable or with powers.
$+ \times + = +$ |
$+ \times - = -$ |
$- \times + = -$ |
$- \times - = +$ |
Substitute the value into the expression and then calculate the answer.
Find the value of $6n+7$ when $n=8$.
$\begin {aligned}6n+7 &= 6 \times 8 + 7 \\ &=\underline {55} \\\end {aligned}$
Find the value of $6n+7$ when $n=-2$.
$\begin {aligned}6n+7 &= 6 \times -2 + 7 \\ &= \underline{-5} \\\end {aligned}$
Find the value of $\frac {ab} c$ when $a=15, b=4, c=3$.
$\begin {aligned}\frac {ab} c &= \frac {15 \times 4} 3 \\ &= \underline{20} \\\end {aligned}$
The volume of the cuboid is given by $V = Lwh$. Find the volume when $L=5, w=2, h=3$.
$\begin {aligned}V &= L \times w \times h \\& = 5 \times 2 \times 3 \\&= \underline{30} \end {aligned}$
FAQs
Question: What are the rule for multiplying negative numbers?
Answer: When multiplying two numbers, if one of the numbers is positive and one is negative, then the answer will be negative. If both numbers are negative, then the answer will be positive.
Question: What is substitution?
Answer: Substitution means replacing. In algebra we replace the variable (or letter) with a number.
Question: What is substituting into an expression?
Answer: Substitution means replacing the variables in an algebraic expression with their numerical values. We can then work out the value of the expression.
Theory
Exercises
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