Book Isle successive percentages: update the base after every change

An increase of twenty percent followed by a decrease of twenty percent need not restore the start: the second base matters. Read an original quantity card in Book Isle, recording base, change and result, then calculate recovery. This is mathematics reading, not pricing, investment-return or real inventory guidance.

1. Preserve the quantity card and line identities

Save a readable original card starting with one hundred fictional cards; no real files need adding/removing. Check percent signs, directions and ordering, recording a returnable location. Use actual note controls or paper rather than claiming automatic calculation tracking. Preserve originals and separate questions from answers so the final result is not mistaken for given data or the changing-base premise overlooked.

2. Separate base, amount and result for each step

Copy the two steps without immediately adding their signed rates. Use base/rate/change/new-value fields; step two takes step one’s result as its base. Convert twenty percent to 0.2 before multiplying. If an actual passage explicitly uses the original base twice, record that different premise instead of mixing it with sequential changes and declaring the author wrong.

Start: 100 fictional cards
Step A: increase current count by 20%
Step B: decrease the result of A by 20%
Question: final count and change relative to Start

3. Increase, then decrease from the new base

Apply the original-value/change relationship in OpenStax percent applications. A adds twenty to one hundred, yielding 120. B subtracts twenty-four from its new base 120, yielding 96. Retaining both amounts explains equal rates but unequal counts. Check old value plus signed change equals new value at each step. Discrete real counts may need integer constraints; this example’s integer results do not make all percentage calculations integral.

4. Use the initial base for the overall change

Overall change is 96−100=−4, divided by initial 100 for −4%. Its base is the start, not final 96 or an average. Final 96 is 96% of the start, not a 96% increase. Write “fraction of original” and “relative change” as separate complete statements. Recalculate counts after an input change rather than editing the question to obtain a familiar answer.

5. Reverse the order and retain its own amounts

For a reverse-order control, reduce 100 by twenty to eighty, then add twenty percent of eighty, sixteen, to reach 96. Equal endpoints do not make intermediate paths equal: 120 versus eighty, with different step amounts. Commuting these numerical factors does not make real processes order-independent. Preserve separate controls rather than copying sixteen into the first version’s decrease.

6. Recalculate recovery from the current base

Recovering from 96 to 100 requires four, with rate 4/96=1/24, approximately 4.1667%. Adding only four percent adds 3.84, yielding 99.84, still short. Retain the exact fraction and approximation rather than attributing a wrong denominator to rounding. Recovery is a separate paper task. Equal counts do not establish identical real objects or restored file contents.

7. Troubleshoot reused bases and sign errors

One hundred suggests reusing the old base; 144 suggests an increase instead of a decrease. Overall 4/96 suggests borrowing the recovery base. Locate and correct a specific row while retaining the error/reason rather than merely replacing the endpoint with 96. Do not invent calculators or automatic feedback. Book Isle retrieval helps recover the question, not replace arithmetic. Check an actual text’s explicit rate conditions before comparing it with this example.

8. Return and independently refill the four fields

Leave and return to the same anchored card, checking it is not the reverse-order control. Cover answers and refill both four-field rows, obtaining 120, 96 and overall −4%, then independently check recovery’s denominator 96. Preserve both orders, recovery and approximation notes with original dates/excerpts. Explain every base rather than memorize 96. Unperformed export/sync remains unverified, and this paper reasoning is not a promise about real business returns.

Related tutorials and sources

Percentage denominators, Stepwise example records.

Checked on November 13, 2026 against the official Book Isle App Store listing and Apple public lookup: Book Isle 1.1.4, requiring iOS / iPadOS 15.6 or later. Use existing reading, available notes or external records and verify controls in your installed version. Original samples and manual calculations are not new automatic analysis features. No physical-device, private-file or universal export-environment testing is claimed.