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2. What is of cardinal importance before attempting to add or subtract fractions?
3. Show whether you are able to do the following:
3.1 8 - 4 $\frac{3}{7}$
3.2 3 $\frac{1}{9}$ - 1 $\frac{1}{2}$
e.g. 2 $\frac{4}{7}$ - 1 $\frac{6}{7}$
2 – 1 = 1 and
$\frac{4}{7}$ - $\frac{6}{7}$
( 4 – 6 --- this is not possible. Carry one whole: 1 = $\frac{7}{7}$ )
( 4 + 7 = 11 --- yes, 11 – 6 = 5)
Answer: $\frac{5}{7}$
4. Do the following:
4.1 4 $\frac{1}{7}$ + 4 $\frac{\text{16}}{\text{42}}$
4.2 36 － 15 $\frac{6}{\text{11}}$ _{}
4.3 $\frac{1}{8}+\mathrm{0,}\text{625}-\frac{3}{8}$
4.4 $4\frac{5}{\text{10}}+7\frac{1}{2}+6\frac{3}{4}$
4.5 7 $\frac{1}{3}$ - 4 $\frac{7}{8}$
4.6 7 a - $\frac{a}{4}$ a / _{4}
4.7 $\frac{9}{a}+\left(\frac{6}{\text{ab}}-\frac{3}{b}\right)$
4.8 - 6 + 2 $\frac{6}{7}$
4.9 5 - (4 $\frac{4}{9}$ + 2 $\frac{2}{3}$ )
4.10 3 $\frac{1}{3}$ a - 2 $\frac{1}{2}$ a
1. Multiplication:
Try the following:
2. Division:
Use an example to explain this term.
e.g. $\frac{1}{3}\xf7\frac{2}{3}$
3. Do the following:
3.1 8 ÷ $\frac{8}{\text{11}}$ _{}
3.2 18 ÷ $\frac{7}{8}$ _{}
3.3 $\frac{5}{6}\xf7\frac{5}{2}$
3.4 -2 $\frac{2}{3}$ ÷ -1 $\frac{7}{9}$
3.5 6 $\frac{3}{4}$ mn ÷ -6 m ^{3}
3.6 $\frac{-4\text{xy}}{3\text{ab}}\xf7\frac{-\mathrm{2x}}{\mathrm{3a}}$ ^{-}
Learning outcomes(LOs) |
LO 1 |
Numbers, Operations and RelationshipsThe 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 standards(ASs) |
We know this when the learner: |
1.2 recognises, classifies an represents the following numbers to describe and compare them: |
1.2.2 decimals, fractions and percentages; |
1.2.5 additive and multiplicative inverses; |
1.2.6 multiples and factors; |
1.2.7 irrational numbers in the context of measurement (e.g. $\pi $ and square and cube roots of non-perfect squares and cubes); |
1.3 recognises and uses equivalent forms of the rational numbers listed above; |
1.6 estimates and calculates by selecting and using operations appropriate to solving problems that involve: |
1.6.1 rounding off; |
1.6.2 multiple operations with rational numbers (including division with fractions and decimals); |
1.7 uses a range of techniques to perform calculations, including: |
1.7.1 using the commutative, associative and distributive properties with rational numbers; |
1.7.2 using a calculator; |
1.9 recognises, describes and uses: |
1.9.1 algorithms for finding equivalent fractions; |
1.9.2 the commutative, associative and distributive properties with rational numbers (the expectation is that learners should be able to use these properties and not necessarily to know the names of the properties). |
ACTIVITY 1
1. Natural numbers
Counting numbers
Integers
Real numbers
2. $\frac{a}{b}$ ; b ≠ 0
3.1 Q
4.
$$ | 0 | $\sqrt{1}$ | $\sqrt{3}$ | $\sqrt[3]{9}$ | $\sqrt[3]{8}$ | 2,47 | $\sqrt{\mathrm{1,}\text{45}}$ | $\sqrt{}$ | $\sqrt{}$ | |
Rational | √ | √ | √ | √ | √ | √ | ||||
Irrational | √ | √ | √ | √ |
6. Equal in value
7. $\frac{4}{\text{14}}$ = $\frac{6}{\text{24}}$ etc
ACTIVITY 2
1. 2,15
5.1 $\frac{\mathrm{7,}\text{000}}{9}$ = 0, $\stackrel{}{7}$
5.2 -5,8 $\stackrel{}{3}$ $\frac{\mathrm{5,}\text{000}}{6}$ = 0,8333 . . .
5.3 3, $\stackrel{}{1}$ $\stackrel{}{3}$ $\frac{\text{13},\text{0000}}{\text{99}}$ = 0,1313 . . .
7.1 $\frac{3}{9}$ = $\frac{1}{3}$
7.2 $\frac{\text{45}}{\text{99}}$ = $\frac{5}{\text{11}}$
7.3 $\frac{\text{23}}{\text{990}}$
7.4 $\frac{3}{\text{900}}$ = $\frac{1}{\text{300}}$
9. 0, $\stackrel{}{4}$ $\stackrel{}{5}$ = x
x = 0,4545 . . .
100 x = 45,4545 . . .
x = $\frac{\text{45}}{\text{99}}$ = $\frac{5}{\text{11}}$
ACTIVITY 3
2.1 $\frac{\text{17}\mathrm{x5}}{\text{20}\mathrm{x5}}$ = 85%
2.2 $\frac{\text{19}}{\text{40}}$ x $\frac{\text{100}\text{}}{1}$ = 47,5%
2.3 $\frac{\text{38}\mathrm{x2}}{\text{50}\mathrm{x2}}$ = 76%
2.4 $\frac{\text{45}}{\text{60}}$ x $\frac{\text{100}\text{}}{1}$ = 75%
3.1 $\frac{\text{55}}{\text{100}}$ = $\frac{\text{11}}{\text{20}}$
3.2 $\frac{\text{15},5}{\text{100}}$ = 0,155 = $\frac{\text{155}}{\text{1000}}$ = $\frac{\text{31}}{\text{200}}$
3.3 $\frac{\text{33}}{\text{200}}$
3.4 $\frac{20}{\text{30 {}0}$ = $\frac{2}{\text{30}}$
4.a) $\frac{\text{33}}{\text{800}}$ x $\frac{\text{25500}}{1}$ $$ 1 052
b) $\frac{3}{5}$ x $\frac{\text{25500}}{1}$ = 15 300
c) $\frac{\text{85}}{\text{1000}}$ x $\frac{\text{25500}}{1}$ = 2 167,5 $$ 2 168
4.4
4.5 $\frac{3}{5}$ x $\frac{2}{1}$ = $\frac{6}{5}$ = $1\frac{1}{5}$
ACTIVITY 4
1.1 $\frac{\text{39}}{7}$
1.2 $\frac{\text{70}}{9}$
2. Numbers must be the same
3.1 $3\frac{4}{7}$
3.2 $2\frac{2-9}{\text{18}}$ = $1\frac{\text{20}-9}{\text{18}}$ = $1\frac{\text{11}}{\text{18}}$
4.1 $\frac{\text{29}}{7}$ + $\frac{\text{184}}{\text{42}}$ = $\frac{\text{174}+\text{184}}{\text{42}}$ = $\frac{\text{358}}{\text{42}}$ = $8\frac{\text{22}}{\text{42}}$ = $8\frac{\text{11}}{\text{21}}$
4.2 21 - $\frac{6}{\text{11}}$ = $\text{20}\frac{5}{\text{11}}$
4.7+ $(\frac{6-\mathrm{3a}}{\text{ab}})$ = $\frac{\mathrm{9b}+6-\mathrm{3a}}{\text{ab}}$
4.8 $\frac{-6}{1}$ + $\frac{\text{20}}{7}$ = $\frac{-\text{42}+\text{20}}{7}$ = $\frac{-\text{22}}{7}$ = $-3\frac{1}{7}$
=– $\frac{\text{64}}{9}$
= $\frac{\text{45}-\text{64}}{9}$
= $\frac{-\text{19}}{9}$ = $-2\frac{1}{9}$
= $\frac{\mathrm{5a}}{6}$
ACTIVITY 5
1. $\frac{5}{{}_{1}4}$ x $\frac{5}{2}$ x $\frac{{4}^{1}}{1}$ = $\frac{\text{25}}{2}$ = $\text{12}\frac{1}{2}$
3.1 $\frac{8}{1}$ ÷ $\frac{8}{\text{11}}$ = $\frac{{8}^{1}}{1}$ x $\frac{\text{11}}{{8}_{1}}$ = 11
3.2 $\frac{\text{18}}{1}$ x $\frac{8}{7}$ = $\frac{\text{144}}{7}$ = $\text{20}\frac{4}{7}$
3.3 $\frac{{5}^{1}}{{6}_{3}}$ x $\frac{{2}^{1}}{{5}_{1}}$ = $\frac{1}{3}$
3.4 $\frac{-{8}^{1}}{3{}_{1}\text{}}$ x $\frac{-{9}^{3}}{1{6}_{2}}$ = $\frac{3}{2}$ = $1\frac{1}{2}$
3.5 $\frac{2{7}^{9}\text{mn}}{4}$ x $\frac{1}{-6{}_{2}\text{}{m}^{3}}$ = $\frac{-\mathrm{9n}}{{\mathrm{8m}}^{2}}$
3.6 $\frac{-{4}^{2}\text{xy}}{3{}_{1}\text{}ab}$ x $\frac{3a}{-2x}$ = $\frac{\mathrm{2y}}{b}$
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