Lesson about Fraction: Multiplying and Dividing Fractions and Whole NUmbers

Unit 15. Lesson 1:
Multiplying and Dividing
Fractions

• To divide fractions by applying ‘K.C.F’.
• To divide a fraction and write the answer in its simplest form.
• To divide mixed number fractions.
• To divide fractions.
Learning Objective
Success Criteria

Can you show the
calculation applicable
for each picture?
Example: 1 x 1 = 1

Starter: Equal to 1
1. 10
2. 5
What do you have to multiply each of these numbers by to obtain the
answer 1?
Extension: Explain, in your own words, any patterns that you notice.
–
1
2
–
2
8
–
2
3
× 2 or –
2
1
× —
1
10
× 4 or –
8
2
× –
1
5
× 1 – or –
1
2
3
2

Reciprocals
• Looking at the first question, if you multiply – by 2, you get the
answer 1.
1
2
• We call this number a reciprocal.
• The product of a number and its reciprocal must be 1.
• Or, equivalently, the reciprocal of a number is 1 divided by that
number.
• The reciprocal of a fraction is the fraction turned upside down.
• For example, the reciprocal of 12 is —. This is because 12 is the same
as —; and — upside down is —.
1
12
12
1
12
1
1
12

Dividing Fractions
Dividing fractions isn’t as tricky as it might seem; we can use a short-
cut.
K = Keep
C = Change
F = Flip
We can use something called K.C.F.

Dividing Fractions
Now, we can follow our steps for multiplying fractions.
—
6
4
3 x 2
4 x 1
4
–
3
÷ 2
–
1
1. We keep the
first fraction as it
is.
4
–
3
2. We change the
÷ sign to a × sign.
×
3. We flip the last
fraction to give its
reciprocal.
1
–
2
– = 1 –
3
2
1
2
So our answer is 1–
1
2

1. We can rewrite this fraction as the super fraction:
–
—
1
2
3
4
Dividing Fractions
– ÷ –
1
2
3
4
2. We are going to simplify – ÷ – by making the
denominator of the super fraction equal to 1.
3
4
1
2
3. To do this we must multiply by the reciprocal of – , which is – .
1
2
2
1
4. Remember, the new super fraction must still be equivalent so
we multiply both the numerator and denominator by –.
2
1
5. We can therefore rewrite our super fraction:
3
4
2
1
–
3
4
1
2
— — =
–
–
2
1
–
×
×
– –
×
2
1
1
which is equivalent to – × –
1
4
2
3

Dividing Fractions
1. Apply ‘Keep, Change, Flip’.
2. Multiply the numerators together.
8 × 2 = 16
3. Multiply the denominators together.
5 × 3 = 15
4. —. This can’t be simplified so it is our final answer.
8
– ÷ –
5 2
3
5
– ÷ –
8
2
3
5
– × –
8
3
2
15
16

Dividing Fractions
1. Turn your mixed number fractions into improper fractions.
2. Apply ‘Keep, Change, Flip’.
3 × 3 = 9
3. Multiply the numerators together.
4. Multiply the denominators together.
2
1 – ÷ 1 –
1 1
3
3
– ÷ –
2
4
3
3
– × –
2
3
4
2 × 4 = 8
5. Write your answer as a mixed number fraction.
9
– = 1 –
8
1
8

Which calculation is the odd
one out? Explain your
answer.

HOMEWORK: WORKBOOK PAGE 158
PRACTICE 4, 5, 6

Lesson about Fraction: Multiplying and Dividing Fractions and Whole NUmbers

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