Complete Grade 12 Mathematical Literacy study guide in English, aligned to the CAPS curriculum. 17 chapters with explanations, worked examples, exercises with solutions, and original practice papers with memos.

Chapters

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

Every day in South Africa you read and use numbers without thinking about them. A till slip at a Shoprite in Polokwane shows R249,95. A road sign on the N1 outside Bloemfontein gives a distance of 387 km. A water meter at a Cape Town home reads 14 320 litres. Mathematical Literacy starts here, with the skill of reading numbers correctly, calculating with them sensibly, and knowing when an answer is reasonable. This chapter builds the number sense that every later chapter, from budgeting to measurement, depends on.

1.1 Types of numbers and place value

You work mostly with three kinds of numbers. Whole numbers count things that cannot be split, such as 32 learners in a class. Decimals describe amounts between whole numbers, such as R8,50 for a loaf of bread or 1,8 m of fabric. Negative numbers show values below zero, such as a temperature of -3 degrees Celsius in Sutherland or a bank balance of -R120 when an account is overdrawn.

The place value of a digit depends on its position. In R3 425, the 3 means three thousand, the 4 means four hundred, the 2 means twenty and the 5 means five. After the comma the positions are tenths and hundredths, so in R12,75 the 7 is seven tenths of a rand (70 cents) and the 5 is five hundredths (5 cents). Reading place value correctly stops you confusing R1 500 with R15 000, an easy and expensive mistake.

Example: Write the value of the digit 6 in each amount. In R6 240 the 6 is in the thousands place, so it is worth R6 000. In R45,06 the 6 is in the hundredths place, so it is worth 6 cents. In 360 km the 6 is in the tens place, so it is worth 60 km.

1.2 Rounding numbers

To round a number you replace it with a nearby simpler value. Look at the digit just after the place you are rounding to. If that digit is 5 or more, round up; if it is 4 or less, round down (keep the digit the same). South African shops often round cash totals to the nearest 5 cents because the smallest coin in circulation is 10 cents and many tills round to 5 cents.

Example: Round R37,48 to the nearest rand. The digit after the rand is 4, which is less than 5, so you round down to R37. Now round 2 microseconds aside and round 1 286 people to the nearest hundred: the tens digit is 8, which is 5 or more, so you round up to 1 300 people.

1.3 Estimation and reasonableness

An estimate is a quick rough answer used to check whether a calculation makes sense. Before paying, you might estimate a trolley of groceries by rounding each item to the nearest R10 and adding. If three items cost about R30, R50 and R20, your estimate is R100, so a till total of R98,75 looks right but a total of R987 warns you of an error.

Round each number to a convenient value before adding or multiplying.
Compare your estimate with the exact answer to catch big mistakes.
Use estimation to decide if there is enough money or enough material.

1.4 The four operations in context

Mathematical Literacy is about choosing the right operation for a real situation. You add to find a total, subtract to find change or a difference, multiply for repeated equal groups, and divide to share equally or to find how many groups fit.

Example: A family in Durban buys 4 bus tickets at R23 each and pays with a R200 note. The cost is found by multiplication: \( 4 \times R23 = R92 \). The change is found by subtraction: \( R200 - R92 = R108 \). If the R92 were shared equally among the 4 family members, division gives \( R92 \div 4 = R23 \) each.

1.5 Order of operations

When a calculation mixes operations, you must do them in the correct order or you get the wrong answer. The rule is brackets first, then multiplication and division (left to right), then addition and subtraction (left to right).

Example: A learner buys 3 pens at R7 each and 1 ruler at R5. The cost is \( 3 \times 7 + 5 \). Doing multiplication first gives \( 21 + 5 = R26 \), which is correct. Working left to right wrongly would give \( 3 \times 12 = R36 \), so order matters.

1.6 Using a calculator wisely

A calculator speeds up arithmetic but does not think for you. Enter numbers carefully, keep brackets where needed, and always check that the answer is reasonable against an estimate. If you calculate the cost of 12 textbooks at R189 and the screen shows R226,80 you should notice it is far too small, because 12 times about R200 is roughly R2 400.

Estimate first, then calculate, then compare.
Watch the comma: R1 234,50 is not the same as R123 450.
Re-enter the calculation if the result looks unreasonable.