# 3.1 Recognise and classify ordinary fractions

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## To recognise and classify ordinary fractions in order to compare them [lo 1.3.2]

RELATIONSHIP SIGNS (<;>; =)

1. Compare the following fractions and then fill in<,>or =.

1.1 $\frac{3}{5}$ ____ $\frac{7}{\text{10}}$

1.2 $\frac{1}{3}$ ____ $\frac{1}{4}$

1.3 $\frac{5}{8}$ ____ $\frac{1}{2}$

1.4 $\frac{1}{7}$ ____ $\frac{1}{5}$

1.5 $\frac{3}{4}$ ____ $\frac{6}{8}$

1.6 $\frac{3}{8}$ ____ $\frac{1}{2}$

1.7 $\frac{3}{4}$ ____ $\frac{9}{\text{12}}$

1.8 $\frac{3}{5}$ ____ $\frac{7}{\text{10}}$

1.9 $\frac{2}{\text{11}}$ ____ $\frac{1}{\text{12}}$

1.10 $\frac{\text{12}}{\text{12}}$ ____ $\frac{9}{9}$

2. Compare the following fractions and draw a circle around the one that is the greatest in each of the following:

2.1 $\frac{1}{2}$ ; $\frac{3}{4}$

2.2 $\frac{2}{3}$ ; $\frac{3}{6}$

2.3 $\frac{3}{5}$ ; $\frac{9}{\text{10}}$

2.4 $\frac{1}{2}$ ; $\frac{2}{6}$

2.5 $\frac{3}{8}$ ; $\frac{1}{2}$

2.6 $\frac{4}{5}$ ; $\frac{4}{\text{10}}$

Class discussion

HOW can we determine the answers for no. 1 and if we don’t have a diagram to help us?

3. In the following activity you will see how important your knowledge of equivalent fractions is. Once you have mastered it, you will find that it is child’s play to compare the fractions with each other.

Use the rule as determined during your class discussion and fill in<,>or =.

3.1 $\frac{3}{5}$ ____ $\frac{7}{\text{15}}$

3.2 $\frac{7}{\text{11}}$ ____ $\frac{\text{13}}{\text{22}}$

3.3 $\frac{5}{9}$ ____ $\frac{\text{15}}{\text{27}}$

3.4 $\frac{5}{6}$ ____ $\frac{\text{20}}{\text{24}}$

4. Now use your knowledge and fill in<,>or =.

4.1 $\frac{4}{5}$ ____ $\frac{5}{6}$

4.2 $\frac{2}{3}$ ____ $\frac{4}{5}$

4.3 $\frac{5}{6}$ ____ $\frac{7}{9}$

4.4 $\frac{7}{8}$ ____ $\frac{6}{7}$

## To calculate by selecting and using operations [lo 1.8.3]

1. Split up into groups of three. See if you know how to solve the problems.

1.1 Gizelle and her twin brother, Donovan, receive pocket money every month. Gizelle saves two sixths of her pocket money. Donovan saves four ninths of his. Who saves most if they get the same amount of pocket money?

1.2 Mom likes making pancakes. She gives Jake and his friends three quarters to eat. Then Mom makes the same number of pancakes. She sends four fifths of the pancakes to school for Dimitri and his friends to enjoy. Who got the most pancakes from Mom?

1.3 Vusi and Sipho wrote the same test. Vusi answered four sevenths of the questions correctly. Sipho had five eighths right. Who did better in the test?

1.4 Two identical taxis transport passengers between Johannesburg and Pretoria. The one taxi is two thirds full, while the other one is three quarters full. Which taxi transports the most passengers?

Another BRAIN-TEASER!

Arrange the following fractions from biggest to smallest:

$\frac{2}{3}$ ; $\frac{1}{2}$ ; $\frac{5}{6}$ ; $\frac{7}{9}$

SIMPLIFYING

Did you know?

In order to write a fraction in its simplest form we divide the numerator and denominator by the same number. The value of the fraction does not change because we are actually dividing the fraction by 1.

 E.g. $\frac{\text{18}}{\text{24}}$ 
 6  6
= $\frac{3}{4}$ and $\frac{\text{10}}{\text{15}}$
 5 5
= $\frac{2}{3}$

## To simplify common fractions [lo 1.3.2]

1. Now that you know how to simplify a fraction, see whether you can complete the following table:

 Fraction ÷ by Simplified E.g. $\frac{\text{18}}{\text{27}}$ $\frac{9}{9}$ $\frac{2}{3}$ 1.1 $\frac{\text{40}}{\text{45}}$ .................. .................. 1.2 $\frac{\text{15}}{\text{25}}$ .................. .................. 1.3 $\frac{\text{12}}{\text{16}}$ .................. .................. 1.4 $\frac{\text{24}}{\text{30}}$ .................. .................. 1.5 $\frac{\text{48}}{\text{54}}$ .................. ..................

## To use a series of techniques to do calculations [lo 1.10.3]

1. In the previous modules you often rounded off whole numbers. Now we are going to round off mixed numbers to the nearest whole number. Connect the number in column A to the correct answer in column B.

can someone help me with some logarithmic and exponential equations.
20/(×-6^2)
Salomon
okay, so you have 6 raised to the power of 2. what is that part of your answer
I don't understand what the A with approx sign and the boxed x mean
it think it's written 20/(X-6)^2 so it's 20 divided by X-6 squared
Salomon
I'm not sure why it wrote it the other way
Salomon
I got X =-6
Salomon
ok. so take the square root of both sides, now you have plus or minus the square root of 20= x-6
oops. ignore that.
so you not have an equal sign anywhere in the original equation?
Commplementary angles
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Sherica
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Sherica
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Tamia
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Kim
The answer is neither. The function, 2 = 0 cannot exist. Hence, the function is undefined.
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Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
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