multiplying and dividing rational numbers. the term rational numbers refers to any number that can...
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Multiplying and Multiplying and Dividing Rational Dividing Rational
NumbersNumbers
• The term Rational Numbers refers to any number that can be written as a fraction.
• This includes fractions that are reduced, fractions that can be reduced, mixed numbers, improper fractions, and even integers and whole numbers.
• An integer, like 4, can be written as a fraction by putting the number 1 under it.
Rational NumbersRational Numbers
4 4
1
• When multiplying fractions, they do NOT need to have a common denominator.
• To multiply two (or more) fractions, multiply across, numerator by numerator and denominator by denominator.
• If the answer can be simplified, then simplify it.
• Example:
• Example:
Multiplying FractionsMultiplying Fractions
2
5
9
2
2 9
5 2
18
10
3
4
5
2
35
4 2
15
8
2
2
9
5
• When multiplying fractions, we can simplify the fractions and also simplify diagonally. This isn’t necessary, but it can make the numbers smaller and keep you from simplifying at the end.
• From the last slide:
• An alternative:
Cross CancellingCross Cancelling
2
59
2
2 9
5 2
18
10
2
2
9
5
2
59
2
1
1
19
5 1
9
5
You do not have to simplify diagonally, it is just an option. If you are more comfortable, multiply across and simplify at the end.
• To multiply mixed numbers, convert them to improper fractions first.
Mixed NumbersMixed Numbers
32
5
1
1
4
17
5
5
4
17
5
5
4
1
1
17 114
17
4
Multiply the following fractions and mixed numbers:
Try These: MultiplyTry These: Multiply
1) 6
5
1
3
2) 5
1
36
5
3) 13
4
3
1
2
4)
4
96
8
Solutions: MultiplySolutions: Multiply
1) 6
5
1
3
6
15
3
3
2
5
2) 51
36
5
16
3
6
5
96
15
3
3
32
5
3) 13
4
3
1
2
7
4
7
2
49
8
4) 4
96
8
24
72
24
24
1
3
Solutions (alternative): MultiplySolutions (alternative): Multiply
1) 6
5
1
3
2) 51
36
5
16
36
5
4) 4
96
8
Note: Problems 1, 2 and 4 could have been simplified before multiplying.
2
5
32
5
1
2
2
1
1
96
2
1
2
1
93
11
3
1
3
1
3
• When dividing fractions, they do NOT need to have a common denominator.
• To divide two fractions, multiply by the reciprocal…flip it and multiply.
Dividing FractionsDividing Fractions
2
5
9
2
2
5
2
9
Change Operation.
Flip 2nd Fraction.
• Finish the problem by following the rules for multiplying fractions.
Dividing FractionsDividing Fractions
2
5
9
2
2
52
9
4
45
• Divide the following fractions & mixed numbers:
Try These: DivideTry These: Divide
1) 6
5
1
2
2)
3
2
1
2
3) 21
33
2
34)
7
31
2
3
Solutions: DivideSolutions: Divide
1) 6
5
1
2
6
5
2
1
12
5
2) 3
2
1
2
3
2
2
1
6
2
2
2
3
13
3) 21
33
2
3
7
3
11
3
7
3
3
11
21
33
3
3
7
11
4) 7
31
2
3
7
3
5
3
7
33
5
21
15
3
3
7
5