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Signed Rationals
Place ValueLet’s look at position after the decimal to help us do some rounding!
Rounding and Estimating
When rounding a decimal you must look at the number to the RIGHT of the place value to which you are going to round.
If that number if 5 or greater, then you must raise the number by one in the position to which you are trying to round.
Example
Round 73.410 to the nearest whole number.
Round 2145.721 to the nearest whole number.
Example
Round 36.480 to the nearest tenth.
Round 9641.702 to the nearest hundredth.
You Try: Round 58.97360 to the nearest
Whole Number
Tenth
Hundredth
Thousandth
Ten Thousandth
Comparing Decimals
Using Models – A Graphical Approach
If you are comparing tenths to hundredths, you can use a tenths grid and a hundredths grid. Here, you can see that 0.4 is greater than 0.36.
Another Way…..
Line up the numbers vertically by the decimal point.
Add “0” to fill in any missing spaces.
Compare from left to right.
Let’s put these numbers in order:
12.5, 12.24, 11.96, 12.36Fill in the missing space with a zero.
You Try: Arrange the following numbers from least to greatest.
0.4, 0.38, 0.49, 0.472, 0.425
Add and Subtract Decimals
The Basic Steps to Adding or Subtracting Decimals: Line up the numbers by the decimal point.
Fill in missing places with zeroes.
Add or subtract.
Be sure to put the larger number on top when subtracting.
Example: 28.9 + 13.31
You Try
3.04 + 0.6 8 + 4.7
Ex: Subtract the following:
4 – 1.5 25.1 – 0.83
Compute:
Compute:
Subtracting Across Zeroes
If you have several zeroes in a row, and you need to borrow, go to the first digit that is not zero, and borrow.
All middle zeroes become 9’s.
The final zero becomes 10.
Example: 15 – 29.372
Multiply and Divide Decimals
To Multiply Decimals: You do not line up the factors by the decimal. Instead, place the number with more digits on
top. Line up the other number underneath, at the
right. Multiply Count the number of decimal places (from the
right) in each factor. Use the total number of decimal places in your
two factors to place the decimal in your product.
Example: 5.63 x 3.7
Example: 0.53 x -2.61
Try This: -6.5 x 15.3
Example: 0.00325 2.5
Example: 2.00124.55
You Try: 3.0015.0
Compute: 1.3923.8
Compute: 88.1201.87
Compute: 118.37.27
Compute: 77.887.3
You Try the following:
278.867.5)4
2.319.7)3
29.887.23)2
87.3267.5)1
Fractions
Fractions
Top # is the numerator.
Bottom # is the denominator.
Reducing Fractions
A fraction is said to be in its lowest terms (or reduced) when the numerator and denominator are relatively prime (have no common divisors other than 1).
Reduce:
6/10
You Try… Reduce it:90
54
Mixed Numbers and Improper Fractions The number 2¾ is an example of a mixed
number. It is called a mixed number because it is made up of an integer and a fraction.
2¾ means 2 + ¾ An improper fraction is a fraction whose
numerator is greater than its denominator.
Example: Convert to Improper Fractions.
Example: Convert to a mixed number.
5
8
Example: Convert to a mixed number.
8
225
Multiplication of Fractions Multiply the numerators and multiply the
denominators together then reduce if necessary.
Examples
3 7
5 8
2 4
3 9
7 11 28 4
Reciprocal The reciprocal of any number is 1 divided by
that number. The product of a number and its reciprocal
must equal 1.
Division of Fractions To find the quotient of two fractions,
multiply the first fraction by the reciprocal of the second fraction.
Evaluate:
.4
3
7
5
Addition and Subtraction of Fractions Before we can add or subtract fractions,
the fractions must have a lowest common denominator.
Add/ Sub
16
7
16
5
21
8
21
13
Adding or Subtracting Fractions with Unlike Denominators
5 3
12 10
Compute:
18
1
12
1
Compute:
5
3
4
1
Compute:
4
12
3
26
Homework
P. 16 (2-40) even
P. 19 (2-46) even