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What is a ratio?
A ratio is a comparison between two or more quantities or magnitudes
What does ratio tell us?
A ratio gives us information about how parts of a whole relate to each other, and how those parts relate to the whole
A ratio only portrays a relationship between quantities. By itself, it doesn’t provide the actual numbers of those quantities
What is a ratio multiplier?
A ratio multiplier is a value multiplied by both the numerator and denominator of a ratio to represent the actual amounts of two quantities
How can we determine the ratio multiplier?
When we are given the quantity of one of the items
We are given the quantity of all the items in the ratio
Sum of the quantities of each item must equal the total number of items being considered in the ratio. Sometimes the ratio multiplier is not an integer
How do you calculate multipart ratio?
Find the common variable between the two ratios
Make the common variable same by taking the LCM
Are we able to add/subtract/multiply/divide a quantity to get the desired ratio?
To be able to add/subtract/multiply/divide a quantity to get the desired ratio, we must find the actual quantity of each component first. This is applicable for both part-to-part ratios as well as part-to-total ratios
What is proportion?
2 equal ratios are called proportions.
If a/b = c/d, then we have a proportion and it must be true that ad = bc
What is direct variation?
Describes the relationship between 2 variables
If y varies directly with x i.e. if x increases or decreases by a factor, y will increase or decrease by the same factor
Can be represented by y = kx, where k is constant
What is inverse variation?
Describes the relationship between 2 variables
When we have inverse variation between 2 variables x and y, then they can be related by the equation y = k/x, where k is a positive constant. When x increases by a factor, y will decrease by the same factor.
On the other hand, when x decreases by a factor, y will increase by the same factor
What is combined variation?
Single variable can have both direct and inverse variation with one variable and inverse variation with another.
In such situations, both relationships can be combined into one equation
For eg: If y varies directly with x and inversely with z, then the 3 variables are related by the equation y = kx/z, where k is a constant
What is joint variation?
Variable varies directly jointly with 2 other variables if it varies directly with each of them
Eg: If y varies directly jointly with x and z, then the three variables are related by the equation y = kxz, where k is a constant.
A single variable can also vary inversely with 2 other variables simultaneously.
Eg: If y varies inversely jointly with x and z, then the three variables are related by the equation y = k/xz, where k is a constant
Convert from LHS → RHS:
Dollar to cents
Metres to Km
Quarts to pints
1$ = 100cents
1000m = 1Km
1 Quart = 2 Pints
How do you tackle a unit conversion problem in which we need the final answer in squared units?
We raise both sides of the original unit to the second power, and then convert the squared units
How do you tackle a unit conversion problem in which we need the final answer in cubic units?
We raise both sides of the original unit to the third power, and then convert the cubic units
Answer the following questions:
what is:
Area of rectangle
Area of square
Volume of box
Volume of cube
Surface area of box
Surface area of cube
Area of rectangle = Length x width
Area of square = (side)²
Volume of box = length x width x height
Volume of cube = (edge)³
Surface area of box = 2(length x width) + 2(width x height) + 2(length x height)
Surface area of cube = 6(edge)³