Numbers

Numbers, ratios and percentages

Place value, rounding, ratio, rate and percentage of a quantity — the working language of every later topic.

CAPS

Grade 10 · Mathematical Literacy · Numbers

Mathematical Literacy uses a context, not a bare sum.

  • Two papers

    Paper 1 uses familiar contexts: pay slips, till slips, maps you have seen, and data in a table. Paper 2 uses less familiar contexts and expects you to decide which method fits. Both papers are 150 marks.

  • What to show

    Write the value with its unit or its rand sign. Say whether you multiply or divide, and round only at the end, in the way the question asked (nearest rand, one decimal place, a whole number of tiles).

  • The relation

    part = percent100 × whole. Percentage of a quantity

  • How a marker reads it

    Write the percent as a decimal first. 10% = 0.10, never 10.

A correct number with the wrong unit, or a VAT amount treated as the full price, loses the mark the context was testing.

-2-1012

Diagram

Numbers, ratios and percentages

Worked example

A Thabazimbi spaza marks a 2-litre cooldrink at R18. It is 10% off. What do you pay?

Before any working — hunt first

Given

Numbers and units already in the sentence: 2 · R18 · 10%. Copy each one into a column. A name without a number is not given.

Missing

After you copy the given, the letter that still has no number is missing. The paper is pointing at: What do you pay. Circle that word — that is the missing variable.

Find

We are required to find: What do you pay. Write that as a symbol on the left, with a question mark, before you touch a formula.

Calculate

Write part = percent100 × whole with empty letters. Cross out every letter that already has a number. Calculate the letter that is still standing — that gives What do you pay.

Simplified approach

Take 10% of 18, then subtract from 18.

Culture note

Till slips in Limpopo shops print the discount as a percentage. That is this calculation.

Formulas

part=percent100×whole

Percentage of a quantity

Exam tricks you must know

These are the moves markers look for — not shortcuts that skip the method, but the habits that earn the method mark.

  • If the price already includes VAT, divide by 1.15 — do not subtract 15%

    How:Total = price × 1.15 when VAT is still to be added. When the till already shows VAT, price excluding = total1.15. Subtracting 15% of the total is a different number and loses the mark.

    When to use it:Till slips, VAT, and SARS-style tax questions.

  • Fencing is perimeter. Grass, paint and tiles are area. Tanks are volume.

    How:Underline the object: wire, border, fence → add the sides. Floor, wall, field, paint → multiply length by width, then divide by coverage and round tins up. Water in a tank → m³ then × 1 000 for litres.

    When to use it:Measurement papers: school fields, paint, Jojo tanks.

Step 1 / 5

Find 10%

10% of 18 = 0.10 × 18 = R1.80.

0.10×18=1.80

Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.

4. Step-by-step working

  1. 01

    Find 10%

    10% of 18 = 0.10 × 18 = R1.80.

    0.10×18=1.80
  2. 02

    Subtract from the marked price

    18−1.80=16.20. You pay R16.20.

More worked examples

Board walkthroughs on this topic. Open one, copy the working, then try the next.

Example 1 / 20

Calculate 15% of R200.

4. Step-by-step working

  1. 01

    Write the formula

    15%=15100.

    15100
  2. 02

    Multiply

    (15/100)×200=30.

    30

How we got there

Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.

Explain in another language · 11

1. What is the question asking?

Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: Calculate 15% of R200.

Before any working — hunt first

Given

Numbers and units already in the sentence: 15% · R200. Copy each one into a column. A name without a number is not given.

Missing

After you copy the given, the letter that still has no number is missing. The paper is pointing at: 15% of R200. Circle that word — that is the missing variable.

Find

We are required to find: 15% of R200. Write that as a symbol on the left, with a question mark, before you touch a formula.

Calculate

Write 15100 with empty letters. Cross out every letter that already has a number. Calculate the letter that is still standing — that gives 15% of R200.

In other words — as if you have never seen this before

If you have never seen this before: Find 10% and 1% first when that makes the arithmetic visible, or multiply by the percentage over 100. We will name a method in words, write the formula with no numbers, then substitute one line at a time.

2. What do we already know?

15% and R200.

3. Which method — and why this one?

Find 10% and 1% first when that makes the arithmetic visible, or multiply by the percentage over 100.

4. Step-by-step working

  1. 01 / 05

    Write the formula

    15%=15100.

    15100

    Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.

  2. 02 / 05

    Multiply

    (15/100)×200=30.

    30

    Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.

  3. 03 / 05

    Sense-check

    100% of R200 is R200. 15% must be smaller than that.

    R30

    Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.

  4. 04 / 05

    Step F — Box the answer with its unit

    R30

    Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.

  5. 05 / 05

    Step H — What the marker is looking for

    On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.

    Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.

5. The answer

R30

Copy onto your answer sheet — in this order

Formula: 15100

Answer: R30

6. Check it like a marker

Moving the decimal the wrong way turns 15% into 150% or into 1.5%.

7. A trap first-timers fall into

First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”

Ntsako · fx-991ZA PLUS. Tap to calculate.