Whole Numbers Divided by Fractions

Dividing with Fractions

Whole Numbers Divided by Fractions (Finding How Many)

We want to find how many parts (fraction) are contained in a whole.

4 ÷ 1 = ______3 0 1 2 3 4

We must divide the line into thirds. Then showing sets or groups (“humps”) we count how many 1/3’s are between 0 and 4. The quotient or answer is 12.

What is 4 ÷ 12? What is 1/3 of 12 or 1/3 x 12 ?

Let’s try 2 ÷ 1 ______4 0 1 2

We must divide the line into quarters. Then using “humps” we count how many 1/4’s are between 0 and 2. The quotient or answer is 8. What is 2 ÷ 8? What is 1/4 of 8?

Try 3 ÷ 3/4 Then from CD on page 109 do 3

1 Now we will look at a more challenging type of dividing a whole number by a fraction.

Let’s use a number line to solve: 2 ÷ 3/4 =

______0 1 2

Cut the line into fourths. Now use the groups (“humps”) method to determine how many 3/4’s are in 2. You will discover 2 sets of 3/4’s and a little more. As you extend the third hump you will see that you can only cover 2 out of 3 of the divisions. Therefore, the answer is 2 and 2/3

Try: 3 ÷ 2/3 4÷ 3/5 2÷ 5/9 3÷ 4/7

do 1a 2a 3a 4ac 5

2 Fractions Divided by a Whole Number

1 ÷ 3 = 2

Cut each half into 3. Shade in one section. What fraction of the whole is the shaded section? 1 6

1 ÷ 2 = 2

Cut each half into 2. Shade in one section. What fraction of the whole is the shaded section? 1 4

3 Page 107 - CD do 1ab

1a) 1 ÷ 3 = Use a circle and cut the half into three. 2 Shade one section. What fraction of the whole is the shaded section?

1b) 2 ÷ 4 = Use a circle and cut a third into four. 3 Shade 2 sections. What fraction of the whole are the shaded sections? 2 12

do 1bd 2bd do 3ad (use fraction bars divided into fifths ) do 4ab

Using circle pieces to show Mixed Number divisions:

1 1 ÷ 4 or 3 ÷ 4 = 2 2

Each of the three halves are cut into 4. Shade three sections in the whole circle only. Why? Because fractions are always out of a whole. 1 1 ÷ 4 = 3 2 8 Practice: 1 1 ÷ 5 = 2 1 ÷ 2 = 1 1 ÷ 2 = 2 3 5

4 Dividing Fractions Symbolically

4. Every number has a denominator of ???

Lowest Common Multiple method:

Place the two denominators (ex 5, 2) in a vertical layout. Then…

x1 x2 x3 x4 x5

5 = 5 10 15 20 25

2 = 2 4 6 8 10

The LCM for denominators 5 and 2 is 10

4a) 2 ÷ 2 = 2 ÷ 2 = 3 3 1

The lowest common multiple for 3 and 1 is 3

2 ÷ 2 x 3 = 2 ÷ 6 = 2 ÷ 6 = 2 = 1 3 1x 3 3 3 1 6 3

5 4b) 3 ÷ 3 = 3 ÷ 3 = 4 4 1

The lowest common multiple for 4 and 1 is 4

3 ÷ 3 x 4 = 3 ÷ 12 = 3 ÷ 12 = 3 = 1 4 1x 4 4 4 1 12 4

do 4ef Page 111 - Let’s review the CD together. Page 112 - do 3def 4 5 6bdef Page 114 - do 3ab 4cdef

from UA do 2 Page 115 review 4. Then from UA do 1 2