The “Fraction Trick” for Percent Change

Today I just want to give a quick tip about using fractions to simplify percent change words problems.

Consider the following question. Let’s say I invest X dollars, and the value of my investment goes up by 60% one day, then down by 37.5% the next day. What’s the overall percent change in my investment?

Some people’s first impulse is to use decimals. X times 1.6 times 0.625. The problem is, the arithmetic is horrendous. But what if I use fractions instead of decimals? Well, 1.6 could be written as (8/5), and 0.625 could be written as (5/8). At that point, the arithmetic becomes way simpler, and quickly realize the final values answer is just X.

Now it’s true I engineered that question to demonstrate my point. But the idea is – using fractions on percent change word problems often creates opportunities to cancel. And questions will frequently reward your ability to see that.

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[jeel.kankotiya]

Isn’t the overall change in % +22.5 at the end of Wednesday since the original investment made? I don’t understand how there is no change in investment? The value did go up overall, no?

[dc]

Are you using .625 instead of .375 (or 37.5%) because you’re decreasing