Card 1 of 20
EasyStudy card 1
Prompt
What is the master percent equation?
Translate ‘is’ and ‘of.’
Answer
\(P=rW\), where \(P\) is part, \(r\) is decimal rate, and \(W\) is whole.
Example
\(30\%\) of \(80\) gives \(P=0.30(80)\).
MathChapter 7: Percents
Flashcards
Percents and Equations Flashcards
Twenty concise cards on the part-rate-whole model, language translation, proportions, checks, and symbolic reasoning.
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Card 1 of 20. Answer hidden.
Card 2 of 20
EasyStudy card 2
Prompt
In percent language, what does ‘is’ usually identify?
It sits on the equals side of \(P=rW\).
Answer
The part \(P\).
Example
‘\(24\) is \(30\%\) of \(80\)’ has \(P=24\).
Card 3 of 20
EasyStudy card 3
Prompt
In percent language, what does ‘of’ usually identify?
The rate multiplies the whole.
Answer
The whole \(W\).
Example
In ‘\(20\%\) of \(150\),’ the whole is \(150\).
Card 4 of 20
EasyStudy card 4
Prompt
How do you find a part when rate and whole are known?
Write the rate as a decimal.
Answer
Multiply: \(P=rW\).
Example
\(0.18(250)=45\).
Card 5 of 20
EasyStudy card 5
Prompt
How do you find a percent rate when part and whole are known?
Part goes above whole.
Answer
Divide: \(r=P/W\), then convert to percent form.
Example
\(42/168=0.25=25\%\).
Card 6 of 20
MediumStudy card 6
Prompt
How do you find a whole when part and rate are known?
The rate must be decimal form.
Answer
Divide: \(W=P/r\).
Example
If \(63\) is \(35\%\), then \(63/0.35=180\).
Card 7 of 20
MediumStudy card 7
Prompt
How is ‘What is \(p\%\) of \(W\)?’ modeled?
The unknown is the part.
Answer
\(P=(p/100)W\).
Example
‘What is \(12\%\) of \(50\)?’ becomes \(P=0.12(50)\).
Card 8 of 20
MediumStudy card 8
Prompt
How is ‘\(P\) is what percent of \(W\)?’ modeled?
Solve by dividing \(P/W\).
Answer
\(P=rW\), with \(r\) unknown.
Example
\(18=r(72)\) gives \(r=25\%\).
Card 9 of 20
MediumStudy card 9
Prompt
How is ‘\(P\) is \(p\%\) of what number?’ modeled?
Solve by dividing by the decimal rate.
Answer
\(P=(p/100)W\), with \(W\) unknown.
Example
\(54=0.30W\) gives \(W=180\).
Card 10 of 20
MediumStudy card 10
Prompt
What percent proportion is equivalent to \(P=rW\)?
Keep part over whole.
Answer
\(P/W=p/100\), where \(p\) is the percent number.
Example
\(30/120=p/100\) gives \(p=25\).
Card 11 of 20
MediumStudy card 11
Prompt
When should a rate above \(100\%\) produce a part above the whole?
Its decimal rate is above \(1\).
Answer
Always, when the quantities are positive.
Example
\(140\%\) of \(60\) is \(84\).
Card 12 of 20
MediumStudy card 12
Prompt
What does a rate below \(1\%\) imply about the part?
Convert the rate with care.
Answer
The part is a very small fraction of a positive whole.
Example
\(0.4\%\) of \(500\) is \(2\).
Card 13 of 20
MediumStudy card 13
Prompt
Why is \(35\) not the decimal rate for \(35\%\)?
Divide by \(100\).
Answer
Percent means per hundred, so the decimal rate is \(0.35\).
Example
\(35\%=35/100=0.35\).
Card 14 of 20
MediumStudy card 14
Prompt
How can units help identify part and whole?
Check dimensional consistency.
Answer
Part and whole share the same units; the rate is unitless.
Example
\(45\) students out of \(180\) students gives a unitless rate.
Card 15 of 20
MediumStudy card 15
Prompt
What is the first check after solving for a whole?
Undo the division.
Answer
Substitute it into \(P=rW\) and verify the known part.
Example
If \(W=240\) and \(r=0.30\), then \(P=72\).
Card 16 of 20
MediumStudy card 16
Prompt
What mistake reverses the percent rate?
Use \(r=P/W\).
Answer
Dividing whole by part instead of part by whole.
Example
\(20\) out of \(80\) is \(20/80=25\%\), not \(400\%\).
Card 17 of 20
MediumStudy card 17
Prompt
What mistake occurs when finding the whole by multiplication?
Use \(W=P/r\).
Answer
Multiplying \(P\) by \(r\) makes it smaller instead of undoing the rate.
Example
If \(24\) is \(30\%\), the whole is \(80\), not \(7.2\).
Card 18 of 20
HardStudy card 18
Prompt
If both part and whole are multiplied by the same positive factor, what happens to the rate?
The common factor cancels in \(P/W\).
Answer
It remains unchanged.
Example
\(20/80=40/160=25\%\).
Card 19 of 20
HardStudy card 19
Prompt
If \(a\) is \(p\%\) of \(b\), how is \(p\) expressed?
Start from \(a=(p/100)b\).
Answer
\(p=100a/b\).
Example
If \(a=3\) and \(b=8\), then \(p=37.5\).
Card 20 of 20
HardStudy card 20
Prompt
If \(x\) is \(125\%\) of \(y\), what is \(y\) as a percent of \(x\)?
Use the reciprocal relationship.
Answer
\(80\%\).
Example
\(x=1.25y\), so \(y/x=1/1.25=0.80\).
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