Instruction 3-5

Round off Decimals | Compare and Order Positive and Negative Fractions, Decimals, Mixed Numbers | Interpret and Use Ratios | Use Proportions to Solve Problems | Using LCM to Solve Fraction Problems | Calculate Percentages and Solve Problems

For example, if we wanted to add the fractions , we could use the LCM of 2 and 3 to find the common denominator. We can do this in one of two ways: Comparing multiples or Prime factorization.

Comparing Multiples

This is done by listing the multiples of both numbers, and finding the lowest common multiple. First we list the multiples of both denominators.

The multiples of 2 are:	2	4	6	8	10	12	14	16	18	20
The multiples of 3 are:	3	6	9	12	15	18	21	24	27	30

You will notice that there are many multiples of the numbers 2 and 3, but the smallest is 6, which we can use as the common denominator in this problem.

Prime factorization

Prime factorization is the process of breaking numbers down into their prime components, or the numbers that divide in evenly and can no longer be broken down.

Let’s try this fraction problem to find the common denominator: .

First we use prime factorization to find the prime factors of the two numbers.
The prime factors of 5 are 1 × 5.
The prime factors of 6 are 2 × 3.
The Least Common Multiple is found by multiplying the factors of each number, so in this case we will multiply 2 × 3 × 5 to find our common denominator is 30.

Let’s try prime factorization to find the common denominator in this problem: .

First we use prime factorization to find the prime factors of the two numbers.
The prime factors of 4 are 2 × 2.
The prime factors of 6 are 2 × 2 × 2.
The Least Common Multiple is found by multiplying the largest number of each factors of the two numbers being used to find a common denominator, so in this case we will multiply 2 × 2 × 2 to find our common denominator is 8.

Let’s try one more example using prime factorization: .

First we use prime factorization to find the prime factors of the two numbers.
The prime factors of 12 are 2 × 2 × 3.
The prime factors of 9 are 3 × 3.
The Least Common Multiple is found by multiplying the largest number of each factors of the two numbers being used to find a common denominator, so in this case we will multiply 2 × 2 × 3 × 3 to find our common denominator is 36.

Definitions:

Factor: numbers that divide evenly into a larger number

Prime numbers: numbers that can only be evenly divided by the number 1 and themselves

Composite numbers: numbers that can be evenly divided by more than just the number 1 and themselves

Prime factorization: factoring a number into its prime components

Multiple: the product of a number times another number

Denominator: The bottom term of a fraction

Links for Students, Parents and Teachers

Now let's do Practice Exercise 3-5 (top). 

Next Page:  Calculate Percentages and Solve Problems (top)