What is Percent & Part of a Whole as a Percent?

What is Percent & Part of a Whole as a Percent? exercise

• Find the percent of the total.

  Hints

  Remember, to find the percent of a total, you need to solve the equation: $\frac{\text{Part}}{\text{Whole}}$ = Percent

  The part is 350 and the whole is 1,000. You need to solve the equation $\frac{350}{1,000}$ = Percent

  Once you solve $\frac{350}{1,000}$, you need to multiply the result by 100 to get the percent

  Solution

  $\frac{\text{Part}}{\text{Whole}}$ = Percent

  $\frac{350}{1,000}$ = Percent

  $0.35$ = Percent

  $0.35\times100$ = Percent

  $\bf35%$ = Percent

• Find the percent donated.

  Hints

  The part is $£750$ because this is only a piece of the total donated money, while $£5,000$ is the goal so this is the whole.

  If you divide the part by the whole, you must multiply the decimal product by 100 to get the percent.

  Solution

  $\frac{\text{Part}}{\text{Whole}}$ = Percent

  Which value is the part? 750 Which value is whole? 5,000 Therefore, our equation is: $\frac{\textbf{750}}{5,000}$ = Percent

  Divide 750 by 5,000 to find the percent. 0.15 = Percent

  Now multiply to find the percent. $0.15\:\times$ 100 = Percent

  15% = Percent

• Find the number of respondents.

  Hints

  135 is the total, which is 100% of people.

  Remember, what you do to one side, you must do to the other side too. This means if you divide one side by 100, you must divide the other side by 100 too.

  Solution

  81 people responded to the invitation.

• Find 100% of the total.

  Hints

  First set up an equation for: Part = Percent $\times$ Whole

  When you set up the equation with the values, it should look like this:

  $2000=\dfrac{40}{100}\times{x}$

  We can solve the equation by multiplying both sides by the reciprocal fraction to isolate $x$.

  The reciprocal of $\dfrac{40}{100}$ is $\dfrac{100}{40}$, which must be added to both sides of the equation.

  After isolating $x$, the equation should now read:

  $\dfrac{100}{40}$ * 2,000 = $x$

  Solution

  Part = percent $\times$ whole

  $2,000$ = $\dfrac{40}{100}$ $\times$ $x$

  $\dfrac{100}{40}$ $\times$ $2,000$ = $\dfrac{100}{40}$ $\times$ $\dfrac{40}{100}$ $\times$ $x$

  $\dfrac{100}{40}$ $\times$ $2,000$ = $x$

  $2.5$ $\times$ $2,000$ = $x$

  $£5,000$ = $x$

• Find the number of respondents.

  Hints

  First set up a table to help solve the problem.

  With your table set up, find what 1% of the people and percent is. To do this, think about what you need to divide 100% by to get 1%, and do the same for the people column.

  1% of people is 1.5. You need to multiply 1.5 by 30 to find 30% of the people.

  Solution

  First divide the total number of people, 150 by 100 and 100% by 100.

  This gives us 1.5 people and 1%.

  Then multiply what 1% of people is by 30, to get 30% of people.

  Next, do the same to the number of people: $1.5 \times 30$.

  $1.5 \times 30$ = 45 people.

• Find the goal total.

  Hints

  When finding the part, both the percent and whole are important.

  The formula Part = percent $\times$ whole can help.

  The current amount raised can help you find the goal total.

  Remember, $\frac{100}{70}$ $\times$ $\frac{70}{100}$ cancels itself out by cross multiplication.

  $\frac{100}{70}$ is asking you to solve 100 divided by 70, and then multiply this value by the total raised so far.

  Solution

  Part = percent $\times$ whole

  $\frac{100}{70}$ $\times$ £4,900 = $\frac{100}{70}$ $\times$ $\frac{70}{100}$ $*$ $x$

  $\frac{100}{70}$ $\times$ £4,900 = $x$

  £7,000 = $x$

  The goal total is £7,000