Operations with Fractions and mixed numbers Chapter 3 Notes Operations with Fractions and mixed numbers

3.1 Notes – Adding and Subtracting like fractions Like Fractions – Fractions that have the same denominator Step 1: Add or subtract the numerator (top number) Step 2: Copy the denominator (bottom number) EX1: 2 4 + 1 4 = 3 4 EX2: 5 6 - 4 6 = 1 6

3.2 Notes – adding and subtracting unlike fractions Unlike Fractions – Fractions that have different denominators Step1: Find the least common denominator (Hint: Multiply the denominators) Step 2: What you do to the bottom, you do to the top! Find your new numerators Step 3: Add or subtract the numerators and copy the denominators EX1: 1 2 + 1 3 = EX2: 1 3 - 1 4 =

3.3 Notes: Improper Fractions and Mixed Numbers Improper Fraction: A fraction where the numerator is bigger than the denominator. EX: 5 4 10 3 Mixed Number: A number that contains a whole number and a fraction EX: 3 1 2 5 3 5

To write an improper fraction as a mixed number: Step 1: How many “sets” of the denominator can you take out of the numerator? (Write this as your whole number) Step 2: Write what’s left over as a fraction with the same denominator. EX1: 7/4 = 1 ¾ EX2: 19/8 = EX 3: 9/4 = EX 4: 25/5 =

To write a mixed number as an improper fraction: Step 1: Multiply the denominator and the whole number; then add the numerator Step 2: This number is the numerator to the improper fraction Step 3: Copy the denominator Ex1: 1 ¼ = EX2: 2 1/5 = EX3: 4 ¾ = EX4: 100 1/8 =

3.4 Notes: Multiplying Fractions Step 1: Multiply the numerators Step 2: Multiply the Denominators Ex1: ½ x ¾ = EX2: 5/6 x 1/8

3.5 Notes: Dividing Fractions Step 1: Rewrite the problem inverting (flipping) the second fraction. Step 2: Multiply these 2 fractions. EX1: 5 6 ÷ 1 2 = EX2: 3 4 ÷ 1 2 =

3.6 Notes: Adding and Subtracting Mixed numbers Step 1: Add or subtract the fraction Step 2: Add or subtract the whole number EX1: 3 1/3 - 1 2/3 = EX2: 6 2/3 - 5 1/6 = USE YOUR CALCULATOR!!!

3.7 notes: Multiplying and dividing mixed numbers Step 1: Convert mixed numbers into improper factions Step 2: Multiply or divide Step 3: Do you have an improper fraction as an answer? Change it back to a mixed number! EX: 3 ½ x 2 1/3 7 2 X 7 3 = 49 6 49 6 = 6 1 6