Transcript 1.5 ( + ) and ( - ) numbers
7.2 Percentages:
You can represent β
a
percent proportion:
is p percent of b
β using the
π πππ
=
π π ο % πππ
Ex: what percent of 56 is 42?
% πππ ππ
=
ππ ο π πππ ππ
=
ππ ππ
=
ππ
cross multiply
ο
divide by 56
ο
56(x) = 100(42) x = 4200/56
π πππ
=
π π ο % πππ ππ
=
ππ
Ex: 125% of what number is 17.5?
% πππ ππ
=
ππ ο πππ πππ
=
ππ.π π
cross multiply
ο
divide by 125
ο
125(x) = 100(17.5) x = 1750/125
π πππ
=
π π ο % πππ ππ
=
ππ
Ex: A family sells a car to a dealership for 60% less than they paid for it. They paid $9000? For the car. What was the price they sold it the car for?
% πππ ππ
=
ππ ο ππ πππ π
=
ππππ
cross multiply
ο
60(9000) = 100(x) divide by 100
ο
x = 540000/100
CLASSWORK: Page 141-142 Problems: 9, 14, 17, 21, 23, 29, 47, 49
2.10 Change Expressed as Percent:
Percent change is the ratio of the amount of change to the original amount: Percent Change
:
πππππ ππ ππππππππ ππ π πππππππ ππππππππ ππππππ
Amount of Increase:
new amount β original amount
Amount of decrease:
original amount β new amount
The average monthly precipitation of Chicago, Illinois, peaks in June at 4.1 in. The average monthly precipitation in December is 2.8 in.
What is the percent decrease from June to December?
πππππ ππ π πππππππ
Percent Change
:
ππππππππ ππππππ
Percent Change
:
ππππππππ βπππ ππππππππ ππππππ
Percent Change
:
π.π βπ.π π.π π.π
=
π.π =
0.317 = 32%
In one year the toll for the passenger cars to use a tunnel rose from $3 to $3.50.
What was the percent increase?
Percent Change
:
πππππ ππ ππππππππ ππππππππ ππππππ
Percent Change
:
πππ βππππππππ ππππππππ ππππππ
Percent Change
:
π.ππ βπ π
=
π.ππ π =
0.166 = 17%
RELATIVE ERROR
:
| ππππππππ ππ ππππππππ πππππ β ππππππ πππππ | ππππππ πππππ
PERCENT ERROR: relative error in percent You think that the distance between your house and a friendβs house is 5.5 mi. The actual distance is 4.75 mi.
What is the percent error in your estimation?
RELATIVE ERROR :
| ππππππππ ππ ππππππππ πππππ β ππππππ πππππ | ππππππ πππππ
You think that the distance between your house and a friendβs house is 5.5 mi. The actual distance is 4.75 mi.
What is the percent error in your estimation?
RELATIVE ERROR :
| π.π ππ β π.ππ ππ | π.ππ ππ | π.ππ ππ | π.ππ ππ
= 0.157 = 16%
CLASS WORK: Pages: 148-149 Problems: 7, 17, 19, 28
MAXIMUM & MINIMUM : The most any measurement can be off by is one half of the unit used in measuring.
Ex: A studentβs height is measured as 66 in. to the nearest in. What are the studentβs maximum and minimum possible heights?
Maximum: (half of the unit more) Since the height is 66 in. and we are using inches, then maximum is .5 in more.
ο
66in. + 0.5 in.= 66.5 in Minimum: (half of the unit less) Since the height is 66 in. and we are using inches, then maximum is .5 in less.
ο
66in. - 0.5 in.= 65.5 in.
MAXIMUM & MINIMUM: The most any measurement can be off by is one half of the unit used in measuring Ex: An ostrich egg has a mass of 1.1 kg. to the nearest tenth of a kg. Find the minimum and maximum possible measurements.
Maximum: (half of the unit more) Since the mass is 1.1 kg and and we are using decimal, then maximum is .05 more since Β½ of 0.1 is 0.05
ο
1.1 kg. + 0.05 kg= 1.15 kg. Minimum: (half of the unit less) Since the mass is 1.1 kg and and we are using decimal, then minimum is .05 less since Β½ of 0.1 is 0.05
ο
1.1 kg. - 0.05 kg= 1.05 kg.