Key takeaway: Percent means per hundred: the symbol % after a number tells how many parts out of 100 are counted, so 45% is the same as 45/100 or 0.45.
Grade 66.RP.A.3cRatios, Rates and Percents
Definition of Percent
A percent measures an amount against 100 equal parts of a whole. The word comes from the Latin per centum, “for each hundred”. If 45% of the students in a survey chose pizza, then about 45 out of every 100 students would choose it, whatever the actual group size.
Percents link fractions and decimals: \(45\% = \frac{45}{100} = 0.45\). Values over 100% describe amounts bigger than the original whole.
Formula and notation
The symbol \(\%\) follows the number. Call that number \(p\). The part, the whole and \(p\) are tied by
\[\text{part} = \frac{p}{100} \times \text{whole} \qquad\text{or}\qquad p = \frac{\text{part}}{\text{whole}} \times 100\]
In calculations, replace \(p\%\) with the fraction \(\frac{p}{100}\) or with a decimal.
Key facts
- Moving the decimal point two places to the right turns 0.45 into 45%.
- 100% is the entire amount, 50% is one half and 25% is one quarter.
- Values above 100% describe amounts larger than the starting whole.
- A percent only has meaning relative to a whole, so always name the whole.
Percent example
In a survey of 60 students, 27 picked pizza as their favorite lunch. (a) What percent picked pizza? (b) What is 35% of 80 students?
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(a) Divide the part by the whole: \(\frac{27}{60} = 0.45\).
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Multiply by 100: \(0.45 \times 100 = 45\), so the share is 45%.
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(b) Write 35% as 0.35 and multiply: \(0.35 \times 80 = 28\).
(a) 45% of the students picked pizza. (b) 35% of 80 is 28 students.
Common mistake
Watch out
Priya computes 8% of 50 as \(8 \times 50 = 400\).
Why it is wrong
She used 8 instead of \(\frac{8}{100}\), which is 0.08. The correct product is \(0.08 \times 50 = 4\). A quick sense check: 8% is a small slice, so the answer must be far below 50.
Related terms and lessons
Browse the glossary: A–Z list · Grade 6 vocabulary · Ratios, Rates and Percents