If a rectangle is divided into 4 equal parts, each part is ¼ of the whole. If each of these parts is then divided into 3 parts, that is into thirds, then there are 12 equal parts and each is 1/(3 ∙4) or 1/12 of the whole.
That is 1/3 of 1/4 is 1/(3 ∙4) or 1/12 and 1/3 ∙ 1/4 = 1/12 is
so another example 2/3 of 4/5 is 2∙4 /(3∙8) or 2/3 ∙4/5 = 8/15
Notice, that the numerator of the product, 8, is the product of the numerators 2 and 4. The denominator of the product, 15, is the product of the denominators 3 and 5
Rule
If a, b, c, and d are whole numbers with b ≠ 0 and d ≠ 0 , then
a/b(c/d) = a∙c/(b∙d)
When multiplying two fractions, you can simplify the multiplication by dividing either of the numerators and either of the denominators by common factors
6/35 ( 7/3) we can simplify first because both 6 and 3 are divisible by 3
2/35 (7/1) and then both 35 and 7 are divisible by 7 so 2/5 (1(1) = 2/5
Try the following
25/6 ( 42/5) What can we do there?
7/8(20/21) How about with these two sets of fractions?
19/20 ( 25/38) … and these fractions?
What happens when you have
15/2(7/8- 5/24)
What must we do first?
PEMDAS... in my classroom...
15/2( 21/24 - 5/24)
= 15/2(16/24)
= 15/2(2/3)
then simplify to
15/1(1/3)
= 5
What about
8/9∗ 15/32∗ 9/10 = 3/8
or 16/11 × 33/20 × 5/3 = 4
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