Notes8th Grade

Pre-Algebra

McDowell

LCM 9/25LCM Least common multiple

The smallest number that is a multiple of both numbers

Steps

To

Find

LCM

1. Make a multiplication table for each number

2. Compare the multiplication tables

3. Pick the smallest number that both (all) tables have

Example Find the LCM of 8 and 3

1 2 3 4 5 6 7 8

8 16 24 32 40 48 56 64

3 6 9 12 15 18 21 24

1. Make a mult table

2. Compare

3. Find the smallest match

The LCM of 8 and 3 is 24

You Try Find the LCM between

1. 10 and 45

2. 12 and 7

Comparing

And

Ordering

fractions

Manipulate the fractions so each has the same denominator

Compare/order the fractions using the numerators (the denominators are the same)

You try Workbook

p 76

# all

Fractions and Decimals 9/28a decimal that ends

1¼ or 1.25

When the same group of numbers continues to repeat forever

4 or 4.33333333333

4.3

Terminating

Decimal

Repeating

Decimal

1. Keep the whole number a whole number

2. Divide the numerator by the denominator

Converting FractionsTodecimals

Example

Converting Terminaldecimals to fractions

1. Find the place value of the terminating decimal

2. Place the numbers after the decimal over the place value

Keep whole numbers as whole numbers

3. Simplify the fraction to lowest terms

Example 6.925 The 5 is in the thousandths place so 1000 is the denominator

9251000 Simplify

925 251000 25

3740

6

6

6

3. Subtract n from both sidesRemember n = 0.6

0.6 = nConverting Repeatingdecimals to fractions

1. Let the decimal = n

2. Multiply both sides by 100

4. Divide both side by 99 to solve for n

0.6 x 100 = n x 10066.6 = 100n

66.6 = 100n-0.6 - n

66 = 99n

66 = 99n99 99

4. Divide both side by 99 to solve for n

66 = n99

5. Reduce the fraction

66 11= n99 11

2 = n3

You try Workbook

p 78

# 3-21 every 3rd

Adding and Subtracting Fractions 9/29

2. Find a common denominator

3. Add or subtract the numerators

Steps

4. Keep the common denominator

5. Write in simplest form (change all improper fractions back into mixed numbers)

1. Convert all mixed numbers into improper fractions

Example Common denominator so add or subtract the numerator

Already in simplest form

Example Common denominator so add or subtract the numerator

Already in simplest form because we do not know what x is

Example Find a common denominator

Add or Subtract numerators

24

x 4

x 4

Already in simplest form

ConvertingA MixedNumberTo anImproper

MAD face

1. Multiply the denominator by the whole number then add the product to the numerator

2. That is the new numerator—keep the old denominator

Multiply, Add, keep the Denominator

6 x 5 + 3 630 + 3 6

33 6

1. Divide the numerator by the dominator

ConvertingAnImproperTo aMixed #

2. The quotient is the whole number

3. The remainder is the new numerator

4. Keep the same denominator

Example Convert 26 to a mixed number 3

3 268

-242

R 2

Example1. Convert all mixed numbers into improper fractions

2. Find a common denominator

3. Add or subtract the numerators4. Keep the common denominator

5. Write in simplest form

Additional

Examples1. .

2. .

You try Workbook

 p 80

# all

Multiplying and Dividing Fractions 9/30

2. Simplify by taking common factors out of the numerators and denominators 3. Multiply numerators together

Steps to multiply fractions

4. Multiply denominators together

5. Write in simplest form (change all improper fractions back into mixed numbers)

1. Convert all mixed numbers into improper fractions

Example2. Simplify by taking common factors out of the numerators and denominators

5

53. Multiply numerators together4. Multiply denominators together

5. In simplest form

Example2. Simplify by taking common factors out of the numerators and denominators

3. Multiply numerators together4. Multiply denominators together

5. In simplest form

x

x 2

2

Additional

Examples1. .

2. .

2. Keep 1st fraction

Steps to divide fractions

3. Change Multiplication to division

1. Convert all mixed numbers into improper fractions

4. Flip Write the reciprocal of the 2nd fraction

5. Follow steps to multiply fractions

Example

Keep

XChangeFlip

Multiply 4

4

You try Workbook

 p 82

# all

Chapter 5 Review 10/1

Chapter 5 Quiz 10/2