Transcript Signed Rationals

Signed Rationals
Place Value
Let’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:
Fill in the missing space
with a zero.
12.5, 12.24, 11.96, 12.36
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:
 55.0124  0.2
You Try:  0.015  0.3
Compute:
 8.923  3.1
Compute:
87.1 120.88
Compute:
27.7   3.118
Compute:  3.87  8.77
You Try the following:
1)  5.67  32.87
2) 23.7  88.29
3) 7.19   3.2 
4)  5.67  8.278
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
54
You Try… Reduce it:
90
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
number.
8
5
to a mixed
Example: Convert to a mixed
number.
225
8
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  1 
1 8  2 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:
5 3
  .
7 4
Addition and Subtraction of
Fractions

Before we can add or subtract fractions,
the fractions must have a lowest
common denominator.
Add/ Sub
5 7
 
16 16
13 8
  
21 21
Adding or Subtracting Fractions
with Unlike Denominators
5 3
 
12 10
Compute:
1 1
  
12 18
Compute:
1 3
  
4 5
Compute:
2
1
6 2 
3
4
Homework

P. 16 (2-40) even

P. 19 (2-46) even