Download REVIEW NOTES FOR THE SECOND BENCHMARK TEST

REVIEW NOTES FOR THE SECOND BENCHMARK TEST
(SOL 7.4)
SIMPLE INTEREST
To find simple interest:
Principal X time X rate
Principal: The amount of money involved.
The amount of money borrowed.
The money amount of the loan.
The amount of money in the account.
Rate: the percent or the number with the % symbol
Time:
the length of time you get to pay off the loan. Time is usually given in years. If the time is given in
months, write the time as a fraction which you convert to a decimal.
Example: the time is 8 months. Think: since a year is equal to 12 months write the fraction as
8/12. Now convert 8/12 into a decimal by dividing 8 by 12.
8/12 = 8 ÷ 12 = .666
Use the decimal when working out the problem
EXAMPLE 1
$100 at 6% for 8 months
Think: (8 months is the same as .666)
100 X .666 X 6 hit % key
(when you hit the % key the number that appears is the answer to the problem)
EXAMPLE 2
$560 at 12 ¾ % for 2 years
think: ¾ is the same as .75 so
$560 X 2 X 12.75 hit % key
USING PERCENTS
The percent proportion:
PART
NUMBER
=
RATE
100
To solve a percent proportion, cross multiply the numbers you can and divide by the extra number.
Example:
15
48
=
X
100
multiply 15 times 100 and divide by 48 (the extra number)
FINDING DISCOUNT
To find amount of discount: amount of money X % (hit % key) answer is the amount of discount.
To find rate of discount: (old price – new price) ÷ old price X 100 answer is the rate of discount
To find the price after a discount is taken: find the amount of discount and subtract it from the
original price, what is left is the amount you pay
FINDING SALES TAX
To find sales tax: amount of money times the tax rate (hit % key) answer is the amount of
To find the cost of an item plus sales tax: amount of money times the tax rate (hit % key) take your
answer and add it to the cost of the item.
FINDING TIPS
To find a 10% tip: take the cost of the meal and move the decimal point one place to the LEFT, this
is the amount of tip you pay
To find a 15% tip: take the cost of the meal times 15 (hit the % key), the answer is the amount of tip
you pay
(SOL 7.6)
RATIOS, RATES, UNIT RATES, PROPORTIONS
A percent is simply another way of writing the ratio “something to 100”
Example: 80% is the same as “80: 100”
A ratio can be written 3 different ways:
3 (Fraction format)
4
3:4
3 to 4
A ratio is a comparison of two like or same items. (students : students)
A rate is a comparison of two different items (students : books)
A unit rate is a comparison of items to 1. (# of books : 1)
A proportion is an equation that has two equivalent ratios. 2 = 5
4
10
CHECKING A PROPORTION
To check to see if two ratios form a proportion, use cross-multiplication. When you cross-multiply
the answer in each case should be the same if it is a proportion. If they are not the same it is not a
proportion.
FINDING A UNIT RATE
To find a unit rate, divide the numerator (top number or first number in the rate) by the denominator
(bottom number or second number in the rate)
CHANGING A RATIO INTO A PERCENT
To change a ratio into a percent: form a decimal by dividing the numerator by the denominator;
move the decimal point two places to the right and add “%”
(SOL 7.22)
LINEAR EQUATIONS AND INEQUALITIES
A one-step equation requires the use of one operation to solve.
Example: x + 3 = -4
A one-step inequality requires the use of one operation to find the solution set.
Example: x - 4 > 9
The inverse or opposite operation for addition is subtraction, for subtraction it is addition.
The inverse or opposite operation for multiplication is division, for division it is multiplication.
Remember: when inequalities are multiplied or divided by negative numbers, the inequality
symbol reverses.
Example: -3x < 15
To solve you will divide each side of the inequality by -3 which causes
the inequality symbol to reverse or flip. Your solution set becomes:
x > -5