Pre Algebra homework help

Equivalent fractions and reducing fractions

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Problem:
Find the missing numerator or denominator:
(a) 35 = ?30
(b) 23 = 22?

Solution:
(a) Comapre the denominators on the two given fractions: 5 x 6 = 30
Do the same with the given numerator
⇒ Missing numerator is 3 x 6 = 18

To do that in a single step,
Missing numerator = (35) x  30 = 18
Or  3 x 305 = 18
Or  3 x  30 ÷ 5 = 18

(b) The numerators are given: 2 x 11 = 22
Do the same with the given denominator
⇒ Missing denominator is 3 x 11 = 33

To do that in a single step,
Missing denominator = 22 x  (32) = 33
Or  22 x  32 = 33
Or  22 x  3 ÷ 2 = 33

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Problem:
Reduce the following fractions to their lowest terms:
(a) 3045
(b) 3240
(c) 1821
(d) 1033

Solution:
(a) 3045
Find a number (except 1) that can divide into both 30 and 45
5 is such a number
   3045   =   30÷ 545÷ 5   =   69
Find a number (except 1) that can divide into both 6 and 9
3 is the only such number
   69   =   6÷ 39÷ 3   =   23
There is no number (except 1) that can divide into both 2 and 3 and therefore,
3045 reduced to its lowest term is 23

Note: If you could figure out that 15 can divide into 30 and 45 both, you would need one less step:
3045   =   30÷ 1545÷ 15   =   23

Lesson: Try to find as large a number as you can to divide

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