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Key Words/Topic
and Assignments
3.1 Estimating Sums and
Differences
Topic 3 Guided Notes
Operations with Decimals
Information, Definitions, Solutions
New Terms
Estimate An _____________ answer or _________.
Review Terms
Rounding Rules When rounding:
1. Look one place value to the right of the place you want to
round to.
2. If that number is 5 or greater, round up. Rounding up
means to increase the value of the place value you are
rounding by 1 digit. All digits after the place you are
rounding to are changed to zeros.
3. If that number is less than 5, round down. Rounding
down means to leave the value of the digit you are
rounding to alone. All digits after the place you are
rounding to are changed to zeros.
Round 12.3 to the nearest whole number
1. Look one place value to the right of the ones place
(tenths place)
2. The number is 3, which is less than 4, so round down.
3. 12.0 or 12
Round 12.379 to the nearest tenth
1. Look one place value to the right of the tenths place
(hundredths place)
2. The number is 7, which is greater than or equal to 5,
so round up.
3. 12.400 or 12.4
Today’s Concept Estimation is a great tool to quickly get an idea of what an
answer should be close to, or to check the reasonableness
(does my answer make sense) of an answer.
Rounding is a great tool to help make estimations. Use the
rounding rules above.
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Group Work
1-10 on page 62.
2.
Show work when
appropriate.
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when appropriate.
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HOMEWORK: 3.1 practice
sheet.
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Key Words/Topic
and Assignments
3.2 Adding & Subtracting
Decimals
Information, Definitions, Solutions
New Terms
Review Terms
Estimate An _____________ answer or _________.
Today’s Concept
Adding and subtracting decimals works the same way as
adding and subtracting whole numbers. The key is to line up
the place values!
12.34
+ 3.27
15.61
12.34
- 3.27
9.07
All place values line up!
To help us line up the place values we sometimes have to
annex (add) a zero placeholder to a number.
12.3 turn this into 12.30
+ 3.27
+ 3.27
15.57
Group Work
1-10 on page 64.
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when appropriate.
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1.
2.
HOMEWORK: 11-22 P. 65
in textbook.
3.
3.2 continued
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Group Work
1-10 on page 64.
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when appropriate.
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HOMEWORK: 11-22 P. 65
in textbook.
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Key Words/Topic
and Assignments
3.3 Estimating Products and
Quotients
Information, Definitions, Solutions
New Terms
Review Terms
Compatible Numbers Numbers that are _______ to the ________ numbers, but are
____________ to compute mentally.
Estimate An _____________ answer or _________.
Product
Quotient
Today’s Concept
Remember that estimation gives you a quick idea of what
the answer should be and helps you to check the
reasonableness (does it make sense) of your answer.
We can use our rounding rules to form compatible numbers
that help us to do quick estimates of multiplication and
division problems.
Group Work
1-10 on page 67.
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appropriate.
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HOMEWORK: 12-22 even,
28-34 P. 67 in textbook.
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3.3 continued
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Group Work
1-10 on page 67.
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6.
7.
HOMEWORK: 12-22 even,
28-34 P. 67 in textbook.
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3.4 Multiplying Decimals
New Terms
Review Terms
Factors
Product
Today’s Concept Multiplying decimals is similar to multiplying whole
numbers with one important difference.
Unlike addition and subtraction of decimals, when
multiplying decimals you do not need to line up the place
values.
What is the answer to 43.25*3.5?
43.25
X 3.5
21625
+129750
151375 –How did I know where
to put the decimal?
1. Count up the number of total decimal places there are in
the factors. 43.25 has two decimal places + 3.5 has one
decimal place – for a total of 3 decimal places in the factors.
2. Start at the far right side of the product (the 5) and count
to the left 3 spaces. Place the decimal after the 1, but before
the 3.
151.375
3. You can estimate to see if your answer is reasonable.
40*4 = 160 which is close to 151.375
Group Work
1-10 on page 71.
Now you know everything you need to know to multiply
decimals!
1.
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3.
4.
HOMEWORK: 15-26, 2930 P. 72 in textbook.
3.4 continued
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HOMEWORK: 15-26, 2930 P. 72 in textbook..
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3.5 Dividing a Decimal by
a Whole Number
Review Terms
Quotient The ________ to a __________ problem.
Dividend The ________ that is being _________.
Divisor The ________ that is doing the _________.
Today’s Concept Using decimals with division is more precise than using
remainders – so say goodbye to remainders!
You must understand the basic division algorithm to
succeed. Once you understand basic division then you only
need to understand how to work with the decimal portion of
the number.
What is the answer to 150 ÷ 4?
1. Set the problem up like any division problem.
4 150
2. Begin the standard division algorithm. How many 4s can
you get from 1? None, so move to the tens place.
Group Work
1-8 on page 74
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HOMEWORK: 11-24 P. 75
in textbook.
3.5 continued
3. How many 4s can you get from 15? 3. 3x4 = 12
3
4 150
- 12_
30 – bring down the zero
4. How many 4s can you get from 30? 7. 7x4 = 28
37
4 150
- 12
30
- 28
2
5. Now we have a remainder, but we don’t stop! Annex
(add) a decimal place after the 0 in 150 and place one zero
after the decimal place. Put a decimal point right after the 7
in the quotient, right above the decimal in the dividend.
Then bring the zero down.
37.
4 150 .0
- 12
30
- 28
20
6. How many 4s can you get from 20? 5. 5x4=20
37.5
4 150 .0
- 12
30
- 28
20
-20
0 –Once you have zero down here and there are no
more numbers to bring down you are done!
Group Work
1-8 on page 74
Check your work by multiplying the quotient by your
divisor. The product should equal the dividend. Does
37.5*4=150? Yes!
1.
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HOMEWORK: 11-24 P. 75
in textbook.
2.
3.
4.
3.5 continued
5.
Group Work
1-8 on page 74
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appropriate.
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6.
HOMEWORK: 11-24 P. 75
in textbook
7.
8.
3.6 Dividing a Whole
Number by a Decimal
New Terms
Review Terms
Quotient
Dividend
Divisor
Today’s Concept You Divide whole numbers by decimals by moving the
decimal place an equal number of places in the dividend as
you move the decimal in the divisor.
Multiply the divisor and the dividend by the same power
of 10 to move the decimal place.
How do you divide 80 by 3.2?
3.2 80
The divisor MUST become a whole number.
To make 3.2 a whole number you multiply 3.2 by 10.
This makes 3.2 equal to 32-you are moving the decimal
place over by 1 place.
If you multiply the number outside the “house” (the
divisor) by 10, you MUST multiply the number inside the
“house” (the dividend) by 10.
Your problem becomes:
Group Work
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1.
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HOMEWORK: 11-21, 28,
31, 32 p. 76 in textbook.
3.
32 800
3.6 Continued
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5.
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HOMEWORK: 11-21, 28,
31, 32 p. 76 in textbook.
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10.
Key Words/Topic
and Assignments
3.7 Dividing Decimals
Information, Definitions, Solutions
New Terms
Review Terms
Quotient
Dividend
Divisor
Today’s Concept Guess what? This works exactly the same as our last topic.
How do I solve 3.60  1.20
1. Rewrite the problem with the divisor on the outside of the
“house” and the dividend on the inside of the “house”.
1.20 3.60
2. If the divisor has digits to the right of the decimal, move
the decimal right to the very end of the divisor.
1.20 360
3. Move the decimal in the dividend to the right the same
number of places.
120 360
4. Move the decimal up to the top of the “house”.
3.
120 360
5. Divide
6. If you need to add zeros and bring them down, you can
and should!
Group Work
1-8 on page 78.
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HOMEWORK: 11-25 P. 79
2.
in textbook.
3.7 Continued
Group Work
1-8 on page 78.
3.
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HOMEWORK: 11-25 P. 79
in textbook.
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Key Words/Topic
and Assignments
3.8 Evaluating
Expressions
Information, Definitions, Solutions
New Terms
Evaluate To find a ___________ that an algebraic __________ names
by replacing a ___________ with a given value.
Review Terms
Expression A mathematical ______ containing variables or ________
and including at least one _______________.
Order of Operations PEMDAS
Today’s Concept Evaluating an expression is the same as solving the equation
(finding the answer). Sometimes the expression has a
variable.
If there are parentheses and/or brackets in the expression
you must solve those parts of the expression first.
If there are parentheses within parentheses (nested
parentheses), you start from the parentheses most on the
inside and work your way out.
If there is a variable, then you substitute (plug in) the
value for the variable to solve the expression.
Group Work
1-8 on page 80.
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HOMEWORK: 10-21 P. 81
in textbook.
3.8 Continued
3.
Group Work
1-8 on page 80.
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HOMEWORK: 10-21 P. 81
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