Proportions and percent
A proportion is an equation that says that two or more ratios are equal. For instance if one package of cookies contain 20 cookies that would mean that 2 packages contain 40 cookies
201=402
A proportion is read as "x is to y as a is to b".
xy=ab
xy⋅y=ab⋅y
x⋅b=ab⋅yb
xb=ay
The products xb and ay are called cross products. The cross products of a proportion are always equal. If we want to check if two ratios form a proportion we can just check their cross products.
Example
Use cross product to determine if the two ratios form a proportion.
216,540
216?=540
216⋅16⋅40?=540⋅16⋅40
216⋅16⋅40?=540⋅16⋅40
2⋅40?=5⋅16
80=80
Here we can see that 2/16 and 5/40 are proportions since their cross products are equal.
Percent means hundredths or per hundred and is written with the symbol, %. Percent is a ratio were we compare numbers to 100 which means that 1% is 1/100.
Example
In a box of eight donuts two have pink sprinkles. Try to express how many percent of the donuts in the box that have pink sprinkles using proportions.
28=x100
28⋅8=x100⋅8
2⋅100=8x100⋅100
2008=8x8
x=25%
This proportion is called the percent proportion.
ab=x100
Fractions, percent and decimals can all represent the same number, but they are expressed differently.
Decimal è percent: We can convert decimals into percent by writing the decimal as a fraction with the denominator 1. We then extend the fraction by 100 to get the decimal in percent.
Example
Write 0.27 in percent.
0.27→0.271⋅100=27100or27%
Percent è decimal: write the percent as a fraction with the denominator 100. A good thing to remember is that 100% = 1 since
100100=1
Example
Write 89% as a decimal.
x100=89100=0.89
Video lesson
Write in percent or as decimals