Download Chapter 7

Chapter 7
Decimals, Real Numbers &
Proportional Reasoning
Position Names
Expanded Form
• 25.3 = 2x101 + 5 x 100 + 3 x 10 -1
• 136.72 = 1x102 + 3x101 +6x100 +7x10-1 +2x10-2
• 1.235 = 1x100 + 2x10-1 + 3x10-2 +5x10-3
Squares,
Strips & Flats
Base Ten Blocks
Activity 2c
Activity 1 &2
Negative Exponents
• 10-2 = 1/102
• 10-3 = 1/103
• 10-4 = 1/104
• 5-2 = 1/52
• A negative exponent means I over.
• Usually a negative exponent means a fraction.
Converting Decimals to Fractions
• 17/40 = 17 ÷ 40
.925
• 40 17.00000
Converting Decimals to Fractions
.355 = 355
1000
.256
.58
= 5 x 71
5 x 200
= 71
200
Repeating Decimal
• .3333…
• .242424…
Ordering Decimals
• To order positive decimals. Line up the
decimal points and determine the first digit
that is greater. (Add zeros at the end of the
decimaqls to have the same number of
decimal places.)
• .256
• .238
• .2563
Irrational Numbers
• Non-terminating, non-repeating decimals.
• .0123456789101112131415….
• .0100100010000100001……
• The square root of any non perfect square.
Homework
• Pg 431 # 1,2,3,5,6,7,8,10,31,32
Adding & Subtracting
• To Add or Subtract Decimals write the
numbers in vertical style, lining up the decimal
points and then add or subtract just as we add
integers. BRING THE DECIMAL POINT
STRAIGHT DOWN.
• 37.6 + 12.45
• 37 + 12 is 49. Our answer should be around
49
• 37.6
• +12.45
• 50.05
• 23.47 + 7.81
• 351.42 – 217.815
Multiplying & Dividing Decimals
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.9 x .25 =
9/10 x 25/100 =
9 x 25 / 10 x 100 =
225 / 1000 = .225
2.3 x 3.2
2.3 x 1.8
Activity 5
2.5
x.19
225
25
.475
1 digit to the right of
the decimal point
2 digits to the right of
the decimal point
3 digits to the right of
the decimal point
2.56
1.2
512
256
3072
• Think about what the answer should be.
Where would you put the decimal point?
Why?
2.56
1.2
512
256
3.072
2 digits to the right of
the decimal point
1 digit to the right of
the decimal point
3 digits to the right of
the decimal point
471.2
X 2.3
14136
9424
108376
Think about what the answer should be. (2x471)
Where would you put the decimal point? Why?
537.6 ÷ 2.56 =
÷
=
x
= 210
210.
2.56 537.60
We don’t divide by a decimal, so we make the
divisor a whole number. We multiplied the
divisor by 100, so we have to multiply the
dividend by 100 (move the decimal 2 places to
the right.)
• We don’t divide by a decimal, so we make the
divisor a whole number. We multiplied the
divisor by 100, so we have to multiply the
dividend by 100 (move the decimal 2 places to
the right.)
Homework
• Pg 441 # 1,2,4,10,32-35
Ratios & Proportions
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A comparison of 2 numbers by division.
Ratio(nal) number
Should express ratios in simplest form.
Joe missed 12 free throws out of 45 attempts.
Ratio of:
Shots made to number attempted 33:45
Shots missed to number attempted 12:45 =4:15
Shots made to number missed 33:12 = 11:4
285 Boys & 228 Girls
• Ratio of:
• Boys to Girls
• Boys to students
One seventh of the students are
nonswimmers.
• What is the ratio of nonswimmers to
swimmers.
• Divide the students into 7 groups.
• 1 group will be non-swimmers.
Proportions
• A statement that says 2 ratios are equal.
• Then axd = cxb
•
•
28 x 21 = 49 x
12 = x
• Marci liked to make mixed nuts by combining
6 cups of cashews with 2 cups of pecans.
• If she has 5 cups of pecans, how many cups of
cashews does she need?
• If she has 20 cups of cashews, how many cups
of pecans does she need?
The ratio of boys to girls in Mr. A’s class is 5 to 7
The ratio of boys to girls in Mr. B’s class is 2 to 5
• What fraction of Mr. A’s class are boys?
• What fraction of Mr. B’s class are girls?
• There are 24 students in Mr. A’s class. How
many are girls?
• If Mr. A’s class is bigger than Mr. B’s class, what
would be a reasonable number of students in
Mr. B’s class?
Similar Triangles
• Page 455- 7.21
Homework
• Pg 457 # 1 all, 2,3,4,5,637,38,39
Percents
• Percent from the Latin meaning per hundred.
• 25% = 25/100
• Pg 463
• Activity 11
3 Basic Problems
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Find x
% of # =x
15% of 1750
% of x = #
15% of x is 262.50
X% of a # is another #
x% X 1750 = 262.50
% of #
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By Multiplying
15% of 1750
15% X 1750 =
.15 X 1750 = 262.50
% of #
• By Proportion
• 15% of 1750
% of #
• By Diagram:
% of x = #
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By equation
92% of x is 23
.92 X = 23
X = 23 / .92
X = 25
% of x = #
• By Proportion
• 92 X = 23 x 100
• X = 2300 / 92
• X = 25
X% of a # is another #
x% of 35 is 28
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By Equation
X x 35 = 28
X = 28 / 35
X = .8 = 80%
X% of a # is another #
x% of 35 is 28
• By Proportion
• 35 x = 28 x 100
• X = 2800 / 35 = 80%
• 45% of the students at a college are males.
• If the college has an enrollment of 22,500
students, how many are male? Use the 100
grid in your solution.
Homework
• Page 470 # 1,2,3,4,5,6all,7,9,10,37,38