RATIO- FINDING THE RELATIONSHIPS BETWEEN ITEMS
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THERE ARE 3 WAYS Item to item Item to all items Some items to some items
The order you are asked is important. Writing it in the wrong order is wrong
Ratios-percentHow do we write ratios? o In word form o In colon form o In fraction form
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Ratio of black notes to all notes
6 to 8 6:8 6 8
Equivalent ratios Ratios can be made bigger and smaller by simply multiply the left and right side by the same number
EG. 4:10 dentist prefer a certain brand of tooth brush. If 100 dentists were asked how many liked that tooth brush. 4 to 10 means 4 out of a total of 10. By changing the total to 100 we multiply the 10 by 10. Therefore, we must multiply the 4 by 10 to get 40 dentists.
How do we write percent There are 3 ways to write percent: a) Words
Twenty five percent
b) Symbol c) Fraction out of 100
25% 25 100
Exploring percentEstimating % on a shape (benchmarks) We use successive approximate estimations. This is a estimation that adds on to other estimation.
25% rule- A square or circle can be divided into 4 equal parts. 33% rule- A square or circle can be divided into 3 equal parts. 50% rule- A square or circle can be broken into 2 equal halves.
Exploring percentEstimating % on a shape 2this is purple? How much or Since this can be broken into 4 quarters, we can estimate this is 25%+ 25%+ 25% or 75%.
Here we can see it is less than 25%. It is roughly in the middle of 25% therefore 13%
Exploring percentgrid math Percent means out of an equal division of 100 pieces. A 10x10 grid is divided 100 ways equally. When we shade in some pieces we can find percent out of 100
Colour in and show students
Exploring Percent- Number lines Estimating with benchmarks We can look at the length of a numberline and estimate how far something is by using bench marks 25% 33% 50%
0%
25%
0%
33%
0%
50%
75% 100%
66%
50%
100%
100%
There are 2 ways to make a fraction into a percent ďƒź Division and multiplication ďƒź Find an equivalent fraction over 100
A percent can be made a fraction in only one way
Exploring PercentHow are they related to fractions? Take your bottom number and divide into top then multiply the answer by 100 and round to a whole number Multiply the numerator and denominator by the same number so that the denominator equals 100. The numerator is the percent You take the percent and put it over 100. Reduce until it is in lowest terms
Eg. 23 =96% 24
Exploring Percent- Converting to decimal There are two ways to do this A. Division by 100
B. Moving a decimal 2 step to the left
23% = 23 รท 100 = 0.23 8% = 8 รท 100 = 0.08
18% = 018.0 move decimal two places left = 0.18 1% = 001.0 move decimal two places left = 0.01
Exploring Percent-mixed formats Rank these greatest to least Some times you may need to compare two or more formats. The best solution is to convert them all to one easiest format, rank them then give the answer in the old format you started with.
15%
7 0.12 10 a) 15%= 15% b) 7 70 10= 100 =70% c) 0.12 = 0.12 x100= 12% Therefore greatest to least is 7 , 15%, 0.12 10