A student prints 24 mono pages at 40c each and 18 colour pages at 60c each. Colour pages receive a 15% discount, and a R2.00 card fee is added. The total is:

R20.78. Mono is 24 times 40c, or R9.60. Colour before discount is 18 times 60c, or R10.80. Fifteen percent of R10.80 is R1.62, so colour after discount is R9.18. Adding the R2.00 fee gives R20.78. Skipping the discount, skipping the fee, or stopping after mono each leaves a different total.

Three housemates pay for 3 washer cycles at R16 each and 40 dryer minutes at 50c per minute, with 10% off the dryer only, then split equally. Each person pays:

R22. Three washers cost R48. Forty minutes at 50c is R20, and 10 percent off leaves R18 for the dryer. Forty-eight plus 18 is R66, and R66 divided by 3 is R22 each. The household total, the washer total, and the dryer total are intermediate lines, not the per-person share.

A campus clinic starts with 160 doses. It uses 2/5 for first-years and then 25% of the remainder for staff. Packed in boxes of 8, the leftover doses fill:

9 boxes with no doses left over. Two-fifths of 160 is 64 doses, leaving 96. Twenty-five percent of 96 is 24 staff doses, leaving 72. Seventy-two divided by 8 is 9 boxes exactly. Sixty-four and 72 are dose counts, not box counts; 8 is the box size.

Multi-Step Calculation without a Calculator | Free Guide 2026

Several steps, still no calculator

NBT Test Content for Quantitative Literacy includes calculations involving multiple steps, done accurately. QL is still 50 multiple-choice questions in AQL, still not MAT, and still calculator-free. Independent OpenExamPrep multi-step practice uses campus print jobs, household laundry shares, clinic dose packs, and municipal kilolitre accounts. It does not copy confidential booklet items.

A multi-step item fails in predictable places: skipping a discount, applying a percent to the wrong base, mixing cents with rands or kL with L, or treating 2^n as n × 2. The cure is a running total you can defend after each line, plus an estimate that would have caught a tenfold slip.

Two official materials rules, not one

No calculator is common to both modes. Working paper is not.

Pencil-paper venue. The official what-to-expect list is no scrap paper, no notebooks, and no smart devices. Do not pack a second pad because QL looks numerical.
Online. The online FAQ allows one piece of paper and a pen or pencil in the room. That sheet is for running totals, not for a dictionary, a phone, or a second device.

Practise both habits. Venue writers need mental placeholders and option-as-checkpoint discipline: after step 1, glance at whether remaining options are still possible. Online writers may write the four lines of a print-job total on the allowed sheet. Do not reverse the two rules, and do not assume a venue will issue rough paper.

Method: estimate, compute, keep units, judge

Estimate with round numbers so you know the neighbourhood of the answer.
Compute one step, converting to convenient units (cents, minutes, litres) if decimals invite slips.
Keep the unit on the line you just wrote.
Judge reasonableness: a discount must lower a price; a part cannot exceed its whole; a per-person share must be smaller than the household total.
Interpret the last number in the original story.

If a formula is needed, it will be in the item. Your job is the chain, not recalling an unpublished identity.

Worked example: campus printing (four steps)

A student prints 24 mono pages at 40c each, then 18 colour pages at 60c each. Colour pages get a 15% student discount. A R2.00 copy-card fee is added at the end.

Estimate. Mono about 25 × R0.40 = R10. Colour about 20 × R0.60 = R12, less about R1.80 discount, plus R2. Neighbourhood: about R21.

Step 1 — mono. 24 × 40c = 960c = R9.60.

Step 2 — colour before discount. 18 × 60c = 1080c = R10.80.

Step 3 — 15% of colour only. 10% of 10.80 = 1.08; 5% of 10.80 = 0.54; discount = R1.62. Colour after discount: 10.80 − 1.62 = R9.18. (Applying 15% to mono as well would be the wrong base.)

Step 4 — add the card fee. 9.60 + 9.18 = 18.78; 18.78 + 2.00 = R20.78.

R20.78 sits next to the R21 estimate. R22.40 is the total with the discount skipped. R18.78 is the total with the card fee skipped. R9.60 is mono alone.

Worked example: household laundry share (four steps)

Three housemates use a campus laundry: 3 washer cycles at R16 each, a dryer for 40 minutes at 50c per minute, then a 10% loyalty discount on the dryer only. They split the bill equally.

Estimate. Washers 3 × 16 = 48. Dryer 40 × 0.50 = 20, less R2, total about R66, then about R22 each.

Step 1. 3 × 16 = R48 washer total.

Step 2. 40 × 50c = 2000c = R20.00 dryer before discount.

Step 3. 10% of 20 = R2.00; dryer after discount = R18.00.

Step 4. Combined 48 + 18 = R66. Each housemate: 66 ÷ 3 = R22.

Reasonableness: R22 is less than the R66 household total and more than one R16 wash, which matches “wash plus a share of the dryer.” R66 as an option forgot the split. R220 would be a place-value error.

Worked example: clinic doses (four steps)

A campus clinic starts with 160 vaccine doses. It uses 2/5 for first-years, then 25% of the remainder for staff, then packs leftover doses in boxes of 8.

Step 1. 2/5 of 160: 160 ÷ 5 = 32; 2 × 32 = 64 doses for first-years. Remainder: 160 − 64 = 96.

Step 2. 25% of the remainder is 1/4 of 96 = 24 staff doses. (25% of 160 would be the wrong base.)

Step 3. Leftover: 96 − 24 = 72 doses.

Step 4. 72 ÷ 8 = 9 boxes, no doses left over. 8 × 9 = 72.

An option of 64 boxes confuses doses with boxes. An option of 72 boxes skips the packing. An option of 8 boxes uses the box size as the count.

Worked example: municipal kilolitres (units on every line)

A residence records 3.6 kL of water in September. The teaching tariff here is R18 per kL plus a R45 basic charge. A 5% prompt-payment reduction applies to the kilolitre charge only.

Unit check. 3.6 kL = 3.6 × 1000 = 3600 L. Treating 3.6 kL as 3.6 L would understate use by a factor of 1 000.

Step 1. Usage charge: 3.6 × 18. 3 × 18 = 54; 0.6 × 18 = 10.8; R64.80.

Step 2. 5% of 64.80: 0.05 × 60 = 3; 0.05 × 4.80 = 0.24; discount R3.24. Usage after discount: 64.80 − 3.24 = R61.56.

Step 3. Add the basic charge (not discounted in this story): 61.56 + 45 = R106.56.

Estimate: 4 kL × R18 = R72, minus about R3.60, plus R45 ≈ R113. The exact R106.56 is lower because 3.6 is below 4, which is reasonable. Applying 5% to R45 as well would be a different policy than the item stated.

Holding the chain when you cannot write much

At a venue sitting you may have no scrap paper. Practise saying the running total in units: “nine rand sixty, then nine eighteen, then two, twenty seventy-eight.” Use the four options as fences: if every remaining option is near R20 and your running total is still R9.60, you have steps left. Online, use the one allowed sheet for those same four lines. Neither mode brings back a calculator.

Traps

Applying a second percent to the original whole instead of to the remainder
Skipping the last add-on fee
Mixing cents and rands, or kL and L
Packing a notebook into a venue because the item is numerical
Treating online’s one sheet as a venue entitlement, or venue’s no-scrap rule as an online ban on the allowed page

Independent OpenExamPrep multi-step QL practice is accuracy under those constraints: several operations, visible units, a reasonableness check, and the official materials rule that matches the sitting you booked.

National Benchmark Tests (NBT, South Africa)

6.3 Multi-Step Calculation without a Calculator

Key Takeaways