ch3

Ratio, Proportion & Percentage

ratio

• A ratio is a comparison of two similar quantities obtained by dividing one quantity by the other.

The ratio of 6 to 3 The ratio of 3 to 6

• a comparison or relation between quantities

>>> the ratio of 6 miles to 3 miles is only 2, not 2 miles

• can be written as fractions

• Can be a ratio only if it is expressed in terms of the same unit

• Can you find these ratios?

• 5 dollars to 25 cents

• 3.4 meters to 3 kilograms

• 5 dollars = 500 centsso, the ratio of 500 cents to 25 cents = 500 / 25 = 20

• Meters cannot be expressed in terms of kilograms, so this ratio cannot be expressd.

• An eccentric person leaves instructions in his will that a certain sum of money is to be divided between his relatives so that Patrick will receive half and Quentin will receive one fifth. The remainder is to be divided so that Rufus receives three quarters and the rest goes to Simon.If Simon eventually received �324 how much did each of the rest receive? How much money had been divided between his relatives?

• The money for Rufus and Simon was divided in the ratio 3:1 so Simon's �324 was one part of it.Therefore Rufus received 3 x �324 = �972 and between them they received �1296.

• Now we need to find what fraction this was of the total amount of money left to the relatives.

• We know that half went to Patrick and one fifth to Quentin.

• The �1296 to be divided between Rufus and Simon was 3/10 of the total.>>> Therefore �1296/3 = �432 is 1/10 of the total and the eccentric left 10 x �432 = �4320 to be divided between his relatives.

• Of this, Patrick received �4320/2 = �2160 and Quentin received �4320/5 = �864.

proportion

• A proportion is a statement of the equality of two ratios.

Cross multiplying

There are 48 beads in a jar. For every 2 purple beads there are 6 red beads. How many red beads are

there altogether?

• Add the 2 and 6 together to make 8. If you then divide 48 by 8 you get 6.

• To find out how many purple and red beads, you would multiply 2 and 6 by 6 = 12, 36

Proprotion problems

• Find the value of x in 16 : 8 = x : 5

• A pipe transfers 236 gallons of fuel to the tank of a ship in 2 hours. How long will it take to fill the tank of the ship that holds 4543 gallons?

How to find A: B: C, if A: B and B: C are given?

Let A: B = 2: 3, and B: C = 4: 5, then

A: B: C = ?

Ans

A: B: C = 8: 12: 15

Percent (%)

• Percent means "out of 100.“

• 8 out of every 100 professional basketball players are female," >>>>> "8% of professional basketball players are female."

• a decimal can be written as a percent, by moving the decimal point two places to the right :

In a school, 25 % of the teachers teach basic math. If there are 50 basic math teachers, how many teachers are there in the

school?

• 25% of all teachers in the school equal number of teachers teaching basic math = 50

• 25% of ____ = 50

or 25% × ___ = 50

or 0.25 × ____ = 50

ANS

50/0.25 = 200Therefore, we have 200

teachers in the school

In fact, 0.25 × 200 = 50

24 students in a class took an algebra test. If 18 students passed the test, what percent do not pass?

• Number of students who did not pass is 24 − 18 = 6

>>> 6/24 = 0.25 = 25/100 = 25%

therefore 25% of students did not pass

Move the decimal point two places to the right to change it from a decimal to a percent

Discount

A $12 baseball cap is $15 after tax. What was the sales tax percentage?

Sale tax

A $25 pair of jeans is on sale at 60% off. What is the sale price?

A colony of 4,800 bacteria grows by 20%. How many bacteria are there now?

A video game is on sale at 75% off. The sale price is $15. What was the original price?

An investment grew by 22% and is now worth $1525. How much was invested originally?

Interest

• how much is paid for the use of money (as a percent, or an amount)

• Alex wants to borrow $1,000. The local bank says "10% Interest". So to borrow the $1,000 for 1 year will cost:

$1,000 × 10% = $100

Simple interest

• Alex borrows $1,000 for 5 Years, at 10% simple interest:

• Interest = $1,000 × 10% x 5 Years = $500• Plus the Principal of $1,000 means Alex needs to pay $1,500 after 5 Years

Jan borrowed $3,000 for 4 Years at 5% interest rate, how much interest is that?

Compound interest

• Alex would pay $110 interest in the second year, not just $100.

• Because Alex is paying 10% on $1,100 not just $1,000

You take out a loan of £800 and the bank charges you 15% compound interest per year. If you don't

pay off any of the loan in 4 years, how much would you owe the bank?

• After 1 year you would owe the bank £800 x 1.15 = £920.

• how much is owed after four years ?

• >>>> £800 x 1.154 = £1399.21

You invest £4000 in a fund which earns an 11% compound return per year. How much would the

fund be worth after 10 years?

• for 10 years we the sum on our calculator will be £4000 x 1.1110 = £11357.68

If you have a bank account principle = $1000, and your bank compounds the interest twice a year

at an interest rate of 5%, how much money do you have in your account at the year's end?