Prairie Minds
MATH · GRADE 7Number

Percent: Discounts, Taxes, and Tips

A percent is a ratio with 100 as its second term.

Grade 7
35 % = 25 % + 10 %BENCHMARKS BUILD ANY PERCENT025355010035 %

What a percent is

A percent is a ratio whose second term is 100. The symbol % is shorthand for "out of 100." So 35 % is 35 / 100, which is also 7 / 20, which is also 0.35.

The previous lesson built equivalent ratios. A percent is the equivalent ratio whose second term has been scaled to 100. To convert any ratio to a percent, scale until the second term is 100; to convert a percent to a ratio, simplify x : 100 to lowest terms.

The five benchmarks

The Alberta curriculum names five benchmark percentages: 1, 5, 10, 25, 50. Every other percent can be built from these as a sum.

The five benchmarks

1%5%10%25%50%0100EVERY OTHER PERCENT IS A SUM OF THESE FIVE

35 % is 25 % + 10 %. 75 % is 50 % + 25 %. 12 % is 10 % + 1 % + 1 %. A student who knows the five benchmarks can compute almost any percent mentally — find 10 % of the number, scale it up or down by combining the chunks.

Try it

Stack benchmark chunks until you hit the target.

target: 35%100%

running total

0%

Decomposition

— empty —

Add benchmarks (1, 5, 10, 25, 50) until your running total hits the target. There's usually more than one way to get there.

The widget covers all three of the curriculum's named cases: the ordinary percent (35 %), the greater-than-100 % case (150 % is "one and a half times as much"), and the less-than-1 % case (0.5 % builds from a finer set of chunks: 0.1, 0.5, 1, 2, 5).

A percent isn't capped at 100. A 200 % increase doubles a value. A 0.05 % GIC interest rate is real — small, but real.

Convert between ratio, fraction, decimal, and percent

The same number lives under four names.

720=7:20=0.35=35%\frac{7}{20} = 7 : 20 = 0.35 = 35\%

The conversion routine is short:

  • Ratio → percent: scale the second term to 100. 7 : 20 becomes 35 : 100 = 35 %.
  • Percent → fraction: write as x / 100, then simplify. 35 % = 35/100 = 7/20.
  • Decimal → percent: multiply by 100 (shift two places right). 0.35 = 35 %.
  • Percent → decimal: divide by 100 (shift two places left). 35 % = 0.35.

Every form means the same thing. Picking the most useful one is half the skill.

Discounts, taxes, tips, and other applications

Percent is mostly used as a multiplier on a base number. A 30 % discount on a $48 jacket reads 0.30 × 48 = 14.40 off — so the sale price is $48 − $14.40 = $33.60. Tax is the same shape.

Try it

Type a price. Pick a discount. The receipt updates live.

$

Pick a discount

Receipt — Alberta

Subtotal$48.00
After discount$48.00
+ GST 5%$2.40
Total$50.40

Discount comes off the sticker price first; GST applies to whatever is left. A till-style calculator. The student types a sticker price and picks a discount chip; a receipt-style breakdown shows the subtotal, the discount line, the after-discount subtotal, the GST 5% line, and the total. The discount comes off the sticker first; GST applies to whatever's left.

A 15 % tip is 0.15 × bill. A 5 % GST is 0.05 × pre-tax total. A 10 % markup is 1.10 × wholesale price. A 30 % discount on a $48 jacket leaves 0.70 × 48 = $33.60. All shaped the same way: a percent is a multiplier, and the multiplier is the percent divided by 100.

Where it shows up in real life

The till from the last section shows up at every cash register from Cross Iron Mills in Calgary to Bonnyville Centre to a corner store in Beaumont. Real Alberta numbers:

  • Sales tax: 5 % GST, no PST. (0.05 × subtotal)
  • A typical sit-down restaurant tip: 15–20 %.
  • An interest rate on a high-interest savings account in 2026: around 2–4 % per year.
  • Markdown signs at a shopping centre: typically 20, 30, 50 %.
  • AB-grade beef yield off the live weight at a Lethbridge feedlot: about 62 % of live weight ends up as carcass weight.

Same arithmetic, different applications. The till math is the practice.

Worksheet

These aren't graded. Try one approach per question — benchmarks for the friendly numbers, decimal multiplication for the awkward ones.

Question 1 of 4

Try it

What is 25 % of 80?

Multiple choice: what is twenty-five percent of eighty? Four cards: twenty, two, two hundred, sixteen.

Benchmark decompositions

30 % = 25 + 5

75 % = 50 + 25

12 % = 10 + 1 + 1

Going further

Percent is everywhere downstream. In Grade 8, interest (simple and compound) reuses the percent multiplier across multiple periods. Percent change problems compute (new − old) / old and report the result as a percent — useful for everything from stock prices to pine-beetle damage assessment.

Statistics in this same Grade 7 strand uses percentages to summarize sample proportions; the Grade 9 stats outcomes pick that back up in confidence-interval form. The conversion routines in this lesson reappear unchanged.