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

xyy=aby

xb=abyb

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

2161640?=5401640

2161640?=5401640

240?=516

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

288=x1008

2100=8x100100

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.

0.270.271100=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