1. 7th Grade Pre-algebra
Chapter 5 Notes 1

2. 5.1 Writing Fractions as Decimals
Vocabulary
Terminating Decimal: a decimal which ends (non-repeating) Ex
Repeating Decimal: a decimal which repeats one or more digits Ex
Bar notation: used to indicate a repeating number in a decimal. Ex.
Period: the digit that repeats in a repeating decimal
Mixed Number: a fraction written as the sum of whole number and a fraction. 2

3. Writing a Fraction as a Decimal
Write a a decimal Write as a decimal

4. Writing Repeating Decimals
Write as a decimal Write as a decimal

5. Writing Mixed Numbers as Decimals
Write as a decimal Write as a decimal

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

7. 5.2 Rational Numbers Vocabulary
Rational Numbers: a number that can be written as a fraction.
Ex can be written as 7

8. Writing Mixed Numbers and Integers as Fractions

9. Writing Terminating Decimals as Fractions
0.48
3.375

10. Write Repeating Decimals and Fractions

11. 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. 11

12. Multiplying Fractions
To multiply fractions, multiply the numerators and multiply the denominators. Simplify.

13. You Try…

14. Multiplying Negative Fractions
To multiply negative fractions, attach the negative sign to the numerator of the fractions, then multiply.

15. Simplifying BEFORE Multiplying
When multiplying you can cross cancel first

16. Multiplying Algebraic Fractions

17. 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 17

18. Find Multiplicative Inverses

19. Dividing by a Fractions
To divide by a fraction, multiply by its multiplicative inverse

20. You Try…

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

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

23. 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. 23

24. Adding and Subtracting Fractions

25. Adding and Subtracting Mixed Numbers
To add or subtract mixed numbers with common denominators, first add the whole numbers, then add the fractions. Simplify.

26. Adding and Subtracting Algebraic Fractions
Follow the same rules as adding fractions

27. 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. 27

28. 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

29. 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

30. Least Common Multiples
Method 2: Use prime factorization
Write 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 ∙ 3 ∙ 3 ∙ 3 = ∙ 33
240 = ∙ 2 ∙ 2 ∙ 2 ∙ 3 ∙ 5 = ∙ 3 ∙ 5
LCM = 33 ∙ 24 ∙ 5 = 2160

31. LCM
Find the LCM of 24 and 32
Find the LCM of 45, 30, 35

32. LCM of Monomials
Find the LCM of 18xy2 and 10y

33. Least Common Denominator
Step 1: find the LCM of the denominators
Step 2: rewrite the fractions using the LCD
Step 3: compare the numerators.

34. LCD

35. LCD of Algebraic Fractions

37. 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. 37

38. Adding Unlike Fractions

39. Subtracting Unlike Fractions

40. 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.

41. Practice…

42. 5.8 Measures of Central Tendency
Vocabulary
Measures of Central Tendency: using one or more numbers to represent a whole set of data 42

43. Finding the Mean
Find the Mean of the data set

44. Find the Median
Find the Median of the data set

45. Find the Mode
Find the Mode of the data set

46. You Try…

48. 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.

49. Extreme values

51. Problem Solving

52. 5.9 Solving Equations with Rational Numbers
Review
Solve the following equations:
1. 3x + 4 = 52

53. Solving Addition and Subtraction Equations

56. 5.10 Arithmetic and Geometric Sequences
Vocabulary
Sequence: an order list of number
Arithmetic sequence: a sequence in which the difference between any two consecutive terms is the same
Geometric sequence: a sequence in which the quotient of any two consecutive terms is the same.
Term: each number in a sequence
Common Difference: the differences in a arithmetic sequence
Common Ratio: the quotient in a geometric sequence 56

63. 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.
2, 5, 8, 11, ….
4, 1, ¼, 1/16, ….
25, 22, 19, 16, …
2, 6, 18, 54