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.

20 = 40

1 2

A proportion is read as "x is to y as a is to b“.

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 justcheck their cross products.

x/y = a/b

x/y • y = a/b • y

x • b = a/b • yb

xb = ay

Example: Use cross product to determine if the two ratios form a proportion.

Here we can see that 2/16 and 5/40 are proportions since their cross products are equal.

2/16, 5 /40

2/16 =? 5/40

2/16 • 16 • 40 =? 5/40 • 16 • 40

2/16 • 16 • 40 =? 5/40 • 16 • 40

2• 40 =? 5 • 16

80 = 80

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.

2/8 = x/100

2/8 • 8 = x/100 • 8

2 • 100 = 8x/100 • 100

200/8 = 8x/8

X = 25%

This proportion is called the percent proportion.

a = x

b 100

Fractions, percent and decimals can all represent the same number, but they are expressed differently.

Decimal and 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 0.27/1 • 100 = 27/100 or 27%

Percent as decimal: write the percent as a fraction with the denominator 100. A good thing to remember is that 100% = 1 since 100/100 = 1.

Example:

Write 89% as a decimal.

x/100 = 89/100 = 0.89

Video lesson: Write in percent or as decimals

To see the solution look at the video in the next page.

Let’s do an exercise in which we talk about converting things between decimals and percentages and vice versa. So if we’re given a percentage say 37%, can we re-write this as a decimal? It’s actually a very simple exercise. The basic rule is you take the decimal place, which is of course after the numbers here, and move it to the left two. That’s because a percentage is a number divided by 100. So this is 37 out of 100 so 37%. So again the rule is just move the decimal places over 2. So this percentage is the same as the decimal of 0.37. So we’ve just moved the decimal place over two. Now if we want to write something from a decimal to a percentage, say we have 0.04, we can write that as a percentage by doing the opposite; moving the decimal place to the right two. So if we do that in this case, then we have 4%. So 0.04 is the same as 4% because this divided by 100 gives us this decimal.

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