Summary sheet
Key Terms
Ratio and Proportion
Ratio: Comparison of two or more things.
Ways of expressing ratios: 3:4, 4:7, 45:7
Simplifying ratios: 3:6= 1:2
Divide each term by the constant
Simplifying unknown proportions: cross multiply
X/4= 6/8, after cross-multiplying, 8x=24, then divide each sides by 8, 8x/8, 24/8. Therefore 8=3
A problem involving a proportional situation contains data that you must organize to solve problems Solving equations
To solve an equation means to find a numerical value for the variable that satisfies the equation. It makes the equation equal and true.
After solving an equation, a solution can be checked by following the steps below:
• Substitute your solution for the variable in both sides of the original equation.
• Simplify both sides of the equation separately, If both sides simplify to the same number, your solution is correct.
Example:
Solving word problems
In mathematics education, the term word problem is often used to refer to any mathematical exercise where significant background information on the problem is written as text rather than in mathematical notation. Word problems commonly include mathematical modelling questions, where data and information about a certain system is given and you are required to develop a model.
For example: Amber is twenty years younger than Abbey, and in five years' time she will be half her age. What is Amber’s age now?
Strategies
Cross multiplication- Multiply the numerator of the left side fraction with the denominator of the right side fraction. In addition, add the right side denominator with the left side numerator.
GRASS method
G for given- information provided in question
R for required- What are you trying to find? (Variable)
A for arranged- Manipulate the formula
S for substitute + solve- do the work
S for statement- Therefore sign, include units and appropriate decimals.
Rearranging formulae
V= IxR, for finding r...