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2.11 Fractions - 07

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Mathematics

Common fractions

Educator section

Memorandum

18.1

ADDITION

1 2 size 12{ { { size 8{1} } over { size 8{2} } } } {} + 1 2 size 12{ { { size 8{1} } over { size 8{2} } } } {} + 1 2 size 12{ { { size 8{1} } over { size 8{2} } } } {} + 1 2 size 12{ { { size 8{1} } over { size 8{2} } } } {} + 1 2 size 12{ { { size 8{1} } over { size 8{2} } } } {}

1 4 size 12{ { { size 8{1} } over { size 8{4} } } } {} + 1 4 size 12{ { { size 8{1} } over { size 8{4} } } } {} + 1 4 size 12{ { { size 8{1} } over { size 8{4} } } } {} + 1 4 size 12{ { { size 8{1} } over { size 8{4} } } } {} + 1 4 size 12{ { { size 8{1} } over { size 8{4} } } } {} + 1 4 size 12{ { { size 8{1} } over { size 8{4} } } } {}

3 7 size 12{ { { size 8{3} } over { size 8{7} } } } {} + 3 7 size 12{ { { size 8{3} } over { size 8{7} } } } {}

2 3 size 12{ { { size 8{2} } over { size 8{3} } } } {} + 2 3 size 12{ { { size 8{2} } over { size 8{3} } } } {} + 2 3 size 12{ { { size 8{2} } over { size 8{3} } } } {}

2 5 size 12{ { { size 8{2} } over { size 8{5} } } } {} + 2 5 size 12{ { { size 8{2} } over { size 8{5} } } } {} + 2 5 size 12{ { { size 8{2} } over { size 8{5} } } } {} + 2 5 size 12{ { { size 8{2} } over { size 8{5} } } } {}

PRODUCT

2 1 2 size 12{ { { size 8{1} } over { size 8{2} } } } {}

1 1 2 size 12{ { { size 8{1} } over { size 8{2} } } } {}

6 7 size 12{ { { size 8{6} } over { size 8{7} } } } {}

2

1 3 5 size 12{ { { size 8{3} } over { size 8{5} } } } {}

b) numerators x numerators

denominators x denominators

d)

(i) 21 10 size 12{ { { size 8{"21"} } over { size 8{"10"} } } } {}

= 2 1 10 size 12{ { { size 8{1} } over { size 8{"10"} } } } {}

(ii) 12 3 size 12{ { { size 8{"12"} } over { size 8{3} } } } {}

= 4

(iii) 84 9 size 12{ { { size 8{"84"} } over { size 8{9} } } } {}

= 9 1 3 size 12{ { { size 8{1} } over { size 8{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 = 3 2 size 12{"" lSub { size 8{ {} rSub {} rSup {} } } lSup {} { {3} over {2} } } {} = 1 1 2 size 12{ { { size 8{1} } over { size 8{2} } } } {} c = 16 15 size 12{ { { size 8{"16"} } over { size 8{"15"} } } } {} = 1 1 15 size 12{ { { size 8{1} } over { size 8{"15"} } } } {}

7 4 3

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

4 5 3 10

m = 28 n = 51 10 size 12{ { { size 8{"51"} } over { size 8{"10"} } } } {}

n = 5 1 10 size 12{5 { { size 8{1} } over { size 8{"10"} } } } {}

6

(iii) = 18 x 8

5 3

1

= 48 5 size 12{ { { size 8{"48"} } over { size 8{5} } } } {}

p = 9 3 5 size 12{ { { size 8{3} } over { size 8{5} } } } {}

19.1

a) 1

b) 1

c) 1

d) 1

19.2 Product is 1 every time

19.4 a) 20 17 size 12{ { { size 8{"20"} } over { size 8{"17"} } } } {}

b) 1 40 size 12{ { { size 8{1} } over { size 8{"40"} } } } {}

c) 5 31 size 12{ { { size 8{5} } over { size 8{"31"} } } } {}

d) 8 73 size 12{ { { size 8{8} } over { size 8{"73"} } } } {}

19.5 c) 5 31 size 12{ { { size 8{5} } over { size 8{"31"} } } } {} : First make an improper fraction ( 31 5 size 12{ { { size 8{"31"} } over { size 8{5} } } } {} )

d) 8 73 size 12{ { { size 8{8} } over { size 8{"73"} } } } {} : First make an improper fraction ( 73 8 size 12{ { { size 8{"73"} } over { size 8{8} } } } {} )

20. a) 1 2 3 size 12{ { { size 8{2} } over { size 8{3} } } } {} x 1 2 size 12{ { { size 8{1} } over { size 8{2} } } } {}

= 5 3 size 12{ { { size 8{5} } over { size 8{3} } } } {} x 1 2 size 12{ { { size 8{1} } over { size 8{2} } } } {}

= 5 6 size 12{ { { size 8{5} } over { size 8{6} } } } {} m = 83, 3 . size 12{ {3} cSup { size 8{ "." } } } {} cm

b) 5 6 size 12{ { { size 8{5} } over { size 8{6} } } } {} x 1 3 size 12{ { { size 8{1} } over { size 8{3} } } } {} = 5 18 size 12{ { { size 8{5} } over { size 8{"18"} } } } {} m

= 27, 7 . size 12{ {7} cSup { size 8{ "." } } } {} 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:

SUM SKETCH REPEATED ADDITION PRODUCT
e.g. 5 × 1 2 size 12{ { { size 8{1} } over { size 8{2} } } } {} 1 2 + 1 2 + 1 2 + 1 2 + 1 2 size 12{ { { size 8{1} } over { size 8{2} } } + { { size 8{1} } over { size 8{2} } } + { { size 8{1} } over { size 8{2} } } + { { size 8{1} } over { size 8{2} } } + { { size 8{1} } over { size 8{2} } } } {} 2 1 2 size 12{2 { { size 8{1} } over { size 8{2} } } } {}
6 × 1 4 size 12{ { { size 8{1} } over { size 8{4} } } } {} .................................................. .................
2 × 3 7 size 12{ { { size 8{3} } over { size 8{7} } } } {} .................................................. .................
3 × 2 3 size 12{ { { size 8{2} } over { size 8{3} } } } {} .................................................. .................
4 × 2 5 size 12{ { { size 8{2} } over { size 8{5} } } } {} .................................................. .................

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

..........................................................................................................................................

..........................................................................................................................................

..........................................................................................................................................

c) TAKE NOTE!

You could also follow this method:

1. Write both numbers as fractions e.g. 6 × 1 4 = 6 1 × 1 4 size 12{6 times { { size 8{1} } over { size 8{4} } } = { { size 8{6} } over { size 8{1} } } times { { size 8{1} } over { size 8{4} } } } {}

2. Multiply the numerators: 6 × 1 = 6

3. Multiply the denominators: 1 × 4 = 4

4. Simplify the answer: 6 4 = 1 2 4 = 1 1 2 size 12{ { { size 8{6} } over { size 8{4} } } =1 { { size 8{2} } over { size 8{4} } } =1 { { size 8{1} } over { size 8{2} } } } {}

d) Calculate:

(i) 7 × 3 10 size 12{7 times { { size 8{3} } over { size 8{"10"} } } } {}

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(ii) 2 3 × 6 size 12{ { { size 8{2} } over { size 8{3} } } times 6} {}

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(iii) 12 × 7 9 size 12{"12" times { { size 8{7} } over { size 8{9} } } } {}

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e) We would represent 6 × 1 4 size 12{6 times { { size 8{1} } over { size 8{4} } } } {} in another way using a number line:

f) Represent the following on a number line: x = 4 × 2 3 size 12{x=4 times { { size 8{2} } over { size 8{3} } } } {}

18.2 Multiplying fractions with fractions

a) Look carefully at the following examples:

(i) Half ( 1 2 size 12{ { { size 8{1} } over { size 8{2} } } } {} ) of three quarters ( 3 4 size 12{ { { size 8{3} } over { size 8{4} } } } {} ) can be shown like this:

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Source:  OpenStax, Mathematics grade 7. OpenStax CNX. Sep 16, 2009 Download for free at http://cnx.org/content/col11075/1.1
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