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Working with Percents

Mike McGarry
Lesson by Mike McGarry
Magoosh Expert
Summary
Percent problems on the ACT become much easier when you translate words into math using decimal multipliers. The key method is to treat percent as a multiplier, convert verbal statements into equations, and use fraction shortcuts only when the percent matches a very simple fraction.
  • Percent problems often appear both as standalone questions and as parts of larger ACT math problems, so it is important to handle them quickly and accurately.
  • The central rule is to use the decimal form of a percent as its multiplier, since taking a percent of a number simply means multiplying by that decimal.
  • Basic translation rules make setup straightforward: 'is' means equals, 'of' means multiply, percents change to decimals, and unknown quantities become variables.
  • This method solves problems such as finding a part of a number or finding the whole when a percent and part are given, as in solving equations like x = 0.8 times 200 or 240 = 0.3x.
  • The same setup also finds an unknown percent: solve for the decimal multiplier first, then convert that decimal to a percent, as with 56 = x times 800 leading to 7%.
  • Fraction shortcuts help only when the percent is an easy fraction, such as 75% equaling three-fourths, which can make mental math faster and cleaner.
  • The overall strategy is to rely primarily on percent multipliers, use the same equation structure for unknown percentages, and apply fraction equivalents selectively when they simplify the work.
Chapters
00:00
Using Percent Multipliers
00:35
Translating Percent Statements into Equations
01:41
Finding an Unknown Percent
02:17
Using Fraction Shortcuts for Friendly Percents
02:51
Practice and Core Takeaways

Solutions to the Practice Problems:

1) What is 60% of 60 

Let's translate this into a simple equation.

What --> "x" or what we are trying to find.

is --> "="

60% --> 60/100 or .6

of --> " *" 

x = .6 * 60

x = 36

So all we did was multiply 0.6*60 and we get 36 as our answer.

2) 52 is 40% of what number?

is --> "="

40% --. 40/100 or .4

of --> " * "

what number --> x

52 = .4 * x

We divide both sides by 0.4 and we get X = 52/0.4 = 130

Let's do a check and make sure we did everything right.

3) 18 is what percent of 45?

Before we do anything math let's do a ball park. We know that half of 45 is 22.5 So without doing any math/computation we know that 50% of 45 is 22.5 so 18 is going to be less than 50>#/p###

is --> " ="

what percent --> x/100 

of --> "*"

18 = (x/100) * 45

18/45 = x/100

.4 = x/100

40 = x

So 18 is 40% of 45. 

Notice we can simply divide 18 by 45 to get .4

.4 is 40% in decimal form.

4) What is 50% of 128? [64]

This one you're just dividing 128 by 2.

x = .5 * 128 or 128/2

128/2 = 64