7th Grade Pre-algebra

Chapter 5 Notes

5.1 Writing Fractions as Decimals

Vocabulary

Terminating Decimal: a decimal which ends (non-repeating) Ex. 0.25

Repeating Decimal: a decimal which repeats one or more digits Ex. .6666..

Bar notation: used to indicate a repeating number in a decimal. Ex.

Period: the digit that repeats in a repeating decimalMixed Number: a fraction written as the sum of whole

number and a fraction.

Writing a Fraction as a Decimal

Write a a decimal Write as a decimal8

3

38

16

5

516

Writing Repeating Decimals

Write as a decimal Write as a decimal11

6

15

2

Writing Mixed Numbers as Decimals

Write as a decimal Write as a decimal2

13

8

15

Comparing Fractions and Decimals

• To compare Fractions and Decimals, change the fractions to decimals and compare using <, >, or =

5.2 Rational Numbers

Vocabulary

Rational Numbers: a number that can be written as a fraction.

Ex. .33333 can be written as 31

Writing Mixed Numbers and Integers as Fractions

4

33

6

Writing Terminating Decimals as Fractions

0.48

3.375

Write Repeating Decimals and Fractions

5.3 Multiplying Rational Numbers

Vocabulary

Dimensional Analysis: the process of including units of measurement when you compute. Used to check whether an answer is reasonable.

Multiplying Fractions

To multiply fractions, multiply the numerators and multiply the denominators. Simplify.

2

1

12

6

43

32

4

3

3

2.

You Try…

5

3

4

1.

6

5

5

2

Multiplying Negative Fractions

To multiply negative fractions, attach the negative sign to the numerator of the fractions, then multiply.

7

2

2

1

Simplifying BEFORE Multiplying

When multiplying you can cross cancel first

8

3

12

5

Multiplying Algebraic Fractions

d

b

b

a 22

4

312 k

jk

5.4 Dividing Rational Numbers

Vocabulary

Multiplicative Inverse: Two numbers whose product is one.

Reciprocal: Two numbers whose product is one.

* To find the multiplicative inverse or reciprocal of a number, write it as a fraction and ‘flip’ the fraction

Find Multiplicative Inverses

8

3

7

3

6

Dividing by a Fractions

To divide by a fraction, multiply by its multiplicative inverse

You Try…

Dividing by a Whole Number

To divide by a whole number, first rename the whole number as a fraction, then multiply by the reciprocal.

68

5

Dividing by Mixed Numbers

To divide by a mixed number, rename the mixed numbers as improper fractions, multiply by the multiplicative inverse.

5.5 Adding and Subtracting Like Fractions

To add fractions with like denominators, add the numerators and write the sum over the denominator.

To subtract fractions with like denominators, subtract the numerators and write the difference over the denominator.

Adding and Subtracting Fractions

Adding and Subtracting Mixed Numbers

To add or subtract mixed numbers with common denominators, first add the whole numbers, then add the fractions. Simplify.

Adding and Subtracting Algebraic Fractions

Follow the same rules as adding fractions

8

5

8

nn

11

2

11

6 rr

5.6 Least Common Multiple (LCM)

Vocabulary

Multiple: the multiple of a number is a product of that number and a whole number.

Common Multiples: when two or more numbers share the same multiple

Least Common Multiple: The smallest non-zero multiple that two or more numbers share

Least Common Denominator: the LCM of the denominators of two or more fractions.

Common Multiples

List the first 10 multiples of each number, then find any multiples the numbers share

Find the common multiples of 4 and 6

Least Common Multiples

Method 1: List out multiples

List the first 10 multiples of each number, then determine which common multiple is the smallest.

Find the least common multiples of 4 and 6

Least Common Multiples

Method 2: Use prime factorizationWrite the prime factorization of each number, write in exponent form.

Find the greatest power of each number between the numbers and circle them. Multiply these circled numbers together to find the LCM.

Find the LCM of 108 and 240

180 = 2 ∙ 2 ∙ 3 ∙ 3 ∙ 3 = 22 ∙ 33

240 = 2 ∙ 2 ∙ 2 ∙ 2 ∙ 3 ∙ 5 = 24 ∙ 3 ∙ 5

LCM = 33 ∙ 24 ∙ 5 = 2160

LCM

Find the LCM of 24 and 32

Find the LCM of 45, 30, 35

LCM of Monomials

Find the LCM of 18xy2 and 10y

Least Common Denominator

Step 1: find the LCM of the denominators

Step 2: rewrite the fractions using the LCD

Step 3: compare the numerators.

LCD

LCD of Algebraic Fractions

aband

b 8

3

12

52

5.7 Adding and Subtracting Unlike Fractions

To add or subtract fractions with unlike denominators, rename the fractions with common denominators, usually the LCD. Then add and simplify.

Adding Unlike Fractions

12

7

8

3

3

2

4

1

3

2

7

3

Subtracting Unlike Fractions

7

6

12

5

4

1

7

3

8

5

4

3

Adding and Subtracting Mixed Numbers

To add or subtract mixed numbers, write the mixed numbers as improper fractions, then rename using the LCD, add or subtract, simplify.

Practice…

5.8 Measures of Central Tendency

Vocabulary

Measures of Central Tendency: using one or more numbers to represent a whole set of data

Finding the Mean

Find the Mean of the data set

Find the Median

Find the Median of the data set

Find the Mode

Find the Mode of the data set

You Try…

Finding Extreme Values

• Extreme Values are numbers in a set that are much greater or much less than the rest of the data. Extreme values can affect the mean of the data and overall the usefulness of the data.

Extreme values

Problem Solving

5.9 Solving Equations with Rational Numbers

ReviewSolve the following equations:

1. 3x + 4 = 13 2. 375

x

Solving Addition and Subtraction Equations

5.10 Arithmetic and Geometric Sequences

Vocabulary

Sequence: an order list of numberArithmetic sequence: a sequence in which the difference

between any two consecutive terms is the sameGeometric sequence: a sequence in which the quotient of

any two consecutive terms is the same.Term: each number in a sequenceCommon Difference: the differences in a arithmetic

sequenceCommon Ratio: the quotient in a geometric sequence

You Try…

Determine whether each sequence is arithmetic, geometric, or neither. If it is arithmetic or geometric, state the common difference or common ratio and write the next three terms of the sequence.

1. 2, 5, 8, 11, ….

2. 4, 1, ¼, 1/16, ….

3. 25, 22, 19, 16, …

1. 2, 6, 18, 54