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    This module is included inLens: Siyavula: Mathematics (Gr. 7-9)
    By: SiyavulaAs a part of collection: "Mathematics Grade 7"

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Fractions - 06

Module by: Siyavula Uploaders. E-mail the author

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)

= 12211221 size 12{ { { size 8{"12"} } over { size 8{"21"} } } } {} + 14211421 size 12{ { { size 8{"14"} } over { size 8{"21"} } } } {}

= 26212621 size 12{ { { size 8{"26"} } over { size 8{"21"} } } } {}

= 1 521521 size 12{ { { size 8{5} } over { size 8{"21"} } } } {}

b)

= 510510 size 12{ { { size 8{5} } over { size 8{"10"} } } } {} + 610610 size 12{ { { size 8{6} } over { size 8{"10"} } } } {}

= 11101110 size 12{ { { size 8{"11"} } over { size 8{"10"} } } } {}

= 1 110110 size 12{ { { size 8{1} } over { size 8{"10"} } } } {}

c)

= 36453645 size 12{ { { size 8{"36"} } over { size 8{"45"} } } } {} - 25452545 size 12{ { { size 8{"25"} } over { size 8{"45"} } } } {}

= 11451145 size 12{ { { size 8{"11"} } over { size 8{"45"} } } } {}

d)

= 4646 size 12{ { { size 8{4} } over { size 8{6} } } } {} - 3636 size 12{ { { size 8{3} } over { size 8{6} } } } {}

= 1616 size 12{ { { size 8{1} } over { size 8{6} } } } {}

16.

a)

= 11231123 size 12{"11" { { size 8{2} } over { size 8{3} } } } {} + 1717 size 12{ { { size 8{1} } over { size 8{7} } } } {}

= 111421111421 size 12{"11" { { size 8{"14"} } over { size 8{"21"} } } } {} + 321321 size 12{ { { size 8{3} } over { size 8{"21"} } } } {}

p = 111721111721 size 12{"11" { { size 8{"17"} } over { size 8{"21"} } } } {}

b)

= 314−19314−19 size 12{3 { { size 8{1} } over { size 8{4} } } - { { size 8{1} } over { size 8{9} } } } {}

= 3 936−436936−436 size 12{ { { size 8{9} } over { size 8{"36"} } } - { { size 8{4} } over { size 8{"36"} } } } {}

t = 3 536536 size 12{ { { size 8{5} } over { size 8{"36"} } } } {}

= 6 3434 size 12{ { { size 8{3} } over { size 8{4} } } } {} – (3 1212 size 12{ { { size 8{1} } over { size 8{2} } } } {} + 1 2323 size 12{ { { size 8{2} } over { size 8{3} } } } {})

= 6 3434 size 12{ { { size 8{3} } over { size 8{4} } } } {} – 3 3636 size 12{ { { size 8{3} } over { size 8{6} } } } {} + 4646 size 12{ { { size 8{4} } over { size 8{6} } } } {}

= 6 3434 size 12{ { { size 8{3} } over { size 8{4} } } } {} – 4 1616 size 12{ { { size 8{1} } over { size 8{6} } } } {}

= 2 912912 size 12{ { { size 8{9} } over { size 8{"12"} } } } {} - 212212 size 12{ { { size 8{2} } over { size 8{"12"} } } } {}

g = 2 712712 size 12{ { { size 8{7} } over { size 8{"12"} } } } {}

d)

= 9 7878 size 12{ { { size 8{7} } over { size 8{8} } } } {} - (4 912912 size 12{ { { size 8{9} } over { size 8{"12"} } } } {} + 812812 size 12{ { { size 8{8} } over { size 8{"12"} } } } {})

= 9 7878 size 12{ { { size 8{7} } over { size 8{8} } } } {} - 5 512512 size 12{ { { size 8{5} } over { size 8{"12"} } } } {}

= 4 7878 size 12{ { { size 8{7} } over { size 8{8} } } } {} - 512512 size 12{ { { size 8{5} } over { size 8{"12"} } } } {}

= 4 21242124 size 12{ { { size 8{"21"} } over { size 8{"24"} } } } {} - 10241024 size 12{ { { size 8{"10"} } over { size 8{"24"} } } } {}

v = 4 11241124 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.

Table 1
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 ( 1313 size 12{ { { size 8{1} } over { size 8{3} } } } {}) + four fifths ( 4545 size 12{ { { size 8{4} } over { size 8{5} } } } {}) or five sixths ( 5656 size 12{ { { size 8{5} } over { size 8{6} } } } {}) – two nineths ( 2929 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.

Table 2
Thus we change both denominators to 15:
1 × 5
3 × 5
=
5
15
en
4 × 3
5 × 3
=
12
15

Thus: 13+45515+12151715121513+45515+121517151215alignl { 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=47+23x=47+23 size 12{x= { { size 8{4} } over { size 8{7} } } + { { size 8{2} } over { size 8{3} } } } {}

___________________________________________________

___________________________________________________

___________________________________________________

___________________________________________________

b) y=12+35y=12+35 size 12{y= { { size 8{1} } over { size 8{2} } } + { { size 8{3} } over { size 8{5} } } } {}

___________________________________________________

___________________________________________________

___________________________________________________

___________________________________________________

c) d=45−59d=45−59 size 12{d= { { size 8{4} } over { size 8{5} } } - { { size 8{5} } over { size 8{9} } } } {}

___________________________________________________

___________________________________________________

___________________________________________________

___________________________________________________

d) k=23−12k=23−12 size 12{k= { { size 8{2} } over { size 8{3} } } - { { size 8{1} } over { size 8{2} } } } {}

___________________________________________________

___________________________________________________

___________________________________________________

___________________________________________________

16. Work together with a friend and calculate:

a) p=723+417p=723+417 size 12{p=7 { { size 8{2} } over { size 8{3} } } +4 { { size 8{1} } over { size 8{7} } } } {}

___________________________________________________

___________________________________________________

___________________________________________________

___________________________________________________

b) t=514−219t=514−219 size 12{t=5 { { size 8{1} } over { size 8{4} } } - 2 { { size 8{1} } over { size 8{9} } } } {}

___________________________________________________

___________________________________________________

___________________________________________________

___________________________________________________

c) g=634−212+123g=634−212+123 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=978−334+123v=978−334+123 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:

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