AlgebraUnit 2

Comparing additive and multiplicative changes

Equal additions give arithmetic change. Equal nonzero multipliers give geometric change.

  • Equal additions give arithmetic change. Equal nonzero multipliers give geometric change.
  • Check consecutive differences or ratios before choosing a model.

Example 1

Decide whether the change is additive or multiplicative. State the common difference or ratio.

4, 7, 10, 13. +3. +3. +3

Additive change: the same difference links consecutive terms.

Example 2

Decide whether the change is additive or multiplicative. State the common difference or ratio.

32, 16, 8, 4. \times\frac{1}{2}. \times\frac{1}{2}. \times\frac{1}{2}

Multiplicative change: the same nonzero ratio links consecutive terms.

Your turn

5 practice questions
Question 1

Decide whether the change is additive or multiplicative. State the common difference or ratio.

6, 10, 14, 18.
Check answer6, 10, 14, 18. +4. +4. +4

Additive change: the same difference links consecutive terms.

Question 2

Decide whether the change is additive or multiplicative. State the common difference or ratio.

135, 45, 15, 5.
Check answer135, 45, 15, 5. \times\frac{1}{3}. \times\frac{1}{3}. \times\frac{1}{3}

Multiplicative change: the same nonzero ratio links consecutive terms.

Question 3

Decide whether the change is additive or multiplicative. State the common difference or ratio.

8, 15, 22, 29.
Check answer8, 15, 22, 29. +7. +7. +7

Additive change: the same difference links consecutive terms.

Question 4

Decide whether the change is additive or multiplicative. State the common difference or ratio.

7, 21, 63, 189.
Check answer7, 21, 63, 189. \times3. \times3. \times3

Multiplicative change: the same nonzero ratio links consecutive terms.

Question 5

Decide whether the change is additive or multiplicative. State the common difference or ratio.

10, 13, 16, 19.
Check answer10, 13, 16, 19. +3. +3. +3

Additive change: the same difference links consecutive terms.

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