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• Merry Havens

# Basic rules on fractions

Updated: Oct 25, 2019

With a little practice, fractions can be less dreaded. Once we get the basic rules down, I'll show you some shortcuts that make fractions even simpler.

Basics for adding and subtracting: 1. Find a common denominator. 2. Add (or subtract) the numerators, keep the denominator. Eg. 1/2 + 3/4 = ? Since 2 and 4 are not "common", we need to find one that is the least common multiple of 2 and 4....that's 4 (2 and 4 go into 4). 1/2 can be converted to 2/4 (by multiplying it by 2/2 which doesn't change its value). Our new equation: 2/4 + 3/4 = ? 2+3 =5 over 4 --> 5/4

Basics for multiplying (easier than adding/subtracting!): 1. Multiply the numerators, the product is the new numerator. 2. Multiply the denominators, the product is the new denominator!

Eg. 1/2 X 3/4 = ( 1 x 3) over (2 x 4) = 3/8

Basics for dividing fractions (almost as easy as multiplying!) 1. Keep the first fraction as it is. 2. Invert (switch the numerator with the denominator), then multiply across! Eg. 1/2 divided by 3/4 = ? --> 1/2 X 4/3 = (1 x 4) over (2 x 3) = 4/6

OK, let's practice:

a. 2/3 + 3/4 =

b. 3/4 + 2/5 =

c. 1/8 + 3/16 =

d. 2/3 + 3/7 =

e. 2/3 - 2/5 =

f. 9/11 - 2/3 =

g. 6/7 - 1/3 =

a. 2/3 + 3/4 needs to be converted to a denominator with a 12 (the lowest number that 3 AND 4 go into). 2/3 x 4/4 (multiply numerators to get 8, then denominators to get 12) = 8/12

3/4 x 3/3 (multiply numerators to get 9 and denominators to get 12) = 9/12, then add numerators (8 + 9= 17) keep the common denominator, 12 to get 17/12, reduce to 1 5/12.

b. 3/4 + 2/5 needs a common denominator, 20, the lowest number 4 and 5 go into.

3/4 x 5/5 = 15/20 .... then 2/5 x 4/4 = 8/20 ....15 + 8 = 23 (the numerator) 23/20 = 1 3/20

c. 1/8 (2/16) + 3/16 = 5/16

d. 2/3 (14/21) + 3/7 (9/21) = 23/21 = 1 2/21

e. 2/3 (10/15) - 2/5 (6/15) = 4/15

f. 9/11 (27/33) - 2/3 (22/33) = 5/33

g. 6/7 (18/21) - 1/3 (7/21) = 11/21

2. Let's practice multiplying:

a. 3/4 x 4/5 =

b. 2/3 x 8/11 =

c. 4/5 x 6/8 =

d. 12/13 x 8/22 =

e. 6/20 x 9/11 =

OK, multiplying is easier than adding and subtracting fractions!

Just multiply across!

a. 3 x 4 = 12 and 4 x 5 = 20...so 12/20 reduces to 3/5 (divide numerator and denominator by 4)

b. 2/3 x 8/11 .... 2 x 8 is 16 and 3 x 11 is 33, so 16/33 (no common factor so it is done)

c. 4/5 x 6/8 = 24/40 which reduces to 3/5 (divide the numerator and denominator by 8)

d. 12/13 x 8/22 = 96/286 which reduces to 48/143 (divide numerator and denominator by 2)

e. 6/20 x 9/11 = 54/220 which reduces to 27/110 (divide numerator and denominator by 2)

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