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Ratio, proportion and percent, grade 8

Eighth-grade ratio, proportion and percent.Subjects

The topics, in order:

  • ratio and proportion;
  • directly proportional quantities and ratio problems;
  • scale;
  • percent change.

There are two kinds of lessons:

  • Learning lessons – an explanation, examples and a few questions to try;
  • Practice lessons – questions only.

Go in order.

How the page works: Using a page.

  1. A ratio of three quantitiesLearningRatios of quantities in the same unit, a ratio like 2:3:5 of three quantities, simplifying it, and dividing a quantity in such a ratio.
  2. ProportionLearningAn equality of two ratios, 3:4=6:8: cross-multiplication, checking whether ratios are equal, and finding a missing number.
  3. Directly proportional quantitiesLearningPrice and amount, distance and time: when one quantity doubles, so does the other. Unit price, comparing prices, and proportions in problems.
  4. Ratio problems solved with an equationLearningIn the ratio 3:5 the quantities are 3k and 5k: an equation when the sum is given, when the difference is given, and when the ratio changes.
  5. Practice: ratio and proportionPracticeRatios of three quantities, proportions, directly proportional quantities and ratio problems.
  6. Scale: maps and plansLearningFrom the map to reality and back, finding the scale, comparing maps, and area at a scale.
  7. Percent: the part, the percent and the wholeLearningA percent as a decimal: 35% of 80 is 0.35 times 80. Three questions about one relation – the part, the percent and the whole – and percents over 100.
  8. Percent changeLearningA 15% rise is multiplying by 1.15, a 20% fall is multiplying by 0.8; and the percent change – the change out of the amount before it.
  9. The amount before the changeLearningAfter a 20% discount the price is 120 ₪ – what was it before? An equation: 0.8 times x equals 120. And VAT.
  10. Percent changes one after anotherLearningA 10% rise followed by a 10% fall does not bring back the old price: each change multiplies, and the multipliers are multiplied together.
  11. Practice: percent changePracticeThe part, the percent and the whole, percent change, the amount before a change, VAT and changes one after another.
  12. Review: ratio, proportion and percentPracticeQuestions from every topic: ratio and proportion, directly proportional quantities, scale and percent change.
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