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14. a) denominator
b) common denominator
c) multiple
d) tellers
e) number
f) fractions
g) improper fractions
h) simplify
15.2 a)
= $\frac{\text{12}}{\text{21}}$ + $\frac{\text{14}}{\text{21}}$
= $\frac{\text{26}}{\text{21}}$
= 1 $\frac{5}{\text{21}}$
b)
= $\frac{5}{\text{10}}$ + $\frac{6}{\text{10}}$
= $\frac{\text{11}}{\text{10}}$
= 1 $\frac{1}{\text{10}}$
c)
= $\frac{\text{36}}{\text{45}}$ - $\frac{\text{25}}{\text{45}}$
= $\frac{\text{11}}{\text{45}}$
d)
= $\frac{4}{6}$ - $\frac{3}{6}$
= $\frac{1}{6}$
16.
a)
= $\text{11}\frac{2}{3}$ + $\frac{1}{7}$
= $\text{11}\frac{\text{14}}{\text{21}}$ + $\frac{3}{\text{21}}$
p = $\text{11}\frac{\text{17}}{\text{21}}$
b)
= $3\frac{1}{4}-\frac{1}{9}$
= 3 $\frac{9}{\text{36}}-\frac{4}{\text{36}}$
t = 3 $\frac{5}{\text{36}}$
= 6 $\frac{3}{4}$ – (3 $\frac{1}{2}$ + 1 $\frac{2}{3}$ )
= 6 $\frac{3}{4}$ – 3 $\frac{3}{6}$ + $\frac{4}{6}$
= 6 $\frac{3}{4}$ – 4 $\frac{1}{6}$
= 2 $\frac{9}{\text{12}}$ - $\frac{2}{\text{12}}$
g = 2 $\frac{7}{\text{12}}$
d)
= 9 $\frac{7}{8}$ - (4 $\frac{9}{\text{12}}$ + $\frac{8}{\text{12}}$ )
= 9 $\frac{7}{8}$ - 5 $\frac{5}{\text{12}}$
= 4 $\frac{7}{8}$ - $\frac{5}{\text{12}}$
= 4 $\frac{\text{21}}{\text{24}}$ - $\frac{\text{10}}{\text{24}}$
v = 4 $\frac{\text{11}}{\text{24}}$
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 ( $\frac{1}{3}$ ) + four fifths ( $\frac{4}{5}$ ) or five sixths ( $\frac{5}{6}$ ) – two nineths ( $\frac{2}{9}$ ) 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 |
4 | × | 3 |
5 | × | 3 |
12 |
15 |
Thus: $\begin{array}{}\frac{1}{3}+\frac{4}{5}\\ \frac{5}{\text{15}}+\frac{\text{12}}{\text{15}}\\ \frac{\text{17}}{\text{15}}\\ 1\frac{2}{\text{15}}\end{array}$
15.2 Calculate the following:
a) $x=\frac{4}{7}+\frac{2}{3}$
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b) $y=\frac{1}{2}+\frac{3}{5}$
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c) $d=\frac{4}{5}-\frac{5}{9}$
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d) $k=\frac{2}{3}-\frac{1}{2}$
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16. Work together with a friend and calculate:
a) $p=7\frac{2}{3}+4\frac{1}{7}$
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b) $t=5\frac{1}{4}-2\frac{1}{9}$
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c) $g=6\frac{3}{4}-\left(2\frac{1}{2}+1\frac{2}{3}\right)$
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d) $v=9\frac{7}{8}-\left(3\frac{3}{4}+1\frac{2}{3}\right)$
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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 | $1\frac{1}{2}$ | $2\frac{1}{4}$ | $3\frac{3}{4}$ | $1\frac{1}{2}$ | $\frac{1}{2}$ |
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.
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e) Ask another group to check your answers.
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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