6.1 Quantity, Number and Operations

QL number work is not MAT algebra

Quantitative Literacy (QL) sits inside the combined Academic and Quantitative Literacy (AQL) paper. The official CEA/NBTP AQL teachers' booklet lists QL as 50 multiple-choice questions. Academic Literacy is the larger AQL share, about 75 items. QL scores are reported separately from AL. MAT is a different NBT domain, written as its own afternoon paper when a faculty requires mathematics. Confusing the two wastes an afternoon or leaves a Health Sciences applicant short of a required score.

QL number items ask you to order quantities and to calculate or estimate with whole numbers, fractions, decimals, percentages, ratios, and scientific notation. The allowed operations are addition, subtraction, multiplication, division, and positive exponentiation. There is no calculator. If a formula is needed, the item provides it. Contexts are higher-education: residence notices, campus clinics, faculty surveys, municipal service data. Independent OpenExamPrep number practice for QL teaches those operations in those settings. It is not a MAT algebra course, not a confidential NBTP paper, and not a claim of official sponsorship.

A QL item that mentions 3/8 of a clinic caseload still wants a number you can defend in that clinic. A MAT-style rearrangement of a quadratic is the wrong exam.

Convert first, then order

Quantities arrive in mixed clothing. Ranking them means converting to one representation and, where needed, one unit, then comparing.

Worked example: residence water targets. A campus facilities notice lists four daily targets in litres per student:

Smallest to largest: C 116 L, D 118 L, A 120 L, B 124 L.

Do not rank the surface forms. 1.18 × 10^2 looks “small” if you ignore the power of ten. 58% looks larger than 0.62 if you compare 58 with 0.62. Convert.

Worked example: clinic waiting times. Four queues are posted as 3/4 hour, 0.8 hour, 70% of an hour, and 4.0 × 10^1 minutes.

• 3/4 of 60 min = 180/4 = 45 min
• 0.8 × 60 = 48 min
• 0.70 × 60 = 42 min
• 4.0 × 10^1 = 40 min

Order: 40 min, 42 min, 45 min, 48 min.

Worked example: near-lookalikes. Compare 1/3, 0.33, 33%, and 3.3 × 10^{-1}.

• 1/3 = 0.333…
• 0.33 = 0.33
• 33% = 0.33
• 3.3 × 10^{-1} = 0.33

So 1/3 is strictly larger than the other three, which are equal. Treating 1/3 as 0.3 would reverse the order.

Fraction, decimal, percent, scientific notation

These names are clothing for the same part-to-whole idea.

• Fraction to decimal: divide. For 3/8, 8 into 30 is 3 remainder 6; 60 is 7 remainder 4; 40 is 5. So 0.375.
• Decimal to percent: multiply by 100. 0.375 × 100 = 37.5%.
• Percent to decimal: divide by 100. 37.5% = 0.375.
• Decimal to fraction: 0.375 = 375/1000; divide numerator and denominator by 125 to get 3/8.

Worked example: writing-centre use. A faculty survey reports that 18 of 48 first-years used the writing centre.

Simplify 18/48 by dividing by 6: 3/8. 3/8 = 0.375 = 37.5%.

Trap readings include 18% (the numerator treated as a percent), 48% (the denominator treated as a percent), and 3.75% (a dropped place value).

Scientific notation is another clothing change. 4.60 × 10^3 = 4600. 4.60 × 10^{-2} = 0.046. Move the decimal point as many places as the exponent; left for a negative exponent.

Worked example: three campus counts. Wifi sessions logged as 1.8 × 10^3 = 1800. Library holds logged as 2.4 × 10^2 = 240. A lab colony count logged as 3.0 × 10^3 = 3000. Order: 240, 1800, 3000.

Operations, including positive powers

QL operations are +, −, ×, ÷, and positive exponentiation. For a positive integer n, a^n means a multiplied by itself n times. 2^5 = 2 × 2 × 2 × 2 × 2 = 32, not 2 × 5 = 10, and not 25.

Worked example: municipal pump. A notice rates a pump at 2^5 litres per minute. 2^5 = 32 L/min. Volume in 15 minutes: 32 × 15. 32 × 10 = 320; 32 × 5 = 160; total 480 L. In scientific notation that is 4.80 × 10^2 L.

Worked example: clinic fluids. A student nurse records 2.5 L, then another 3/4 L, then uses 40% of the combined volume in a demonstration.

3/4 = 0.75. 2.5 + 0.75 = 3.25 L combined. 40% of 3.25: 0.4 × 3.25. 0.4 × 3 = 1.2; 0.4 × 0.25 = 0.10; 1.30 L used. Remaining: 3.25 − 1.30 = 1.95 L.

Keep the litre unit on every line. 1.95 L is not 1.95 mL.

Worked example: streetlight upgrade. A municipal notice says 12% of 250 streetlights near a campus gate are LED. 10% of 250 = 25; 2% of 250 = 5; LED count = 30. Remaining: 250 − 30 = 220.

Worked example: lab shelves. Each shelf holds 3^4 sample boxes. 3^4 = 3 × 3 × 3 × 3. 3 × 3 = 9; 9 × 3 = 27; 27 × 3 = 81 boxes per shelf. Two shelves hold 162 boxes. That power is not 3 × 4 = 12.

Estimate, then compute

Estimation is an official QL move, not a shrug. Round to numbers you can multiply, compute a nearby value, then judge whether an exact option can sit near that estimate.

Worked example: campus shop. 19 bottles at R8.90. Estimate: 20 × 9 = R180. Exact: 19 × 8.90 = 19 × 9 − 19 × 0.10 = 171 − 1.90 = R169.10. R169.10 sits slightly below R180, as expected after rounding both factors up. An option of R1 691 moved a decimal. An option of R19 added instead of multiplying.

Worked example: 47% of 198 tutorial seats. Estimate: about half of 200 = 100, then a little less. Exact path: 50% of 198 = 99; 3% of 198 = 5.94; 99 − 5.94 = 93.06. An option of 47 is the percent copied as a count. An option of 198 is the whole group.

Traps

• Ranking 58% against 0.62 without converting
• Reading 2^5 as 10 or as 25
• Treating 18/48 as 18%
• Dropping units (kL read as L, hours left in hours while other times are in minutes)
• Reaching for a calculator: QL is calculator-free
• Doing MAT symbol-pushing when the item is a campus table

On test day, convert to one form, keep units, estimate first, then compute the arithmetic you can show in a few lines. Independent OpenExamPrep QL number teaching stays in higher-education contexts because that is the QL job: numbers that still mean something after the last operation.