fractions review
DESCRIPTION
Fractions Review. Fractions. A number in the form . Numerator. Denominator. Or. N. D. Fractions. The denominator can never be equal to 0. 12. Does not exist!. =. 0. Fractions. A fraction with a numerator of 0 equals 0. 0. 0. =. 0. =. 0. 4. 156. Fractions. - PowerPoint PPT PresentationTRANSCRIPT
Fractions Review
Fractions
A number in the form
NumeratorDenominator
OrND
Fractions
The denominator can never be equal to 0.
0
12= Does not
exist!
Fractions
A fraction with a numerator of 0 equals 0.
156
0= 0
4
0= 0
Fractions• If the numerator is larger than the denominator,
it is called an improper fraction.
Find the improper fraction
11
7
12
10
73
56
9
4
8
10
Math with FractionsFour basic functions
• Multiply
• Divide
• Add
• Subtract
Multiplication• Multiply the numerators and put in
the numerator of the result
• Multiply the denominators and put in the denominator of the result
8 9 8 x 9 72
47 7 x 4 28= =x
Multiplication - Let’s Try It!
9 2
17=x
5 3
17=x
7 11
94=x
4 14
730=x
18
7
15
7
77
36
56
210
56
210 These numbers get pretty big!
What if we needed to multiply again?
Let’s make the fraction more simple, so it will be easier to use in the future.
Simplification• Divide by the Greatest Common Factor
72
28But what is a Common Factor?
Factors• A factor is a number that can be divided
into another number with no remainder– 8’s factors are:
• 1 (8/1 =8)• 2 (8/2 = 4)• 4 (8/4 = 2)• 8 (8/8 = 1)
– 3 is NOT a factor of 8, because 8 is not evenly divisible by 3 (8/3 = 2 with R=3)
Common Factors• A common factor is a factor that
two numbers have in common
– For example, 7 is a factor of both 21 and 105, so it is a common factor of the two.
– The greatest common factor is the largest factor that the two number share
So let’s go back to our simplification problem from before…
Simplification• Divide both numerator and denominator by
the Greatest Common Factor
72
28 Factors are 1, 2, 4, 7, 14, 28
Factors are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 48, 72
Greatest Common Factor is 4
2872 ÷
÷ 44
==
718
So7228 = 7
18
Simplification - Let’s Try It!
31
72
31
6318
=
52
11478
=
72
1913
93
=
8424
=
217
=
156
=
Division• Just like multiplication with one more step• Invert the second fraction and multiply
8 2
13=÷
8 1
23x =
8
6
Division - Let’s Try It!
9 217 =÷
=5 3
17÷
7 1194 =÷
=4 10
720÷
914
521
6344
750
Addition• To add two fractions, you must make
sure they have a Common Denominator
83
165
+
What is a Common Denominator?
Common Denominator• A common denominator is a number with which
both of the denominators share at least one factor that is not the number 1
– For example, if the denominators are 4 and 7, then a common denominator is 28.
– 28 shares the factors 1, 2 and 4 with the number 4, and the factors 1 and 7 with the number 7.So let’s go back to our simplification problem from before…
Addition• To add two fractions, you must make sure
they have a Common Denominator• What can you multiply each fraction by to give the
smallest common denominator?
83
165+
The smallest number that has both of these as factors is 16
8 goes into 16 two times 16 goes into 16 one time
83
22x = 16
5165
11x =
166
165+ =
1611
Once you have a common denominator, add the numerators.
616
Addition - Let’s Try It!
4 211
=+
=8 3
26+
16 824
=+
=16 4
3 13+
43
1217
21
1625
Subtraction• To subtract two fractions, they also must
have a Common Denominator• What can you multiply each fraction by to
give the smallest common denominator?
83
165-
The smallest number that has both of these as factors is 16
8 goes into 16 two times 16 goes into 16 one time
166=8
322x 16
5=165
11x
166
165- =
161
Once you have a common denominator, subtract the numerators.
Subtraction - Let’s Try It!
=8 2
17-
8 216
=-
=16 8
39-
4 1675
=-
83
41
163
1613
Review• A fraction has a numerator and a denominator
• The denominator can never be 0
• You can multiply, divide, add and subtract fractions
• A common factor is a number that both denominators are evenly divisible by
• A common denominator is a number that both denominators share a factor with