Chapter 7: Ratios, Proportions, and Percentages 85An extended ratio compares more than two numbers. Extended ratios are usually written with
colons, because you don’t want to put more than two numbers into a fraction. Extended ratios
are actually a condensed version of several ratios. If the apples, oranges, and pears in a fruit bowl
are in ratio 8:3:2, it means that that the number of apples is 8 times some number, the number of
oranges is 3 times that number, and the number of pears is 2 times that number. It also means
that the ratio of apples to oranges is 8:3, the ratio of oranges to pears is 3:2 and the ratio of apples
to pears is 8:2.
DEFINITION
An extended ratio combines several related ratios into one statement. It is a way to
express the ratios a:b, b:c, and a:c in one statement: a:b:c.Suppose that a smoothie contains pomegranate juice, orange juice, and yogurt, in a ratio of 2:5:3.
If you want to make 5 cups of the smoothie to sip throughout the day, how much of each ingredi-
ent will you need? If the numbers actually were 2 and 5 and 3, they would add to 10 cups. You
need 5 cups, so let’s say 2n cups of pomegranate juice, 5n cups of orange juice, and 3n cups of
yogurt, to make a total of 5 cups.
2 n + 5n + 3n = 5
10 n = 5
n =^1
2
The multiplier is^1
2
, so you need 2 1
2
1 cup of pomegranate juice, 5 1
2
21
2
cups of orange juice,
and 3 1
2
11
2
cups of yogurt.
MATH TRAP
When you’re working with ratios that involve measurements, make sure the units
match. If you try to say the ratio of the length to the width of a room is 15 feet to 120
inches, when you go on to use that relationship, you’ll be confused about whether
your numbers are feet or inches, and you’ll likely get the wrong numbers. Make it
15 feet by 10 feet or 180 inches by 120 inches, and your work will be easier and more
accurate.