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Mathematics

Common fractions

Educator section

Memorandum

14. a) denominator

b) common denominator

c) multiple

d) tellers

e) number

f) fractions

g) improper fractions

h) simplify

15.2 a)

= 12 21 size 12{ { { size 8{"12"} } over { size 8{"21"} } } } {} + 14 21 size 12{ { { size 8{"14"} } over { size 8{"21"} } } } {}

= 26 21 size 12{ { { size 8{"26"} } over { size 8{"21"} } } } {}

= 1 5 21 size 12{ { { size 8{5} } over { size 8{"21"} } } } {}

b)

= 5 10 size 12{ { { size 8{5} } over { size 8{"10"} } } } {} + 6 10 size 12{ { { size 8{6} } over { size 8{"10"} } } } {}

= 11 10 size 12{ { { size 8{"11"} } over { size 8{"10"} } } } {}

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

c)

= 36 45 size 12{ { { size 8{"36"} } over { size 8{"45"} } } } {} - 25 45 size 12{ { { size 8{"25"} } over { size 8{"45"} } } } {}

= 11 45 size 12{ { { size 8{"11"} } over { size 8{"45"} } } } {}

d)

= 4 6 size 12{ { { size 8{4} } over { size 8{6} } } } {} - 3 6 size 12{ { { size 8{3} } over { size 8{6} } } } {}

= 1 6 size 12{ { { size 8{1} } over { size 8{6} } } } {}

16.

a)

= 11 2 3 size 12{"11" { { size 8{2} } over { size 8{3} } } } {} + 1 7 size 12{ { { size 8{1} } over { size 8{7} } } } {}

= 11 14 21 size 12{"11" { { size 8{"14"} } over { size 8{"21"} } } } {} + 3 21 size 12{ { { size 8{3} } over { size 8{"21"} } } } {}

p = 11 17 21 size 12{"11" { { size 8{"17"} } over { size 8{"21"} } } } {}

b)

= 3 1 4 1 9 size 12{3 { { size 8{1} } over { size 8{4} } } - { { size 8{1} } over { size 8{9} } } } {}

= 3 9 36 4 36 size 12{ { { size 8{9} } over { size 8{"36"} } } - { { size 8{4} } over { size 8{"36"} } } } {}

t = 3 5 36 size 12{ { { size 8{5} } over { size 8{"36"} } } } {}

= 6 3 4 size 12{ { { size 8{3} } over { size 8{4} } } } {} – (3 1 2 size 12{ { { size 8{1} } over { size 8{2} } } } {} + 1 2 3 size 12{ { { size 8{2} } over { size 8{3} } } } {} )

= 6 3 4 size 12{ { { size 8{3} } over { size 8{4} } } } {} – 3 3 6 size 12{ { { size 8{3} } over { size 8{6} } } } {} + 4 6 size 12{ { { size 8{4} } over { size 8{6} } } } {}

= 6 3 4 size 12{ { { size 8{3} } over { size 8{4} } } } {} – 4 1 6 size 12{ { { size 8{1} } over { size 8{6} } } } {}

= 2 9 12 size 12{ { { size 8{9} } over { size 8{"12"} } } } {} - 2 12 size 12{ { { size 8{2} } over { size 8{"12"} } } } {}

g = 2 7 12 size 12{ { { size 8{7} } over { size 8{"12"} } } } {}

d)

= 9 7 8 size 12{ { { size 8{7} } over { size 8{8} } } } {} - (4 9 12 size 12{ { { size 8{9} } over { size 8{"12"} } } } {} + 8 12 size 12{ { { size 8{8} } over { size 8{"12"} } } } {} )

= 9 7 8 size 12{ { { size 8{7} } over { size 8{8} } } } {} - 5 5 12 size 12{ { { size 8{5} } over { size 8{"12"} } } } {}

= 4 7 8 size 12{ { { size 8{7} } over { size 8{8} } } } {} - 5 12 size 12{ { { size 8{5} } over { size 8{"12"} } } } {}

= 4 21 24 size 12{ { { size 8{"21"} } over { size 8{"24"} } } } {} - 10 24 size 12{ { { size 8{"10"} } over { size 8{"24"} } } } {}

v = 4 11 24 size 12{ { { size 8{"11"} } over { size 8{"24"} } } } {}

Leaner section

Content

Activity: addition and subtraction of fractions [lo 1.7.3]

14. Addition and subtraction of fractions

LET US REVISE.

The answers to the following questions are hidden below.

Circle them when you find them and then complete the sentences.

a b t t t s o n k o f m n
d e n o m i n a t o r y u
e d e l u o a e n r a j m
n k l l l e a m d o c p e
o h a e t m l e i n t o r
m m v r i e d r g e i o a
i n i s p r f e s g o g t
n s u x l m g p t t n h o
a e q k e l v o l e s t r
t d e f s h j r k l e e s
o q w e r t y p y o l u h
r s d a z d o m u b g e s
s i m p l i f i e d e l h

a) We can only add or subtract fractions if the.................................................. are the same.

b) If the denominators differ, we must find .................................................. fractions with the same denominators.

c) We can find the common denominator easily by using ..................................................

d) We only add the.................................................. together.

e) The .................................................. stays unchanged when we add or subtract.

f) When we add mixed numbers together, we first add the natural numbers and then

the ..................................................

g) When we subtract mixed numbers, we can first change them to ................................................. fractions.

h) Answers must always be .................................................. as far as possible.

15.1 Do you still remember?

When we add or subtract e.g. one third ( 1 3 size 12{ { { size 8{1} } over { size 8{3} } } } {} ) + four fifths ( 4 5 size 12{ { { size 8{4} } over { size 8{5} } } } {} ) or five sixths ( 5 6 size 12{ { { size 8{5} } over { size 8{6} } } } {} ) – two nineths ( 2 9 size 12{ { { size 8{2} } over { size 8{9} } } } {} ) we must first make the DENOMINATORS the same. To do this we must look for the Lowest Common Multiple (LCM) .

If we want the LCM of 3 and 5 we can work as follows:

3: 3 ; 6 ; 9 ; 12 ; 15 ; 18 ; 21 ; etc.

5: 5 ; 10 ; 15 ; 20 ; 25 ; etc.

Thus we change both denominators to 15:
1 × 5
3 × 5
=
5
15
en
4 × 3
5 × 3
=
12
15

Thus: 1 3 + 4 5 5 15 + 12 15 17 15 1 2 15 alignl { stack { size 12{ { { size 8{1} } over { size 8{3} } } + { { size 8{4} } over { size 8{5} } } } {} #= { { size 8{5} } over { size 8{"15"} } } + { { size 8{"12"} } over { size 8{"15"} } } {} # = { { size 8{"17"} } over { size 8{"15"} } } {} #=1 { { size 8{2} } over { size 8{"15"} } } {} } } {}

15.2 Calculate the following:

a) x = 4 7 + 2 3 size 12{x= { { size 8{4} } over { size 8{7} } } + { { size 8{2} } over { size 8{3} } } } {}

___________________________________________________

___________________________________________________

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b) y = 1 2 + 3 5 size 12{y= { { size 8{1} } over { size 8{2} } } + { { size 8{3} } over { size 8{5} } } } {}

___________________________________________________

___________________________________________________

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c) d = 4 5 5 9 size 12{d= { { size 8{4} } over { size 8{5} } } - { { size 8{5} } over { size 8{9} } } } {}

___________________________________________________

___________________________________________________

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d) k = 2 3 1 2 size 12{k= { { size 8{2} } over { size 8{3} } } - { { size 8{1} } over { size 8{2} } } } {}

___________________________________________________

___________________________________________________

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___________________________________________________

16. Work together with a friend and calculate:

a) p = 7 2 3 + 4 1 7 size 12{p=7 { { size 8{2} } over { size 8{3} } } +4 { { size 8{1} } over { size 8{7} } } } {}

___________________________________________________

___________________________________________________

___________________________________________________

___________________________________________________

b) t = 5 1 4 2 1 9 size 12{t=5 { { size 8{1} } over { size 8{4} } } - 2 { { size 8{1} } over { size 8{9} } } } {}

___________________________________________________

___________________________________________________

___________________________________________________

___________________________________________________

c) g = 6 3 4 2 1 2 + 1 2 3 size 12{g=6 { { size 8{3} } over { size 8{4} } } - left (2 { { size 8{1} } over { size 8{2} } } +1 { { size 8{2} } over { size 8{3} } } right )} {}

___________________________________________________

___________________________________________________

___________________________________________________

___________________________________________________

d) v = 9 7 8 3 3 4 + 1 2 3 size 12{v=9 { { size 8{7} } over { size 8{8} } } - left (3 { { size 8{3} } over { size 8{4} } } +1 { { size 8{2} } over { size 8{3} } } right )} {}

___________________________________________________

___________________________________________________

___________________________________________________

___________________________________________________

17. CHALLENGE!

Divide into groups of three. Complete the following table by filling in the number of hours you spent doing homework last week:

NAME Mon Tues Wed Thur Fri
e.g Nomsa 1 1 2 size 12{1 { { size 8{1} } over { size 8{2} } } } {} 2 1 4 size 12{2 { { size 8{1} } over { size 8{4} } } } {} 3 3 4 size 12{3 { { size 8{3} } over { size 8{4} } } } {} 1 1 2 size 12{1 { { size 8{1} } over { size 8{2} } } } {} 1 2 size 12{ { { size 8{1} } over { size 8{2} } } } {}
1. ............................................... ............ ............ ............ ............ ............
2. ............................................... ............ ............ ............ ............ ............
3. ............................................... ............ ............ ............ ............ ............

Answer the following questions:

a) How many hours did each member of the group spend on homework last week?

1. _________________________________

2. _________________________________

3. _________________________________

b) Who spent the most time on homework? _______________________________

c) Who learnt the least? _________________________________

d) Calculate the difference between b en c’s answers.

___________________________________________________

___________________________________________________

___________________________________________________

___________________________________________________

e) Ask another group to check your answers.

Assessment

Learning Outcome 1: The learner will be able to recognise, describe and represent numbers and their relationships, and to count, estimate, calculate and check with competence and confidence in solving problems.

Assessment Standard 1.7: We know this when the learner estimates and calculates by selecting and using operations appropriate to solving problems that involve:

1.7.3: addition, subtraction and multiplication of common fractions.

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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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