- 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**:

1. **Adding and subtracting**: Try these on your own before checking the answers.....

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 =

Answers:

**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)