Chapter 4 - Fractions FRACTIONS A proper fraction is a fraction whose numerator is less than its denominator. Proper fractions have values that are less than 1. An improper fraction is a fraction whose numerator is greater than or equal to its denominator. Improper fractions have values that are greater than or equal to 1.

Improper fractions can be converted to a mixed number. 3 4 = 5 Same denominator. -20 3(R) Mixed numbers

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Solutions

Simplifying (Reducing) Fractions Determine if BOTH the numerator and the denominator share any common factors Divide the numerator and the denominator by the same number Check if you can reduce further. Your answer should be in the lowest terms.  

Which fraction can be reduced?

Which fraction can be reduced? No! No! Common factor: 5 Common factor: 3 Yes! Yes!

Chapter 4 - Fractions Equivalent Fractions

Multiplying Fractions TOP x TOP 1 2 Bottom x Bottom Always Reduce 1st!!!!

Multiplying Fractions Reduce before multiplying (if possible) Multiply straight across the numerator and denominator Don’t forget about the sign, if any. Check if you can simplify your answer

TRY THIS! STEPS 1. Reduce Multiply Across Check if the answer is in the lowest terms

SOLUTIONS 1 STEPS 1. Reduce Multiply Across Check if the answer TOP x TOP 1 STEPS 1. Reduce Multiply Across Check if the answer is in the lowest terms 1 2 1 Bottom x Bottom 1 1 3 6

FLIP = INVERT = RECIPROCATE the fraction DIVIDING FRACTIONS DIVIDING BY A FRACTION IS AS SIMPLE AS , YOU FLIP AND MULTIPLY!!!!!!!! PIE (1. Keep the first fraction), (2. Change division to multiplication), (3. Flip the second fraction) 1 4 FLIP = INVERT = RECIPROCATE the fraction

Dividing Fractions Keep the first fraction Change the division sign to multiplication Flip the second fraction Multiply fractions across the numerator & denominator Follow integer rules for multiplication Check if you can simplify your answer

Adding and Subtracting Fractions You must have a COMMON DENOMINATOR in order to add and subtract fractions Add/Subtract the numerators Keep the same denominator Follow integer rules for addition and subtraction Check if you can reduce your answer To find the LEAST COMMON DENOMINATOR (LCD), use: Guessing, or Listing Multiples, or Prime factorization of denominators

SUBTRACTING FRACTIONS W/UNLIKE DENOMINATORS MULTIPLY BY RATIO OF ONE 3 1. LCD =? 3. SUBTRACT ACROSS KEEP BOTTOM 1 9

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SOLUTION. 5 21

MULTIPLY MIXED NUMBERS 3 3 1 1 1. IMPROPER 1. IMPROPER 2. REDUCE BEFORE MULTIPLYING

DIVIDING MIXED NUMBERS 7 1. IMPROPER 1. IMPROPER 2. FLIP & MULTIPLY 3. REDUCE 5

ADDING MIXED FRACTIONS

ADDING MIXED NUMBERS (Alternative Method) ∙ 2 ∙ 2 1. LCD ∙ 3 1. LCD ∙ 3 MIXED

SUBTRACTING MIXED NUMBERS

SUBTRACTING MIXED NUMBERS (Alternative Method) 1. LCD 2. BORROWING ∙ 2 ∙ 2 ∙ 3 ∙ 3

COMPLEX FRACTIONS A FRACTION IN THE NUMERATOR OR DENOMINATOR

COMPLEX FRACTIONS (ALTERNATIVE WAY) A FRACTION IN THE NUMERATOR OR DENOMINATOR LCD = 15 2. MULTIPLY BY LCD EACH TERM 5 3  15 1 15  1 5 1 15  1  15 1 3 STEPS LCM/LCD MULTIPLY EACH TERM IN TOP & BOTTOM BY LCD (DISTRIBUTIVE PROPERTY) 3. SIMPLIFY