Ratio

Ratio

A ratio is a comparison of two numbers. 

Examples:

Jeannine has a bag with 3 videocassettes, 4 marbles, 7 books, and 1 orange.

1) What is the ratio of books to marbles?

A ratio is a comparison between two or more like quantities in the same units.

Note:

The ratio 1 : 2 is read as '1 to 2' or '1 is to 2'.

Scale Factor

If the ratio is expressed in the form 1 : n, then n is called the scale factor.
E.g.  5 : 20 = 1 : 4
So, 4 is the scale factor.

Note:

We can use ratios to compare more than two quantities conveniently.  Fractions are not usually suitable for this.

 Ratios are used in areas including concentration of solutions, drug dosages, financial mathematics and gears.

Comparing Ratios

To compare ratios, write them as fractions. The ratios are equal if they are equal when written as fractions.
Example:
Are the ratios 3 to 4 and 6:8 equal?
The ratios are equal if 3/4 = 6/8.
These are equal if their cross products are equal; that is, if 3 × 8 = 4 × 6. Since both of these products equal 24, the answer is yes, the ratios are equal.

proportion (Meaning)

pro·por·tion  (pr-pôrshn, -pr-)

n.

1. A part considered in relation to the whole.

2. A relationship between things or parts of things with respect to comparative magnitude, quantity, or degree: the proper proportion between oil and vinegar in the dressing.

3. A relationship between quantities such that if one varies then another varies in a manner dependent on the first: "We do not always find visible happiness in proportion to visible virtue" (Samuel Johnson).

4. Agreeable or harmonious relation of parts within a whole; balance or symmetry.

5. Dimensions; size. Often used in the plural.

6. Mathematics A statement of equality between two ratios. Four quantities, a, b, c, d, are said to be in proportion if ^a/_b = ^c/_d .

tr.v. pro·por·tioned, pro·por·tion·ing, pro·por·tions

1. To adjust so that proper relations between parts are attained.

2. To form the parts of with balance or symmetry.

Proportion

A proportion is an equation with a ratio on each side. It is a statement that two ratios are equal. 

When one of the four numbers in a proportion is unknown, cross products may be used to find the unknown number. This is called solving the proportion.

We compare rates just as we compare ratios, by cross multiplying

Rate

A rate is a ratio

Problems involving rates typically involve setting two ratios equal to each other and solving for an unknown quantity, that is, solving a proportion.


When comparing rates, always check to see which units of measurement are being used. For instance, 3 kilometers per hour is very different from 3 meters per hour! 

Important:

One of the most useful tips in solving any math or science problem is to always write out the units when multiplying, dividing, or converting from one unit to another.

Average Rate of Speed

The average rate of speed for a trip is the total distance traveled divided by the total time of the trip.

Increasing or Decreasing a Quantity in a Given Ratio

If the ratio of a new quantity to an old quantity can be expressed as an improper fraction, then the new quantity is greater than the old quantity.  Applying this ratio to the old quantity is known as increasing the old quantity in a given ratio. If the ratio of a new quantity to an old quantity can be expressed as a proper fraction, then the new quantity is less than the old quantity.  Applying this ratio to the old quantity is known as decreasing the old quantity in a given ratio.

Example 8

Increase 20 in the ratio 3 : 2.

Solution:

Example 9

Decrease 32 in the ratio 3 : 4.

Using a Ratio to Solve Problems

If the ratio of two quantities is known and one of the quantities is given, then the other quantity can be calculated. Example 10 A company wants to reduce its operating cost in the ratio 2 : 3. If the operating cost was $51000 last year, what would be its target cost? to be continue............. http://www.mathsteacher.com.au/year8/ch06_ratios/05_divide/ratio.htm Golden_ratio