1.How many fluid ounces are in 9 And 1/2 cups? Write a proportion and solve. 2. About how many centimeters are in 70 inches? Write a proportion and solve.
3. Find the unit rate for 90% books to 10% magazines. Consider the unit rate to be the number of books per magazine. unit rate=
4. Find the unit rate for 60% water to 40% juice. Consider the unit rate to be the number of liters of water per 1 liter of juice. Unite rate=
5. Find the percentage of red balls and the percentage of green balls in the basket if the unit rate is 1 (Note: The unit rate is the number of red balls per one green ball.)
% red balls to ___%of green balls

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MATH REVIEW: USEFUL MATH FOR EVERYONE

SECTION 1.2. RATIOS AND PROPORTIONS

Ratios and Proportions

Algebraic Expressions

Exponents

Logarithms

Glossary and Links

back to Ratios, Page 1

A proportion is similar to a ratio, except that it indicates a part of a whole, and so the numerator arises from the denominator. For instance, a researcher might say that, for every ten students in the residence hall, five were women. Five over ten (5 / 10) is a proportion. Proportions must have all of the numbers in the same units, and are frequently written as fractions.

What happens when you want to write a proportion, but the numbers are given in different units? Suppose you were asked to write the proportion of 3 cups to 56 ounces (3 cups out of 56 ounces). You must write a proportion of either cups to cups (cups:cups) or ounces to ounces (ounces:ounces), so you will have to convert one of the numbers so that both numbers are expressed in the same unit of measurement. Let's convert cups to ounces so we can express the ratio as ounces:ounces. Since there are 8 ounces in one cup, 3 cups are equal to 24 ounces:

3 cups * 8 ounces/cup = 24 ounces

Now the two numbers 3 cups and 56 ounces can be written as the following ratio:

24 ounces to 56 ounces,

24:56,

or, now that the unit of measurement is the same, 24:56 can also be written as a proportion:

24/56

You may need to solve some problems involving ratios.

If you divided 36 into two parts in the ratio of 1:2 and one part is a and the other is b, you can find the value of a and b:

You know that

a+b = 36

And

a/b = 1/2

You can use these equations to solve for a and b, or you can use the following simple method:

Find out how many units are in 1 part of the ratio. To do this, divide the total by the number of parts.

Number of parts: 1 + 2 = 3.

Number of units in each part: 36/3 = 12.

Then, multiply the number of units in each part by the number of parts in each variable.

a = 1 * 12 = 12

b = 2 * 12 = 24

As an aside . . .

Percentages are so frequently used that we should spend a little time on them here. The powerful thing about percentages is that they all have the same denominator: 100. When two fractions have the same denominator, comparisions can be made very easily.

0.21 = 21% = 21 / 100

Step-by-step explanation:

24: 56

step-by-step explanation:

24 can be divided into 3 and 56 can be divided into 7, where as all the other ratios can't.

geometric series converge the common ratio r has magnitude less than one.

which is equivalent to

for the example we need

|2-x| < 1

-1 < 2-x   and 2-x < 1

x < 3 and x > 1

we can write that

answer: 1 < x < 3

1a. common ratio r=250/25=10 > 1     diverges

1b.   r=50/100=1/2 converges

when these converge they converge to

where a is the first term.

answer: 200

1c. r=-1   so it's not the case that |r| < 1.     diverges

2a. x is the common ratio so we converge when |x|< 1

2b.   r=-10x / -2 = 5x.

we converge when

|5x| < 1

|x| < 1/5

2c.   r=3-2x

-1 < 3-2x and 3-2x < 1

-4 < -2x and 2 < 2x

x < 2 and 1 < x

1 < x < 2

2d. [/tex] r=-48x^3/12 = 4x^3[/tex]

|4x^3| < 1

|x^3| < \frac 1 4

|x| < 4^{-1/3}