Ratios, Proportions, Unit rates, percents
uinit rates
ratios
rate
small to big
meaning
example
how many times a number fits in a other number
or the comparison of two numbers
meaning
Ratios are a comparison of two values, ideas, or quantities. They can be written in a couple of different ways.
example
click to edit
If three shirts cost 300 Rand we can say that : Rands compared to Shirts
R300 to 3 shirts
R300 : 3 Shirts
R3003 Shirts This is the one that we will use most.
Like fractions these can be reduced just as the same by using division. They can also be manipulated to create and look at different comparisons, the same finding equivalent fractions.
Reducing: R30033 Shirts3=R1001 shirt
How much do 6 shirts cost? R300(2)3 Shirts(2)=R6006 shirts or R30033 Shirts3=R100(6)1 shirt(6)=R6006/ shirts
meaning
A unit rate is a rate per 1
ecample
for example, 12 people share 2 pies equally. One unit rate is 6 people per pie, because 12 divided by 2 = 6. The other unit rate is 1/6 of a pie, because 2 divieded by 12 = 1/6
how do you compare rates/ unit rates
you have 2 numbers
you try to get to one to a different number
times them by a number which will get you to the number you want to get to
big to small
how do we do it?
because we are going from small to larger units, we have to divide to make bigger pieces (taking smaller pieces and combining them to get bigger pieces).
by what do we divide?
You take the amount that you have and divide by the conversion factor.
how do we do it?
because we are cutting the big units into smaller pieces (many more of them) we use multiplication.
by what do we multiply?
You multiply the amount that you have by the conversion factor.
precent
number line
tape diagrams
butterfly method
method 2
2)divide by where you are going by where you started
1)
Checking your work
different strategies
Equivalent ratios are equal and the same value but look differently
Equivalent ratios are fractions
Fractions are division problems
Convert the ratios to decimals by dividing
Since equivalent ratios are equal, the decimals have to be the same