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NOTES:Multiplying and Dividing Fractions/Mixed Num  Multiplying and Dividing Fractions/Mixed Number

Multiplying and Dividing Fractions/Mixed Numbers
Multiplying fractions:
Second, Multiply the denominators to get the new denominator.
Lastly, Reduce or Simplify the fraction by dividing numerator and denominator by the GCF(largest number that goes into both the numerator and denominator.) If the fraction is improper, change to a mixed or whole number
¾ x 2/3 = 3 x 2 = 6_ numerator (dividend)
4 x 3 = 12 denominator (divisor)
6/12 can be reduced or simplified because, 6 is the GCF(greatest common factor of 6 and 12), divide numerator and denominator by the GCF of 6:
6 ÷ 6 (GCF) = 1
12 ÷ 6(GCF) = 2 so 6/12 = ½
NOTE: you can reduce before you multiply the numerator and the denominator as long as you simplify any numerator with any denominator
In ¾ x 2/3 the numerator 3 of 3/4 and the denominator 3 of 2/3 can both be divided by 3 so you would have
¼ x 2/1. Now the denominator 4 of ¼ and the numerator 2 of 2/1 can be simplified by 2 so divided 2 by 2 and get 1, then divide 4 by 2 and have 2.
½ x 1/1 = 1/2
Multiplying with a Whole Number: turn a whole number into a fraction by placing a 1 under it 6 = 6/1
In order to multiply 2 1/3 x 1 3/5
First, change each mixed number into an improper fraction by taking the denominator x whole number then adding the numerator to get the new numerator, denominator stays the same.
2 1/3 = 3(denominator) x 2(whole number) = 6 + 1(numerator) = 7 so 7/3
1 3/5 = 5(denominator) x 1(whole number)= 5 + 3(numerator) = 8 so 8/5
Second, multiply 7/3 x 8/5 = Numerators 7 x 8 = 56
Denominators 3 x 5 = 15
Improper to mixed: 56/15 is improper so change into a mixed number 56 divided by 15 (how many times does 15 go into 56?
56 – 45 = remainder of 11
DENOMINATOR STAYS THE SAME when changing improper to mixed or mixed to improper
So 56/15 = 3 11/15 since 11 and 15 only have 1 as a common factor, it cannot be reduced or simplified.
When you divide fractions, you multiply the first fraction by the reciprocal of the 2^{nd} fraction.
Second, multiply numerators and denominators and reduce/simplify if you can
Denominators 8 x 3 = 24 the GCF of 21 and 24 is 3 so divide numerator and denominator by 3
GCF
21 ÷ 3 = 7
24 ÷ 3 = 8 so 3/8 ÷ 3/7 = 7/8
Dividing Mixed Numbers:
When dividing mixed numbers: 4 ½ ÷ 2 ¾