Percent means per cent, per 100: 34 % = 34 / 100
· Review: express as a fraction, decimal and as a percentage:
1/8, 0.45, 0.3333, 23%, 110%
· Ratios: find the ratio of A to B, B to A, A is …. Percent of B:
A = 150, B = 25.
A = 75, B = 480.
· Express first as percentage of second: 25 women in a room of 113 people.
Change: (one thing changes)
Absolute change = new value – reference value
Relative change = (new value – reference value)/ reference value
· Consumer debt in the US increased from $160 billion in 1974 to $850 billion in 1995.
Find the absolute and relative change.
Difference: (2 things differ)
Absolute difference = compared value – reference value
Relative difference = (compared value – reference value)/ reference value
· In 1996, Saudi Arabia produced 8.2 million barrels of crude per day
The US produced 6.4 million barrels of crude per day
Absolute difference?
Relative difference computed 2 ways, with US as reference value, with Saudi Arabia as reference value?
Of versus more than
If the compared value is P% more than the reference value, it is (100 + P)% of the reference value.
Similarly for less than.
· If Jack weighs 40% more than Jill, his weight is …% of Jill’s weight.
· The wholesale cost of a car is 40% less than its retail cost. Therefore the retail cost is … times the wholesale cost.
“percentage points”: absolute change or difference.
“%” or “percent”: relative change or difference.
· The percentage of highschool seniors using alcohol decreased 68.2% in 1975 to 52.7% in 1997.
Express the change in 2 ways: absolute difference in terms of percentage points.
Relative difference in terms of %.
Solving Percentage Problems:
If the compared value is P% more than the reference value:
Compared value = (100 + P)% * reference value
· Bagel sales have reached $3 billion and are growing 20% annually according to Lehman Brothers. At this growth rate, how much will be spent on bagels next year?
Compared value = (100 +20)% * 3 billion
· Your property taxes increase 5% one year and 6% next year. The total tax increase is 11%. True or False, explain.
Beware of shifting reference values!
· The price of cellular service has decreased 150% in the last 10 years.
· Real estate prices have increased 450% in the last 10 years.
· A class with 25 students had an 86% average on the midterm.
A class with 70 students had an 80% average on the midterm.
Total average is 85%?