Number Sense and Percents

Percents and Ratios

Number Sense and Percents

Lesson by Mike McGarry

Magoosh Expert

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Percent Increases

7:55

Lesson by Mike McGarry

Magoosh Expert

Summary

Number sense makes percent problems faster and more intuitive by building from familiar benchmarks like 10%, 1%, and sometimes 50%. The most effective approach is to notice arithmetic patterns, break percentages into manageable parts, and use mental math to reconstruct the answer efficiently.

Number sense is a pattern-based intuition for arithmetic that develops through curiosity, repeated exposure, and active experimentation with numbers rather than memorizing a single rule.
A strong starting strategy for percent problems is to find 10% of a number first, and in some cases also find 1%, because those benchmark values make it easier to build many other percentages.
To find a percent of a whole, break the target percent into simpler chunks: 80% of 200 becomes eight groups of 10%, giving 160, and 37% of 700 becomes 30% plus 7%, giving 259.
To find the whole from a percent, reverse the process: if 240 is 30% of a number, divide by 3 to get 10%, then scale up to 100% to get 800.
To find what percent one number is of another, compare the part to benchmark percents of the whole: since 10% of 800 is 80 and 1% is 8, 56 must be 7% of 800.
Shortcuts with familiar fractions of 100 also help: 55% of 400 can be seen as 50% plus 5%, so 200 plus 20 equals 220.
The key advice is to practice these patterns until they feel natural, because this method depends on flexible thinking, logic, and mental computation speed.

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