2.11 Fractions - 07

Mathematics

Common fractions

Educator section

Memorandum

18.1

ADDITION

$\frac{1}{2}$ + $\frac{1}{2}$ + $\frac{1}{2}$ + $\frac{1}{2}$ + $\frac{1}{2}$

$\frac{1}{4}$ + $\frac{1}{4}$ + $\frac{1}{4}$ + $\frac{1}{4}$ + $\frac{1}{4}$ + $\frac{1}{4}$

$\frac{3}{7}$ + $\frac{3}{7}$

$\frac{2}{3}$ + $\frac{2}{3}$ + $\frac{2}{3}$

$\frac{2}{5}$ + $\frac{2}{5}$ + $\frac{2}{5}$ + $\frac{2}{5}$

PRODUCT

2 $\frac{1}{2}$

1 $\frac{1}{2}$

2

1 $\frac{3}{5}$

b) numerators x numerators

denominators x denominators

d)

(i) $\frac{\text{21}}{\text{10}}$

= 2 $\frac{1}{\text{10}}$

(ii) $\frac{\text{12}}{3}$

= 4

(iii) $\frac{\text{84}}{9}$

= 9 $\frac{1}{3}$

18.2 3 1 2 8

1. (i) 15 x 4 (ii) 18 x 40

8 5 25 27

2 1 5 3

k = ${}_{{}_{}^{}}{}^{}\frac{3}{2}$ = 1 $\frac{1}{2}$ c = $\frac{\text{16}}{\text{15}}$ = 1 $\frac{1}{\text{15}}$

7 4 3

18.3 b) (i) = 38 x 16 (ii) = 17 x 9

4 5 3 10

m = 28 n = $\frac{\text{51}}{\text{10}}$

n = $5\frac{1}{\text{10}}$

6

(iii) = 18 x 8

5 3

1

= $\frac{\text{48}}{5}$

p = 9 $\frac{3}{5}$

19.1

a) 1

b) 1

c) 1

d) 1

19.2 Product is 1 every time

19.4 a) $\frac{\text{20}}{\text{17}}$

b) $\frac{1}{\text{40}}$

c) $\frac{5}{\text{31}}$

d) $\frac{8}{\text{73}}$

19.5 c) $\frac{5}{\text{31}}$ : First make an improper fraction ( $\frac{\text{31}}{5}$ )

d) $\frac{8}{\text{73}}$ : First make an improper fraction ( $\frac{\text{73}}{8}$ )

20. a) 1 $\frac{2}{3}$ x $\frac{1}{2}$

= $\frac{5}{3}$ x $\frac{1}{2}$

= $\frac{5}{6}$ m = 83, $\stackrel{\text{.}}{3}$ cm

b) $\frac{5}{6}$ x $\frac{1}{3}$ = $\frac{5}{\text{18}}$ m

= 27, $\stackrel{\text{.}}{7}$ cm

22.

(a) 32

(b) 15

(c) 25

(d) 25

(e) 45

(f) 2

(g) 8

(h) 7

(i) 7

(j) 6

(k) 6

(l) 8

(m) 8

(n) 8

(o) 100

Leaner section

Content

Activity: multiplication of fractions [lo 1.7.3, lo 2.1.5]

18. MULTIPLICATION OF FRACTIONS

18.1 Multiplication of fractions with natural numbers

You already know that multiplication is repeated addition.

a) See if you can complete the following table:

b) Look carefully at the completed table. Can you think of a shorter way/method to find the answers?

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c) TAKE NOTE!

You could also follow this method:

1. Write both numbers as fractions e.g. $6\times \frac{1}{4}=\frac{6}{1}\times \frac{1}{4}$

2. Multiply the numerators: 6 × 1 = 6

3. Multiply the denominators: 1 × 4 = 4

4. Simplify the answer: $\frac{6}{4}=1\frac{2}{4}=1\frac{1}{2}$

d) Calculate:

(i) $7\times \frac{3}{\text{10}}$

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(ii) $\frac{2}{3}\times 6$

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(iii) $\text{12}\times \frac{7}{9}$

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e) We would represent $6\times \frac{1}{4}$ in another way using a number line:

f) Represent the following on a number line: $x=4\times \frac{2}{3}$

18.2 Multiplying fractions with fractions

a) Look carefully at the following examples:

(i) Half ( $\frac{1}{2}$ ) of three quarters ( $\frac{3}{4}$ ) can be shown like this: