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Door 2 · Grade 7

🔢 Ratios & Proportions (Advanced)

Proportion = two equal ratios

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Solving Proportions Using Cross-Multiplication

A proportion says two ratios are equal: a/b = c/d (where b and d are not zero).
Cross-multiplication rule: If a/b = c/d, then a x d = b x c.
Real-life example: If 3 apples cost 6, how much do 5 apples cost?
3/6 = 5/x => 3x = 30 => x = 10
StepAction1Set up the proportion: a/b = c/d2Cross-multiply: a x d = b x c3Solve for the unknown variable4Check: does the answer make sense?

Worked example

Problem: Solve: 5/8 = 15/x

  1. 5 x x = 8 x 15 => 5x = 120 => x = 24

Answer: 5 x x = 8 x 15 => 5x = 120 => x = 24

Percent Problems — Discount, Tax, Markup

Percent means per hundred (out of 100). Percent problems appear in everyday life as discounts, taxes, and markups.
Problem TypeFormulaDiscountDiscount = Original Price x Discount%. Sale Price = Original - DiscountTaxTax = Price x Tax%. Total = Price + TaxMarkupMarkup = Cost x Markup%. Selling Price = Cost + MarkupPercent Increase(New - Old) / Old x 100%Percent Decrease(Old - New) / Old x 100%Always convert percent to decimal first: 25% = 0.25

Worked example

Problem: A 80 shirt is 25% off. What is the sale price?

  1. Discount = 80 x 0.25 = 20.
  2. Sale price = 80 - 20 = 60.

Answer: Sale price = 80 - 20 = 60.