chapter 6 & 7 notes

A ratio is the quotient of two quantities.

example( a: b)

Rates are used to compare different kinds of quantities.

example 32 miles/12gallons

example(2/24=1/12)

A proportion is a statement that two ratios or rates are equal.

percent comes from the Latin phrase pre centum, which means "per 100. The "%" symbol is used to denote percent.

example: 7% = 7/100

Writing percent as a decimal. Replace the percent symbol with its decimal equivalent, 0.01; then multiply.

example: 43% = 43(0.01) = 0.43

Writing a precent as a fraction. Replace the symbol with its fraction equivalent, 1/100; then multiply. Don't forget to simplify the fraction if possible.

example: 40% = 40 . 1/100 = 40/1 . 1/100 = 40/100 = 2/5

Recognizing key words in a percent problem is helpful in writing the problem as an equation. Three key words in the statement of a percent problem and their meanings are as follows: of means multiplication (.) is means equal (=) what (or some equivalent) means the unknown number.

example: 5 is what percent of 20? 5 = x . 20 = x = 0.25

When we translate percent problems to proportions, the percent, p, can be identified by looking for the symbol % or the word percent. The base, b, usually follows the word of. The amount, a, is the part compared to the whole.

amount/base = percent/100 or a/b = p/100

Example: what number is 4% of 2174? x = 4% . 2174 x = 0.04. 2174 x = 86.96 x = 87

Interest is money charged for using other people's money. When you loan or invest money, you earn interest. The money borrowed, loaned, or invested is called the principal amount, or simply principal. Interest is normally stated in terms of a percent of the principal for a given period of time. The interest rate is the percent used in computing the interest. Unless stated otherwise, the rate is understood to be per year. When the interest is computed on the original principal, it is called simple interest.

I = P.R.T

Writing proportions is a powerful tool for solving problems in almost every field, including business,chemistry, biology, health sciences, and engineering, as well as in daily life.

example: 5miles over 2 inches = x miles over 7inches cross multiply and 5.7=2.x , 35 =2x, divided both by 2, and x = 17.5

example: a square root of 25 is 5 because 5.5 = 25

The square root of a positive number (a) is the positive number (b) whose square is (a). if b2 = a

Two triangles are congruent when they have the same shape and the same size.