Warm up Puzzle 1: There are two lengths of rope. Each one can burn in exactly one hour. They are not necessarily of the same length or width as each other. They are not of uniform width (may be wider in the middle than on one end) thus burning half the rope is not necessarily ½ an hour. By burning the ropes how do you measure exactly 45 minutes of time? Puzzle 2: Count the Fs in the following sentence once. Do not go back and count again. Finished files are the result of year of scientific study combing with the experience of years.

FRACTIONS LESSON 4

TERMINOLOGY NUMERATOR – Top digit of a fraction DENOMINATOR – Bottom digit of a fraction EQUIVALENT FRACTIONS - are fractions that have the same value ex: ½ and 2/4 MIXED FRACTION - is a whole number plus a fraction ex: 3 1/2 IMPROPER FRACTIONS - have the numerator part greater or equal to the denominator part ex: 5/2

EQUIVALENT FRACTIONS We can determine if fractions are equivalent by multiplying the numerator and denominator by the same number EXAMPLE: x2 1 2 2 4 = x2

TRY THESE 3 5 1) 2) 3) = 6 7 = 4 8 =

TRY THESE 3 5 x2 6 10 1) 2) 3) = x2 6 7 = 4 8 =

TRY THESE 3 5 6 10 1) 2) 3) = 6 7 x2 12 14 = x2 4 8 =

TRY THESE 3 5 6 10 1) 2) 3) = 6 7 12 14 = 4 8 x2 8 16 = x2

3 5 MIXED FRACTIONS 3 EXAMPLE: TO CALCULATE THE NUMERATOR when converting  mixed to improper fractions:   1) Multiply the whole number of the mixed fraction by the denominator 2) Add on the numerator of the fraction part 3

CHANGING MIXED TO IMPROPER STEP 1 Multiply 3 x 5 = 15 EXAMPLE: 3 5 3 x

CHANGING MIXED TO IMPROPER STEP 1 Multiply 3 x 5 = 15 STEP 2 Add the result from step 1 to the numerator 15 + 3 = 18 EXAMPLE: 3 5 3

CHANGING MIXED TO IMPROPER STEP 1 Multiply 3 x 5 = 15 STEP 2 Add the result from step 1 to the numerator 15 + 3 = 18 STEP 3 Place result from step 2 in the numerator EXAMPLE: 3 5 3 18 ?

CHANGING MIXED TO IMPROPER STEP 1 Multiply 3 x 5 = 15 STEP 2 Add the result from step 1 to the numerator 15 + 3 = 18 STEP 3 Place result from step 2 in the numerator STEP 4 Keep the same denominator EXAMPLE: 3 5 3 18 ? 18 5

IMPROPER FRACTIONS 14 6 EXAMPLE: TO CHANGE THE IMPROPER fraction to a mixed fraction DIVIDE the numerator by the denominator   The quotient (i.e. the result of division) is the whole number part of the mixed fraction The remainder is the numerator of the fraction part of the mixed fraction

CHANGING IMPROPER TO MIXED STEP 1 Divide 14 ÷ 6 = 2 and remainder of 2 EXAMPLE: 14 6

CHANGING IMPROPER TO MIXED STEP 1 Divide 14 ÷ 6 = 2 and remainder of 2 STEP 2 Remainder is the numerator EXAMPLE: 14 6 2 ? 2

CHANGING IMPROPER TO MIXED STEP 1 Divide 14 ÷ 6 = 2 and remainder of 2 STEP 2 Remainder is the numerator STEP 3 Keep the same denominator EXAMPLE: 14 6 2 ? 2 2 6 2

CHANGING IMPROPER TO MIXED STEP 1 Divide 14 ÷ 6 = 2 and remainder of 2 STEP 2 Remainder is the numerator STEP 3 Keep the same denominator STEP 4 Reduce to lowest terms EXAMPLE: 14 6 2 ? 2 2 6 2 2 6 1 3 2 = 2

TRY THESE CHANGE A MIXED FRACTION TO AN IMPROPER: 1) 2) 2 4 3 3 7 5

2 4 14 4 3 7 TRY THESE 3 5 CHANGE A MIXED FRACTION TO AN IMPROPER: 1) 2) 2 4 14 4 3 = 3 7 5

2 4 14 4 7 2 3 7 TRY THESE 3 5 CHANGE A MIXED FRACTION TO AN IMPROPER: 1) 2) 2 4 14 4 7 2 3 = = 3 7 5

TRY THESE CHANGE A MIXED FRACTION TO AN IMPROPER: 1) 2) 2 4 14 4 7 2 3 = = 3 7 38 7 5 =

TRY THESE CHANGE AN IMPROPER TO A MIXED FRACTION: 1) 2) 22 5 17 6

2 22 5 5 17 6 TRY THESE 4 CHANGE AN IMPROPER TO A MIXED FRACTION: 1) = 2) 2 5 22 5 = 4 17 6

TRY THESE CHANGE AN IMPROPER TO A MIXED FRACTION: 1) 2) 2 5 22 5 = 4 5 6 17 6 2 =