Increasing and decreasing by a given percentage

Find the new amount after increasing or decreasing a quantity by a given percentage, using the decimal-multiplier method (1 plus or minus the rate).

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Learning objective overview

Master Teaching Guide coverage for this objective.

Current NZC (2007)
  • NA5-5
  • NA6-3
New NZC (2026)
  • NZC26-P4-NUM-FIN-K-Y9-02
  • NZC26-P4-NUM-NSO-P-Y9-19
  • NZC26-P4-NUM-FIN-K-Y9-03
  • NZC26-P4-NUM-FIN-K-Y9-04
  • NZC26-P4-NUM-NSO-P-Y10-09
  • NZC26-P4-NUM-FIN-P-Y10-03
  • NZC26-P4-NUM-NSO-P-Y10-10
  • NZC26-P3-NUM-NSO-K-Y8-06
  • NZC26-P3-NUM-FIN-P-Y7-02
  • NZC26-P3-NUM-FIN-P-Y8-02

Resources

Terminology

  • Percentage of a given quantity
  • Of
  • Interest
  • Principal
  • Simple Interest
  • Compound Interest
  • Goods and Services Tax / GST
  • Depreciation

Task goals

  • Increase or decrease a quantity by a given percentage using the decimal-multiplier method (multiply by 1 plus or minus the rate as a decimal).
  • Read a percentage-change bar (100% baseline plus a hatched increase or decrease segment) to find the new amount.
  • Apply the method to money and real-world contexts (discounts, markups, GST, population growth, single-period depreciation).
  • Apply the method with decimal percentage rates and round money answers to the nearest cent.
  • Apply two successive percentage changes (same or different rates, increase then decrease or vice versa) and explain why the result is not generally the same as the starting amount.
  • Work backwards from an original and a new amount to find the percentage rate of change.

Where this fits

What leads into this objective, and where it goes next.

Before

Forming percentages

Forming percentages

Relationship between percentages, fractions, and decimals

Relationship between percentages, fractions, and decimals

You are here

Increasing and decreasing by a given percentage

Increasing and decreasing by a given percentage

Know

Percentages can be used to proportionally increase or decrease a quantity by multiplication and can be presented as decimal multipliers.

Statement▸
Year 9 · Number · Financial mathematics
NZC26-P4-NUM-FIN-K-Y9-02
Do

Increasing or decreasing a number by a given proportion

Statement▸
Year 9 · Number · Number structures and operations
NZC26-P4-NUM-NSO-P-Y9-19

Next

Percentage Change: Increase, Decrease and Reverse Percentages

Percentage Change: Increase, Decrease and Reverse Percentages

Reverse percentage

Reverse percentage

Budgets

Budgets

Also under NA5-5:

Also under NA6-3:

Explore the whole sequence →

For teachers

Need the fuller teaching notes for this objective? Open the Teacher guidance PDF.