Complete Grade 11 Mathematical Literacy study guide in English, aligned to the CAPS curriculum. 16 chapters with explanations, worked examples, exercises with solutions, and original practice papers with memos.

Chapters

Chapter 1. Getting Started: Numbers, Units and Everyday Calculations FREE

Every day in South Africa you read and use numbers without thinking about it. The price of a loaf of bread at a Shoprite in Polokwane might be R18,99. A taxi from Soweto to the Johannesburg CBD might cost R22. A bag of mealie meal might weigh 12,5 kg. Mathematical Literacy starts here, with the everyday numbers that describe real life, and with the skill of working with them confidently and correctly. This chapter builds the foundation on which every later topic, from budgets to building plans, depends.

1.1 Types of numbers we use

We work mostly with three kinds of numbers. Whole numbers are counting numbers such as 0, 1, 2, 3, and they answer the question how many. You cannot have 2,5 learners in a class. Decimals describe amounts between whole numbers, such as a mass of 1,75 kg or a price of R12,50. Fractions describe parts of a whole, such as half a tank of petrol, written \( \tfrac{1}{2} \). In South Africa the comma is the decimal marker, so we write R45,60 and not R45,60. The space is used to group large numbers: 1 250 000 rand, not 1,250,000.

Negative numbers appear when a value drops below zero. A bank account that is overdrawn by R300 shows a balance of -R300. A winter temperature in Sutherland might be -4 degrees Celsius. Numbers placed in order from smallest to largest run -4, -1, 0, 2, 5, and the further left a number sits on a number line, the smaller it is.

1.2 Place value and rounding

Place value tells us what each digit is worth. In R3 472,85 the 3 means three thousand rand, the 8 means eight tenths of a rand, that is 80 cents. Understanding place value lets us round sensibly. To round, we look at the digit immediately after the place we are rounding to: if it is 5 or more we round up, otherwise we round down.

Example: Round R248,67 to the nearest rand. The digit after the rand is 6, which is 5 or more, so we round up to R249. Round 1 463 people to the nearest hundred. The digit after the hundreds place is 6, so we round up to 1 500.

In money we usually round to two decimal places because the smallest coin is one cent. When estimating, rounding to one significant figure is often enough to check whether an answer is reasonable.

1.3 The order of operations

When a calculation has more than one operation, the order matters. We use the rule BODMAS: Brackets, Of (powers), Division and Multiplication, then Addition and Subtraction. Division and multiplication are done together from left to right, and so are addition and subtraction.

Example: A learner buys 3 pies at R15 each and 2 cooldrinks at R12 each. The total is \( 3 \times 15 + 2 \times 12 \). Doing the multiplications first gives \( 45 + 24 = 69 \), so the total is R69. If you wrongly added before multiplying you would get the wrong answer.

1.4 Units of measurement in daily life

A unit tells us what a number measures. A number on its own, like 5, means little until we know whether it is 5 litres, 5 kilometres or 5 rand. Common everyday units include the rand and cent for money, the kilogram and gram for mass, the litre and millilitre for volume, the metre and kilometre for distance, and degrees Celsius for temperature.

Money: 100 cents make R1, so 250 cents is R2,50.
Mass: 1 000 g make 1 kg, so a 500 g packet is half a kilogram.
Volume: 1 000 ml make 1 litre, so a 330 ml can is about a third of a litre.
Distance: 1 000 m make 1 km.

Always write the unit with the answer. An answer of just 12 is incomplete, while 12 litres of petrol is a useful, complete answer.

1.5 Estimation and checking your answer

Estimation means finding a quick, rough answer to check whether the exact answer is sensible. If you buy items costing R19,95, R48,50 and R31,20, you can estimate R20 plus R50 plus R30, which is about R100. If your calculator shows R996, you know a mistake was made. Estimation protects you from accepting a silly answer.

Example: A family of 4 shares a restaurant bill of R612 equally. Estimate first: R612 is close to R600, and \( 600 \div 4 = 150 \). The exact answer is \( 612 \div 4 = 153 \), so each person pays R153. The estimate of R150 confirms the answer is reasonable.

1.6 Using a calculator wisely

Enter long calculations with brackets so the calculator follows the correct order, for example (3 x 15) + (2 x 12).
Read the screen, not just trust it. A wrong key press gives a wrong answer that still looks neat.
Keep the decimal comma in mind. Entering 45,6 on most calculators is read as 45,6, which is correct, but never confuse it with 456.
Round only at the end of a calculation, not in the middle, to avoid building up small errors.

With a firm grasp of number types, place value, rounding, the order of operations, units and estimation, you are ready to apply these skills to ratios, percentages, money and measurement in the chapters that follow.