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The value of a percent

Percent, ratio and scale, grade 6 Lesson 3 of 11Learning

The value of a percent

The value of a percent
A percent is said of a part of a quantity: “50% of the students”, “20% of the price”.

What is 25% of 36?
It is the same question as “what is 14\displaystyle \frac{1}{4} of 36”, since 25%=14\displaystyle {25\%}={\frac{1}{4}}:

25%×36=14×36=9\displaystyle {25\%\times36}={\frac{1}{4}\times36}={9}

As with fractions: 25% is the percent, 36 is the whole quantity, and 9 is the value of the percent.

Calculating in stations

In your head you calculate in stations – from an easy percent to one that is easy to get from it. This is how to find 25% of 36:

  • 100% of 36 is 36.
  • 50% is half of it: 18.
  • 25% is half of 50%: 9.
The stations 10% and 5%

10% is a tenth, so you divide by 10. From 10% you reach many other percents. This is how to find 15% of 60:

  • 10% of 60 is 6.
  • 5% is half of 10%: 3.
  • 15%=10%+5%\displaystyle {15\%}={10\%+5\%}, so 15% of 60 is 6+3=9\displaystyle {6+3}={9}.
Swapping the percent and the quantity

What is 18% of 50?
That is hard in your head. But 18% of 50 is the same as 50% of 18: both multiply 18×50\displaystyle 18\times50 and divide by 100.
50% of 18 is half of 18, that is, 9.

Exercise 1

Find the value of the percent.

a
25% of 48

    / – 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

    b
    10% of 70

      / – 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

      c
      75% of 40

        / – 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

        d
        4% of 25 – swap the percent and the quantity.

          / – 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

          Exercise 2

          Calculate in your head, in stations, and write the stations down.

          • 15% of 80
          • 30% of 90
          • 1212%\displaystyle 12\frac{1}{2}\% of 64
          15% of 80

            / – 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

            30% of 90

              / – 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

              1212%\displaystyle 12\frac{1}{2}\% of 64

                / – 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

                Exercise 3

                There are 32 students in a sixth-grade class.
                On a winter day, 25% of them were absent.
                How many students were absent?

                  / – 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