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All courses Math Foundations · MF.GR.4 43 of 60
Distinguish additive change from multiplicative change in tables, graphs, and contexts.

Tell whether the change is additive or multiplicative

Problem
Look at the number pattern: 5, 9, 13, 17. Is it additive or multiplicative? Write the change type and briefly tell the amount added each time or the factor used each time.
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Hint

Compare neighboring terms by subtracting: 9−5, 13−9, and 17−13.

Additive patterns have the same difference each step. Multiplicative patterns have the same factor each step.

Solution walkthrough

01

Compare each pair of neighboring terms

\[9~-~5~=~4,~13~-~9~=~4,~17~-~13~=~4\]

To decide between additive and multiplicative change, check what happens from one term to the next. Here, each step increases by the same amount.

02

Identify the constant change

\[+4~\text{each}~\text{time}\]

A pattern is additive when the same number is added at every step. Since the change is always 4, this matches additive change.

03

Rule out multiplicative change

\[9/5~≠~13/9~≠~17/13\]

If the pattern were multiplicative, the factor between terms would stay the same. These quotients are not equal, so there is no constant factor.

04

State the classification

\[\text{The}~\text{pattern}~5,~9,~13,~17~\text{is}~\text{additive};~\text{add}~4~\text{each}~\text{time}.\]

This answers both parts of the question: the change type is additive, and the amount added each time is 4.

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Another way

  1. You can continue the pattern mentally: 17 + 4 = 21. That fits the same add-4 rule, which confirms the pattern is additive.

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Common mistake

Calling 5, 9, 13, 17 multiplicative just because the numbers are getting larger. What matters is how they grow. Here the difference stays constant at 4, so it is additive.