Using mental arithmetic to compute with common fractions, decimals, powers, and percents.

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Using mental arithmetic to compute with common
fractions, decimals, powers, and percents.

• By Aron Kollins

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Purpose Slide 1

• To understand common fractions, decimals, and
  percentages related to money by
• mentally computing with the fractions 1/100,
  1/20, 1/10, 1/4 , and 1/2.
• mentally adding, subtracting, multiplying, and
  dividing amounts of money.
• mentally tallying percents.

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Purpose Slide 2

• To understand common powers related to area and
  volume by
• Using the squaring function to determine the area
  of squares.
• Using the cubing function to determine the volume
  of cubes.

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Academic Standards and Prerequisites.

• The Indiana Academic Standard associated with
  this lesson is 8.2.4..
• Prior knowledge of fractions, decimals,
  percentages, and powers is required.

Link to standard 8.2.4.
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What fraction of a Dollar is each coin?
What decimal is each of coins?
What percentage of a Dollar is each coin?
50
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Fractions

• If two people gave me a quarter of a Dollar each,
  what fraction of a Dollar would I be given?

Two quarters equal half a Dollar. 1/41/42/41/2
0.250.250.50
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Fractions

• If then I was also given a tenth and a twentieth
  of a Dollar from another person, what fraction of
  a dollar would I have?

A tenth and twentieth of a Dollar is a 0.10 and
0.20 respectively. Thus, you have sixty-five
cents which is sixty-five hundredths of a
Dollar. 1/21/101/200.500.100.050.65 50/
10010/1005/10065/100
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Fractions

• Now, if I bought a piece of gum that cost a
  quarter of a Dollar (1/4) what fraction of a
  Dollar would I have left?

A quarter is twenty-five hundredths of a Dollar,
and I am subtracting it from sixty-five
hundredths of a Dollar, leaving me with
forty-hundredths of a Dollar, or four
tenths. 65/100-1/465/100-25/10040/1004/10 0.6
5-0.250.40
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Fractions

• Now, if I gave my remaining money away by giving
  equal amounts to four people, what fraction of a
  Dollar would I give to each of these four people?

Four tenths divided among four people is one
tenth for each person. (4/10)/41/100.40/40.10
If I had 4 equivalent piles of change.
How would it be possible to divide my remaining
fraction of a Dollar among four people?
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Decimals

• When dealing with money, the decimal point is
  placed in between whole Dollars and the change
  (e.g. 4.25).

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Decimals

• If I have five Dollars and thirty cents and I pay
  a Dollar and nineteen cents (1.19) for a drink,
  and buy two bags of chips at fifty-five cents
  (0.55) each, how much money do I have left?

5.30-1.19-2(0.55)3.01
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Decimals

• Now, if I find six pennies (0.06) and a quarter
  (0.25) what amount of money would I have?

3.016(0.01)0.253.32
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Percentages

• Many common percentages are in multiples of five
  percent.
• 5, 10, 15, 20, 25, 30, 35,..

• For mental computations, it is sometimes easier
  to use ten percent (10) as a base, then to
  divide this number in half to obtain five percent
  (5). For example, ten percent of six Dollars
  and sixty cents (6.60) is sixty-six cents
  (0.66) , and five percent of six Dollars and
  sixty cents is thirty-three cents (0.33).

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Percentages

• Also, how might I go about calculating five
  percent of a number?

Class, how do I easily calculate ten percent of a
number?
By moving the decimal point one place to the left.
Divide ten percent in half.
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Percentages

• What is ten percent of six Dollars?
• What is twenty-five percent of six Dollars?

Ten percent of six Dollars is sixty cents.
Twenty-five percent of six Dollars is sixty cents
multiplied by two and a half, which is a Dollar
and fifty cents.
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Percentages

• What is fifteen percent of eight Dollars and
  forty cents?

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Percentages

• What is fifteen percent of eight Dollars and
  forty cents?

Ten percent of 8.40 is 0.84.
Therefore, fifteen percent (15) of 8.40 is
1.26.
Five percent of 8.40 is half of ten percent
(0.42).
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Percentages

• If a book that cost 5.00 is on sale for 45 OFF,
  what is the sale price of the movie?

• If a book that cost 5.00 is on sale for 45 OFF,
  what is the sale price of the movie?

Ten percent of 5.00 is 0.50 and five percent of
5.00 is 0.25. Thus, 45 of 5.00 is four times
ten percent plus five percent. 4(0.50)0.252.
25 Therefore, 5.00-2.252.75
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Squares

• A number squared (e.g. X2) is representative of a
  square with side lengths of X.

X
X
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Cubes

• A number cubed (e.g. X3) is representative of a
  cubic volume with side lengths of X.

X
X
X
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Squares

• How many squares (12) are in a square with side
  lengths of two (22)?

1
2
1
1
2
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Squares

• How many squares (12) are in a square with side
  lengths of (32)?

1
3
9
1
3
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Cubes

• How many cubes with side lengths of 1 are in a
  cube with side lengths 2?

2
1
1
8
1
2
2
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Cubes

• How many cubes with side lengths of 1 are in a
  cube with side lengths 3?

1
1
3
27
1
3
3
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Cubes

• How many cubes with side lengths 1 are in a cube
  with side lengths 4?

64
1
1
4
1
4
4
4
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End of Slide Show!

• Please send any questions to
• Aron Kollins.