Download Math Notes for Chapter Three

Math Notes for Chapter Three
Pre Chapter Notes:
Fractions
Fraction: represents part of a whole; written in the
Form a
b
4
whole is broken into 4 parts – this represents the
Denominatior – bottom number
3
4
The shaded part represents the part or the
Numerator – top number
Simplifying Fractions
(Reduce to simplest form or put in lowest terms)
Divide both the numerator and the denominator by the GCF
20 - 4 = 5
28 - 4 = 7
Adding and Subtracting with Decimals:
 Must line up decimal points
 Use “0” as a place holder if needed
 Add or subtract as normal
 Pull down the decimal in the answer
Expressing improper fractions as mixed numbers:
 Divide the denominator into the numerator
 The whole answer is the whole number and
 The remainder become the numerator
 The denominator remains the same
 Reduce or simplify if needed
25
10
25 – 10 = 2 remainder 5 so..
2
5/10
or 2 1/2
Expressing mixed numbers as improper fractions:
Multiply the denominator and the whole number
Add in the numerator and find the answer
The answer becomes the new numerator
The denominator stays the same
2 ¾ ------ 4*4 = 8 + 3 = 11 so
11/4 is the improper fraction
Multiplying Fractions:
1) Multiply numerators
2) Multiply Denominators
3) Reduce if needed
2/5 * 3/8 = 2*3= 6
5*8= 40
6/40 = 3/20
or
Cross Cancel before multiplying
2
5
3
8
4
= 3
20
**Multiplying with Mixed Numbers: you must first change mixed
number to an improper fraction before multiplying.
3 ½ = 2*3=6 + 1= 7
so 3 ½ = 7/2
Lesson 3.1
Dividing Fractions: you are trying to determine how many of one fraction can
go into another fraction
2 – 1/4 = means you are trying to determine how many 4ths
can fit into 2
¼
¼
¼
¼
¼
¼
¼
¼
you can see that 8 ¼’s fit into
2 whole. So what you really did
was multiply 2*4
To divide Fractions:
1) Leave the fist fraction alone
2) Change to multiplication
3) Flip the second fraction upside down
½ -- ¼ =
1/2 * 4/1 = 4/2 = 2
*** Remember when working with mixed numbers you must change
into improper fractions before working.***
Lesson 3.2
Multiplying Decimals:
Method One:
Vertical Method:
15.5
x 2.7
1) Multiply as normal 4185
2) Count decimal places in each number and add (1 + 1)
3) Place total decimal places in answer (2)
15.5 (1)
x 2.7 (1)
.
41 85 (2)
Method Two:
Lattice Method
1 5.5
2
7
a)Multiply as normal 4185
b) Count decimal places in each number and add (1 + 1)
c) Place total decimal places in answer (2) 14.85
Lesson 3.3
Dividing Decimals
Dividend ÷ Divisor = Quotient
Quotient
Divisor )Dividend
If decimal is only in dividend:
 move decimal directly up to the answer in the
exact same place
If decimal is in divisor:
1st Move decimal to the right to make a whole
number
2nd move the decimal in the dividend to the right
The same number of places
3rd move decimal directly up into the answer