Fractions and Decimals Revision Notes for Grade 12 NSC Matric Mathematical Literacy

Fractions and Decimals

Understanding fractions

Fractions are a way to show how something is divided into parts. They help us represent portions or pieces of a whole.

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A fraction consists of two main components that work together to represent a part of a whole. Understanding these components is essential for working with fractions effectively.

A fraction consists of two parts:

Numerator: The top number (shows how many parts we have)
Denominator: The bottom number (shows how many total parts the whole is divided into)

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Understanding Fraction Components

For example, in the fraction $\frac{5}{6}$ :

5 is the numerator (we have 5 parts)
6 is the denominator (the whole is divided into 6 equal parts)

This means we have 5 out of 6 equal parts of something.

Types of fractions

There are three main types of fractions, each representing different relationships between the numerator and denominator.

Proper fractions occur when the numerator is smaller than the denominator. These fractions represent less than one whole unit.

Examples: $\frac{2}{10}$ or $\frac{3}{8}$

Improper fractions occur when the numerator is bigger than the denominator. These fractions represent more than one whole unit.

Examples: $\frac{5}{3}$ or $\frac{7}{4}$

Mixed numbers are created when we convert improper fractions into whole numbers plus a fraction.

Examples: $\frac{9}{2} = 4\frac{1}{2}$ and $\frac{7}{3} = 2\frac{1}{3}$

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Remember the Key Difference:

Proper fractions: numerator < denominator (less than 1)
Improper fractions: numerator > denominator (greater than 1)
Mixed numbers: whole number + proper fraction

Understanding decimals

Decimal fractions are special types of fractions where the denominator is a power of ten (10, 100, 1000, etc.).

The connection between fractions and decimals

When we divide by powers of 10, we can see how decimals work. This connection helps us understand why decimals are just another way of writing certain fractions.

Division	Result
1000 ÷ 10	100
100 ÷ 10	10
10 ÷ 10	1
1 ÷ 10	0,1

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Fraction to Decimal Conversion

The decimal 0,1 is equal to $\frac{1}{10}$ . This shows us that decimals are just another way of writing certain fractions.

Think of it this way:

$\frac{1}{2} = 0,5$
$\frac{1}{10} = 0,1$
$\frac{1}{4} = 0,25$

Place value in decimals

Understanding place value is crucial for working with decimals. Each position in a decimal number has a specific value that helps us understand the number's true meaning.

Hundreds	Tens	Units	Tenths	Hundredths	Thousandths
8	0	8	7	1	3

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Place Value Breakdown: 808,713

In the number 808,713:

The first 8 represents 800 (8 hundreds)
The 0 represents 0 tens
The second 8 represents 8 units
The 7 represents 7 tenths
The 1 represents 1 hundredth
The 3 represents 3 thousandths

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Place Value Pattern: Every digit has a place value that is 10 times more than the digit to its right. This pattern continues in both directions from the decimal point.

Multiplying by powers of 10

When multiplying decimal numbers by 10, 100, or 1000, there's a useful pattern that makes calculations much easier.

The multiplication rules

Understanding these rules will help you multiply by powers of 10 quickly and accurately.

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Multiplication by Powers of 10 Rules:

Multiplying by 10: Every digit moves one place to the left, OR the decimal point moves one place to the right
Multiplying by 100: Every digit moves two places to the left, OR the decimal point moves two places to the right
Multiplying by 1000: Every digit moves three places to the left, OR the decimal point moves three places to the right

The number of places equals the number of zeros in the multiplier!

Worked example: Place value tables

Let's see how 287,5 changes when multiplied by different powers of 10 using place value tables.

HTh	TTh	Th	H	T	U	t
			2	8	7	5
		2	8	7	5		× 10
	2	8	7	5	0		× 100
2	8	7	5	0	0		× 1000

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Step-by-Step Multiplication: 287,5

This gives us:

287,5 × 10 = 2875
287,5 × 100 = 28750
287,5 × 1000 = 287500

Notice the pattern: Each multiplication adds zeros and moves the decimal point right by the number of zeros in the multiplier.

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Using place value tables helps you see exactly how the digits move when multiplying by powers of 10. This visual method prevents common mistakes and builds understanding.

Exam tips

These practical tips will help you succeed when working with fractions and decimals in exams and assignments.

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Essential Exam Strategies:

Always identify whether a fraction is proper, improper, or mixed before working with it
Remember that decimals are just fractions with denominators of 10, 100, 1000, etc.
When multiplying by powers of 10, count how many zeros are in the multiplier - that's how many places the decimal point moves right
Use place value tables for complex calculations involving decimals
Check your work by ensuring the decimal point is in the correct position

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Key Points to Remember:

Fractions show parts of a whole, with the numerator on top and denominator on bottom
Proper fractions have numerators smaller than denominators
Improper fractions have numerators bigger than denominators
Decimal fractions have denominators that are powers of 10
Multiplying by powers of 10 moves digits left or moves the decimal point right
The number of places the decimal moves equals the number of zeros in the multiplier

Fractions and Decimals (Grade 12 NSC Matric Mathematical Literacy): Revision Notes