1. Fractions Addition, Subtraction, Multiplication and Division June 25, 2016June 25, 2016June 25, 2016

2. Fractions – Addition, Subtraction, Multiplication & Division  Reciprocals are two numbers whose product is 1. They are also called multiplicative inverses, Definitions Examples Arithmetic Algebra 3 x 4 = 1 a x b = 1 4 3 b a 4/3 is the b/a is the reciprocal reciprocal of 3/4 of a/b

3. Fractions – Addition, Subtraction, Multiplication & Division Adding & Subtracting Fractions  To add or subtract like fractions, (fractions with the same denominator), add or subtract the numerators and write the result over the denominator. Simplify if necessary. Arithmetic Algebra 1 + 3 = 4a + b = a + b 5 5 5c c c

4. Fractions – Addition, Subtraction, Multiplication & Division Adding & Subtracting Fractions  To add or subtract unlike fractions ( fractions with different denominators ), rename the fractions using the LCD, then add or subtract the numerators as with like fractions. Simplify if necessary. Arithmetic 1 + 3 = 5 + 18 = 23 6 5 30 30 30

5. Fractions – Addition, Subtraction, Multiplication & Division  Add or subtract. Simplify. 1.8 - 2 9 9 9 9 2.5 - 3 6 8 6 8 3.7 + 3 8 4 8 4 4.2 - 1 3 6 3 6 5.3 - 1 4 6 4 6 Practice 2 3 11 24 1 51 5 8 1 2 7 12

6. Fractions – Addition, Subtraction, Multiplication & Division  To multiply fractions, multiply the numerators and multiply the denominators. Simplify if necessary.  To multiply mixed numbers, change them to improper fractions first then multiply. Simplify if necessary. Arithmetic Algebra 1 x 2 = 1 x 2 = 2 a x c = a x c = ac 3 5 3 x 5 15 b d b x d bd Multiplying Fractions

7. Fractions – Addition, Subtraction, Multiplication & Division  To divide by a fraction, change the second number to the reciprocal (multiplicative inverse) and then multiply.  To divide mixed numbers, change them to improper fractions first. Simplify if necessary. Arithmetic Algebra 7 ÷ 3 = 7 x 4 = 28 a ÷ c = a x d = ad 8 4 8 3 24 b d b c bc b, c, d ≠ 0 Dividing Fractions

8. Fractions – Addition, Subtraction, Multiplication & Division  Multiply or Divide. Simplify. 1.1 x 3 4 4 4 4 2.2 x 4 3 3. 3 x 5 1 3 4.4 ÷ 8 5 9 5 9 5. 2 1 ÷ 5 5 3 6 3 6 Practice 1/4 2 2/3 16 9/10 2/5