Grade 7 · Track the percent reference base · 377 of 750
Track the percent reference base · practice 40
An original amount of 110 changes by 50%. Find the signed change and the new amount. Follow the calculation, then test the quantities in the animated example.
Try the question, use a hint when you need one, and compare your reasoning with the worked solution. The animation starts with this chapter’s values; changing its controls explores a new case.
01 · Make a prediction
Your practice question
An original amount of 110 changes by 50%. Find the signed change and the new amount.
Use this scratch space or work on paper. Your notes stay on this page and clear when you leave. Answers are for self-checking; they are not automatically graded.
A starting point
Compute the change from the original amount, then add the signed change.
Work through the reasoning
Step 1
Translate the givens
50% of the original 110 is a signed change of 110 × 50/100.
Step 2
Calculate with the model
Change = 55; new = 110 + (55) = 165.
Step 3
Check and interpret
The same result is 110 × 1.5. Subtracting the original from the new amount recovers 55.
The answer
Change = 55; new amount = 165.
Compare the method as well as the result. A different valid method may reach the same answer. Keep exact values until the last step when the question asks for rounding.
02 · Explore the model
See the mathematical relationship move.
Use Play, Pause, and the timeline to inspect the construction. Reset restores the question’s original settings. The displayed assumptions describe where this model applies.
Watch the relationship
PausedHD animation studio
From experiment to screen.
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The mathematical idea
A percentage change is calculated from a specified original amount. An increase adds a positive part and a decrease adds a negative part. Applying the same percentage to the new amount generally does not undo the first change because the reference whole has changed. Starting quantities: Original amount = 110; Signed percent change = 50.
new = original × (1 + percent/100)
03 · Reflect and transfer
Explain what changes and why.
Why does the same percentage decrease generally not undo an earlier percentage increase?
This is a distinct guided scenario using a reusable mathematical model. Similar-looking diagrams can represent different given values and conclusions; they are not different mathematical theories.