How do I check whether two ratios are actually proportional?
Use cross products to test whether two ratios are equal, with worked examples and a checklist for setting up the comparison correctly.
Read the guide 4 min read
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How can I use benchmark percentages to estimate a calculation quickly?
Estimate a percentage by breaking it into familiar fractions, then combine the parts and check whether the result makes sense.
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How do I calculate a percentage change from a starting amount?
Compare the change with the starting amount—not the ending amount—to calculate percentage change. Follow a labeled example and reusable steps.
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How can I use a unit rate to compare two different-sized groups?
Convert both groups to the same amount per one matching unit, then compare the results to see which offers more.
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Why do two successive percentage changes not always cancel out?
See why equal percentage increases and decreases use different base amounts, with a worked example and a reusable way to track each change.
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What is a unit rate, and how is it different from a ratio?
Learn to tell a general ratio from a unit rate, then rewrite a comparison as an amount per one unit with a clear worked example.
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How can I use a ratio table to find equivalent pairs?
Learn to fill a ratio table by scaling both quantities by the same factor, check that the pairs stay equivalent, and spot the pattern.
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How do I scale a ratio while keeping the same relationship?
Learn to scale both parts of a ratio by one common factor, check the result, and use it to represent a larger or smaller group.
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Why can a percentage be greater than 100 percent?
Learn why percentages can exceed 100% by identifying the reference amount and comparing a larger quantity with it.
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How can I find the whole when I know a percentage and its part?
Use the known part and percentage to calculate the whole, then check your answer by applying the percentage back to it.
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How can I convert a percentage into a fraction in simplest form?
Write the percentage over 100, then divide the numerator and denominator by shared factors to simplify the fraction.
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When is rounding an intermediate answer likely to cause a problem?
See how early rounding can change a multi-step result, when to keep extra digits, and how to round only the final answer.
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Why can dividing by a decimal be rewritten using whole numbers?
See why scaling both numbers keeps a division answer the same, then follow a worked example and reusable method.
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How do I place the decimal point when multiplying decimals?
Multiply the digits, count the decimal places in both factors, and use an estimate to check whether your product is a plausible size.
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How do I convert a fraction with an awkward denominator into a decimal?
Divide the numerator by the denominator, identify whether the decimal repeats, and choose a precision that fits the task.
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How can I convert a fraction with a denominator of 10 or 100 into a decimal?
Use tenths or hundredths to place the digits, and add a zero when needed to keep the value clear.
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What does dividing by a fraction mean in an everyday sharing example?
See fraction division as counting how many small portions fit in an amount, and why the answer can be larger than the starting amount.
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Why do I multiply the numerators and denominators when multiplying fractions?
Understand fraction multiplication as taking a part of a part, with an area model and a worked example that shows where the rule comes from.
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How do I mark overlapping speech so readers can follow both speakers?
Choose a clear overlap notation, preserve both voices when useful, and mark unclear words without guessing.
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How do I handle a player who cannot take any legal action on their turn?
Choose a consistent fallback for blocked turns, match its consequences to your game, and test the rule with clear examples.
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How do I keep a caption and alt text from repeating each other?
Use alt text for an image’s essential information or function in context, and let the caption add useful context or another distinct detail.
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How do I write a text alternative for a map without giving navigation directions?
Describe what the map communicates and how its visible information is organized, without adding routes, locations, or unsupported geographic facts.
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How do I describe a chart without restating every plotted value?
Write a concise chart overview that highlights its purpose and supported patterns, while pointing readers to fuller detail when they need exact values.
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How do I write a text alternative for a diagram with labeled parts?
Learn to turn a diagram’s labels into a concise description of its parts and relationships, with a reusable template that avoids unsupported claims.
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