## STUDY GUIDE - UNIT 12

PAN-BALANCE PROBLEMS, ALGEBRAIC EXPRESSIONS, LINE GRAPHS

AND FORMULAS

Use your Journal pages 393 - 427 to review all the topics presented in this unit. Look over carefully all your Study Links. Make sure that you are comfortable with all the concepts.

1. FACTOR TREE AND PRIME FACTORIZATION: You will need to know how to draw a factor tree. The factor tree starts with the product and proceeds downward with factors until it reaches the end with factors that are only prime numbers, which is called the prime factorization. For example, 60 and 84.

1. FACTOR TREE AND PRIME FACTORIZATION: You will need to know how to draw a factor tree. The factor tree starts with the product and proceeds downward with factors until it reaches the end with factors that are only prime numbers, which is called the prime factorization. For example, 60 and 84.

2. PRIME FACTORS IN COMMON & LEAST COMMON MULTIPLE: You must look at the prime factorization for each number. In the example above:

If we were to circle the same factors for each we would circle 2, 2 & 3. These are the common factors. Then we would multiply these numbers 2 x 2 x 3 to find the the greatest common factor = 12

In order to find the least common multiple we must multiply all the prime numbers together using one of each of the factors for the two products, which are 2 x 2 x 3 x 5 x 7 = 420

In order to find the least common multiple we must multiply all the prime numbers together using one of each of the factors for the two products, which are 2 x 2 x 3 x 5 x 7 = 420

3. USE THE TREE DIAGRAM TO SHOW THE MULTIPLICATION RULE:

Use the multiplication rule to solve the following word problem. Vince is buying a new shirt. He must choose among three colors - white, blue and green. He must decide between short and long sleeves. How many different combinations of color and sleeve length are there?

Use the multiplication rule to solve the following word problem. Vince is buying a new shirt. He must choose among three colors - white, blue and green. He must decide between short and long sleeves. How many different combinations of color and sleeve length are there?

4. YOU MUST KNOW HOW TO SOLVE RATIO PROBLEMS:

Some ratios compare part of a collection of things to the total number of things in the collection. Find the total then express the ratio in a fraction.

For example: 1 out of 6 students in the class is absent. If the total number of students is 12,

then 1/6 of 12 = 2, or 2 students are absent.

It is always best to express a ratio in its simplest form.

BE SURE TO STUDY THE RATIO SECTIONS OF YOUR JOURNAL CAREFULLY.

Some ratios compare part of a collection of things to the total number of things in the collection. Find the total then express the ratio in a fraction.

For example: 1 out of 6 students in the class is absent. If the total number of students is 12,

then 1/6 of 12 = 2, or 2 students are absent.

It is always best to express a ratio in its simplest form.

BE SURE TO STUDY THE RATIO SECTIONS OF YOUR JOURNAL CAREFULLY.