Percent: the part, the percent and the whole
Percent: the part, the percent and the whole
A percent is a hundredth, so any percent can be written as a decimal:
- ;
- ;
- .
35% of 80 is of 80, and “of” is times: .
A question about percents always has three numbers, and one relation between them:
the part = the percent × the whole
- The whole – the entire amount: 100% of it.
- The percent – what part of the whole, in hundredths.
- The part – the amount that this percent of the whole is.
Two of the three are given, and you find the third. Here are the three questions, about the same class: 30 students, and 12 of them are 40% of the class.
40% of 30 students – how many students is that?
.
12 out of 30 students – what percent is that?
The part is of the whole; write it in hundredths: .
12 students are 40% of the class – how many students are in the class?
The whole is unknown, so call it :
Divide by 0.4: .
Solve.
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power
100% is the whole, and a percent over 100 is more than the whole.
- , so 150% of 60 is – one and a half times as much.
- : 200% of an amount is twice that amount.
- Last year a club had 20 children, and this year 25: this year’s number is of last year’s.
85% of the students voted in the student council election.
357 students voted.
How many students are in the school?
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power
A book costs 64 ₪, and a notebook 16 ₪.
- What percent of the book’s price is the notebook’s price?
- What percent of the notebook’s price is the book’s price?
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power
On the year group’s annual trip, 45 students chose the short route.
They are 30% of all the students in the year group.
How many students chose the other routes?
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power