RATIOS AND RATES

GOALS

1. relate ratios to fractions, percents, and decimal

2. use strategies to divide and multiply decimals

3. use scale factor to find distances or lengths

4. understand relationships among ratios, rates, and averages and use them to solve problems

5. identify scale factors in situations of enlargement and reduction

6. identify and use constant and variable relationships

7. distinguish between part-part and part-whole ratios and use either appropriately in problem situations

8. analyze and solve problems dealing with absolute and relative comparisons

9. determine whether and how ratios can be used to solve problems

SECTION SUMMARIES

SECTION A: SINGLE NUMBER RATIOS

1. Ratios can be written as single numbers and used to express averages ( 65 miles per hour ).

2. To do this you may use ratio tables and write equivalent ratios until the second number is one, or you can divide the 1^st number by the 2^nd number. It is important to determine the appropriate number of decimal places to carry out your division.

SECTION B: COMPARISONS

1. Numbers can be used to make comparisons.

2. Comparisons can be absolute, or direct comparisons of numbers such as the total number of telephones in different countries.

3. Comparisons can also be relative, comparing the numbers to a given base, such as telephones per person. This can be written as a ratio or as a single number (an average).

SECTION C: DIFFERENT KINDS OF RATIOS

1. An example of a part-part ratio would be the # of cars speeding to the # of cars not speeding.

2. An example of a part-whole ratio would be the # of cars speeding to the total # of cars.

3. Only a part-whole ratio can be written as a percent.

4. There are different strategies you can use to write a ratio as a percent.

a. You can use the relationship between fractions and percents.

b. You can rewrite the ratio as a comparison to 100.

c. You can use the relationships among fractions, decimals, and percents.

SECTION D: CONSTANT AND VARIABLE RELATIONSHIPS

1. A relationship is constant if the ratio between the two parts stays the same. (the relationship between the circumference and diameter of a circle)

2. A ratio can be written as a fraction, decimal, percent, or with a colon ( : ) .

SECTION E: SCALE FACTORS

1. A scale factor is a number indicating the amount by which a picture has been enlarged or reduced.

2. A scale factor greater than one represents an enlargement, while a scale factor less than one represents a reduction.

3. The use of a scale factor can be shown with arrow language. If you know the original dimension you can then find the dimensions of the enlargement/reduction. Original Ù enlargement/reduction

4. If you know the dimensions of the enlargement or reduction, you can use a reverse arrow to find the original dimension. Original Ù enlargement/reduction.