# Fractions and Mixed Numbers

**Sec. 3.1 Least Common Multiple**

The **least common multiple** (LCM) of two (or 3) numbers is the smallest
number that the 2 (or 3) numbers will divide into. The LCM is used for the least
common denominator which is needed in addition and subtraction of fractions.

**Example:** Find the LCM of 12 and 18, using prime
factorization.

Find the LCM, using prime factorization:

3. 21 and 70

21 =

70 =

LCM =

4. 90 and 105

90 =

105 =

LCM =

5. 15, 21 and 35

15 =

21 =

35 =

LCM =

6. 8, 20 and 60

8 =

20 =

60 =

LCM =

Use prime factorization to find the LCM of…

7. 14 and 35

14 =

35 =

LCM =

8. 21 and 28

21 =

28 =

LCM =

9. 50 and 75

50 =

75 =

LCM =

10. 63 and 90

63 =

90 =

LCM =

11. 15, 27 and 18

15 =

27 =

18 =

LCM =

**Sec. 3.2 & 3.3 Adding and Subtracting Fractions**

A common denominator is needed for adding and

subtracting fractions – it's the LCM!

Add or Subtract, leaving your answer as a reduced fraction:

Solve:

12. John walked 1/2 mile to the student union and then 1/3 mile to class. How far did John walk?

13. Sally bought 1/4 lb. of peanut butter fudge and 3/8
lb. of

rocky road fudge. How much fudge did she buy?

14. Judy has 3/4 lb. of a candy corn and peanut mixture.
If

this contains 1/3 lb. peanuts, how many pounds of candy

corn are in the mix?

**3.4 & 3.5 Adding and Subtracting Mixed Numbers**

Common denominators are needed to add and subtract

mixed numbers, but it is not necessary to change them into

improper fractions. Subtraction may require borrowing.

6. Compare and

**Sec. 3.6 Multiplying & Dividing Mixed Numbers**

Ideas to remember:

* No common denominator is needed.

* Mixed numbers must be changed into improper

fractions.

* When multiplying, try to reduce first by cancelling.

* When dividing, the rule is “invert and multiply.”

Steps:

* Convert mixed #s to

improper fractions

* Try to cancel

* Multiply across

* Check for reducing

Steps:

* Convert mixed #s to

improper fractions

* Invert (flip over) 2nd fraction

* Use steps for multiplying

…try to cancel

…multiply across

…check for reducing

An Assortment of Word Problems for Chapter 3:

1. Jimmy poured yards of cement for a
fountain.

Another fountain took yards. How much cement

was used for both fountains?

2. Tammy has a piece of rope that measures 210 inches.

How many pieces of rope inches long can she
cut

from the original piece?

3. Larry works a maximum of 18 hours per week at his

work-study job at the college he attends. If he works

hours one day,
hours the next day and
hours

the third day, how many more hours must be work to

complete his 18 hours?

4. A stock has a value of
on Monday. On Tuesday it

goes up , and on Wednesday it goes down
.

What is the new value?

5. The framework of a wall is
in. thick. We apply
-in.

wall board and -in. paneling to the inside.
Siding

that is in. thick is applied to the outside.
What is the

finished thickness of the wall?

6. If you cut yd and
yd lengths from a 20-yd roll of

wallpaper, how much paper remains on the roll?

**Sec. 3.7 Order of Operations with Fractions**

Perform the indicated operations in the correct order: