Solving Percent Problems: Part and Whole Given

Solving Percent Problems: Part and Whole Given exercise

• Calculate the percentage of animals Tina saw today.

  Hints

  Set up a proportion.

  $\dfrac{\text{part}}{\text{whole}}=\dfrac{\%}{100}$

  $\dfrac{14}{35}$ = $\dfrac{x}{100}$.

  Now cross multiply.

  $35x = 1400$

  Solve for the missing percent by dividing both sides by $35$.

  $\dfrac{35x}{35}=\dfrac{1400}{35}$

  $x=40$

  Solution

  To find a missing percent, set up a proportion with the percent as the variable.

  $\dfrac{\text{part}}{\text{whole}}=\dfrac{\%}{100}$

  Here are the steps to finding one of the solutions:

  $\begin{array}{l}\frac{16}{20}=\frac{x}{100}\\ \\ 16\left(100\right)=20\left(x\right)\\ \\ \frac{1600}{20}=\frac{20x}{20}\\ \\ x=80\end{array}$

• How many of each animal did she see?

  Hints

  The part is missing. Use the proportion and fill in the information you already know.

  $\dfrac{\text{\bf{part}}}{\text{whole}}=\dfrac{\%}{100}$

  A variable can be used in place of the part.

  $\dfrac{x}{60}=\dfrac{90}{100}$

  Use cross multiplication to solve.

  $\begin{array}{l}\frac{x}{60}=\frac{90}{100}\\ \\ 100x=5400\\ \\ \frac{100x}{100}=\frac{5400}{100}\\ \\ x=54\end{array}$

  Solution

  The proportion $\dfrac{\text{\bf{part}}}{\text{whole}}=\dfrac{\%}{100}$ can be used to find the missing part observed for each animal.

  For example to find the number of hippos observed, you could take the steps seen here:

  $\begin{array}{l}\frac{x}{20}=\frac{50}{100}\\ \\ x\left(100\right)=50\left(20\right)\\ \\ \frac{100x}{100}=\frac{1000}{100}\\ \\ x=10\end{array}$

• Calculate the missing percentages and numbers from the table below.

  Hints

  To find a missing part, whole or percent, use the formula

  $\dfrac{\text{part}}{\text{whole}}=\dfrac{\%}{100}$.

  Using the formula, $\dfrac{\text{part}}{\text{whole}}=\dfrac{\%}{100}$

  • fill in the information you already know
  • replace the missing value with a variable, such as $x$

  Cross-multiplication can help you solve for the missing value.

  Solution

  Here you will find the solutions in the table.

• Calculate the missing percentages and fractions.

  Hints

  To find a percent, the numerator is the part and the denominator is the whole.

  One of the animals has 3 solutions and the other has 4 solutions.

  Fractions can be converted to a percent by dividing the numerator by the denominator and then multiplying by 100.

  For example, $\frac{3}{5}$ can be written as $3 \div 5$ which is equal to $0.6$. This can then be multiplied by 100, to get a percent of $60\%$.

  Solution

  Hermit Crab: 120 out of 160

  • $\frac{120}{160}$
  • $\frac{60}{80}$
  • $\frac{30}{40}$
  • $75\%$

  Lemur: 14 out of 20

  • $\frac{14}{20}$
  • $\frac{7}{10}$
  • $70\%$

• Identify the correct order of instructions to work out the percentages.

  Hints

  Put the information you already know into the formula: $\dfrac{\text{part}}{\text{whole}}=\dfrac{\%}{100}$

  Here you will see an example of the steps taken to find a missing percentage.

  Solution

  1) Use the formula: $\dfrac{\text{part}}{\text{whole}}=\dfrac{\%}{100}$

  2) Substitute the $4$ in the part, the $16$ in the whole and a variable $x$ in the percent.

  $\dfrac{4}{16}=\dfrac{x}{100}$

  3) Cross multiply: $4 \times 100 = 16 \times x$

  4) Divide both sides by 16 to find the solution. $400=16x$

  5) The solution is found. $x=25\%$

• Find the percentage of a number.

  Hints

  Setting up a proportion can help find a missing percentage when the part and whole are know.

  For example; 3 is what percent of 12.

  The proportion used to solve would be:

  $\frac{3}{12}=\frac{n}{100}$

  To solve this proportion,

  $\frac{3}{12}=\frac{n}{100}$

  the following steps can be taken:

  $\begin{array}{l}\frac{3}{12}=\frac{n}{100}\\ \\ 12\left(n\right)=3\left(100\right)\\ \\ \frac{12n}{12}=\frac{300}{12}\\ \\ n=25\end{array}$

  Solution

  • To find a missing percent, given a part and a whole, set up a proportion: $\dfrac{\text{part}}{\text{whole}}=\dfrac{\%}{100}$

  • Fill in the known information and then cross-multiply to solve for the missing value.

  4 is 20% of 20

  5 is 10% of 50

  27 is 45% of 60