Dividing a Fraction by a Fraction

Dividing a Fraction by a Fraction What is 1/2 ÷ 1/4? How many groups of 1/4 could you fit in the half of the rectangle? 2

Dividing a Fraction by a Fraction For the problem 1/2 ÷ 1/4 , how could you get an answer of 2? Can you see how you could manipulate the fractions to get an answer of 2? Isn’t ½ x 4 = 2? Remember that division is the opposite operation of multiplication, so we can do the following… MULTIPLY. 

Dividing a Fraction by a Fraction Basically, in order to divide fractions we will have to multiply the first fraction by the reciprocal of the second. To make a reciprocal, just flip the fraction over the second fraction. 1 1 1 4 x ÷ = 2 4 2 1

Dividing a Fraction by a Fraction From this point, the problem can be solved in the way that you did for multiplying fractions. 2 2 1 4 x 2 = = 2 1 1 1

Let’s Practice Get White Boards 

Set White Boards to the Side  1 3 Set White Boards to the Side 

Dividing of Fractions by Whole Numbers

Dividing a Whole Number by a Fraction What is 3 ÷ ¼ ? Use your prior knowledge and the illustration above to figure it out. Think, “If I start with 3, how many groups that look like ¼ will I have?”

Dividing a Whole Number by a Fraction 1 2 3 4 5 6 7 11 10 12 9 8 If you start with 3, you will have 12 groups of 1/4 . So, 3 ÷ ¼ = 12. Can you see how you could manipulate the fractions to get an answer of 12?

means how many ’s are in ? So, I have 4 groups of 2! Let’s try a fraction: means how many ’s are in ? So, I have 8 groups of ½! 6-5 MULTIPLY FRACTIONS

Dividing a Whole Number by a Fraction What is 5 ÷ 1/3? If you start with 5, you will have 15 groups of 1/3 . So, 5 ÷ 1/3 = 15. Can you see how you could manipulate the fractions to get an answer of 15?

How to Divide Fractions Step 1 – Convert whole numbers and mixed numbers to improper fractions. This example is from a prior slide. 1 3 1 3 = ÷ ÷ 4 1 4

How to Divide Fractions Step 2 – Keep your first fraction. 3 1 3 = ÷ 1 4 1

How to Divide Fractions Step 3 – Change the operation to multiplication. 3 1 3 = x ÷ 1 4 1

How to Divide Fractions Step 4 – Flip the second fraction. Finding the reciprocal. 3 1 3 4 = x ÷ 1 4 1 1

How to Divide Fractions Step 5 – Multiply the numerators, then multiple the denominators. 3 4 12 = x 1 1 1

How to Divide Fractions Step 6 – Simplify (if possible). 3 4 12 = = 12 x 1 1 1

Let’s practice Get White Boards 6-5 MULTIPLY FRACTIONS

Division - Let’s Try More! 7 1 14 4 9 44 ÷ = ÷ = 9 2 9 7 11 63 7 1 21 20 7 50 ÷ = ÷ = 5 3 5 4 10 7

Great job!