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Notes 8 th Grade Pre-Algebra McDowell

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LCM9/25 LCM Least common multiple The smallest number that is a multiple of both numbers

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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

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Example Find the LCM of 8 and 3 12345678 816243240485664 3691215182124 1. Make a mult table 2. Compare 3. Find the smallest match The LCM of 8 and 3 is 24

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You Try Find the LCM between 1.10 and 45 2.12 and 7

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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)

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You try Workbook p 76 # all

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Fractions and Decimals9/28 a 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

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1. Keep the whole number a whole number 2. Divide the numerator by the denominator Converting Fractions To decimals Example

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Converting Terminal decimals 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

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Example 6.925 The 5 is in the thousandths place so 1000 is the denominator 925 1000 Simplify 925 25 1000 25 37 40 6 6 6

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3. Subtract n from both sides Remember n = 0.6 0.6 = n Converting Repeating decimals 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 100 66.6 = 100n -0.6 - n 66 = 99n

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99 4. Divide both side by 99 to solve for n 66 = n 99 5. Reduce the fraction 66 11= n 99 11 2 = n 3

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You try Workbook p 78 # 3-21 every 3 rd

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Adding and Subtracting Fractions9/29 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

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Example Common denominator so add or subtract the numerator Already in simplest form

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Example Common denominator so add or subtract the numerator Already in simplest form because we do not know what x is

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Example Find a common denominator Add or Subtract numerators 24 x 4 Already in simplest form

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Converting A Mixed Number To an Improper 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

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6 x 5 + 3 6 30 + 3 6 33 6

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1. Divide the numerator by the dominator Converting An Improper To a Mixed # 2. The quotient is the whole number 3. The remainder is the new numerator 4. Keep the same denominator

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Example Convert 26 to a mixed number 3 3 26 8 -24 2 R 2

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Example 1. Convert all mixed numbers into improper fractions 2. Find a common denominator 3. Add or subtract the numerators 4. Keep the common denominator 5. Write in simplest form

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Additional Examples 1.. 2..

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You try Workbook p 80 # all

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Multiplying and Dividing Fractions9/30 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

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Example 2. Simplify by taking common factors out of the numerators and denominators 55 5 3. Multiply numerators together 4. Multiply denominators together 5. In simplest form

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Example 2. Simplify by taking common factors out of the numerators and denominators 3. Multiply numerators together 4. Multiply denominators together 5. In simplest form x x 2 2

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Additional Examples 1.. 2..

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2. Keep 1 st 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 2 nd fraction 5. Follow steps to multiply fractions

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Example Keep X Change Flip Multiply 44 44

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You try Workbook p 82 # all

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Chapter 5 Review10/1

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Chapter 5 Quiz10/2

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