Grade 4 · Keep cents aligned when adding money · 518 of 750
Keep cents aligned when adding money: first amount: 755 cents; second amount: 395 cents
An illustrated budget for a classroom activity has costs of $7.55 and $3.95. Find the original combined cost in cents and dollars, explain the calculation, and check a related question.
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 illustrated budget for a classroom activity has costs of $7.55 and $3.95. First find the original combined cost in cents and dollars. Then answer: If the second cost rises by 5 cents, what is the revised total?
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
Represent both costs in cents before combining them. One hundred cents is one dollar, so the decimal point records place value rather than acting as punctuation between unrelated whole numbers.
Work through the reasoning
Step 1
Identify the quantities and the task
An illustrated budget for a classroom activity has costs of $7.55 and $3.95. The first task is to find the original combined cost in cents and dollars. Represent both costs in cents before combining them. One hundred cents is one dollar, so the decimal point records place value rather than acting as punctuation between unrelated whole numbers.
Step 2
Calculate the original result
755 cents + 395 cents = 1150 cents. The planned total is $11.50. This is an invented learning budget with no transaction or purchase attached.
Step 3
Complete the follow-up calculation
If the second cost rises by 5 cents, what is the revised total? $11.55, because the total increases by exactly $0.05.
The answer
755 cents + 395 cents = 1150 cents. The planned total is $11.50. This is an invented learning budget with no transaction or purchase attached. Follow-up: $11.55, because the total increases by exactly $0.05.
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
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From experiment to screen.
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The mathematical idea
An illustrated budget for a classroom activity has costs of $7.55 and $3.95. Represent both costs in cents before combining them. One hundred cents is one dollar, so the decimal point records place value rather than acting as punctuation between unrelated whole numbers. The planned total is $11.50. This is an invented learning budget with no transaction or purchase attached.
755 cents + 395 cents = 1150 cents
03 · Reflect and transfer
Explain what changes and why.
Watch the second cost join the first. Read the same current amount in dollars and cents; every whole dollar contains exactly one hundred cents. Explain which quantity changes and which relationship stays valid. Use the starting values again before checking your written answer.
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.