# Solving Percent Problems: part and whole given

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Chris R.

## Basics on the topicSolving Percent Problems: part and whole given

After this lesson, you will be able to efficiently solve percent problems.

The lesson begins by reviewing that percent is a ratio of part to 100 and can be equivalent to other ratios in a proportion. It leads you to learn that organizing information in a table will easily identify the unknown quantity to be assigned a variable . It concludes by setting the proportion in an equation that leads to the solution.

Learn about solving percent problems by helping Tina become an apprentice to Jungle Jack.

This video includes key concepts, notation, and vocabulary such as percent (part per hundred); whole (the total amount of a certain quantity); and part (an amount of the whole).

Before watching this video, you should already be familiar with ratio, proportion and solving equations.

After watching this video, you will be prepared to real-life problems involving percentage that utilizes multiple steps solution..

Common Core Standard(s) in focus: 6.RP.A.3.C A video intended for math students in the 6th grade Recommended for students who are 11 - 12 years old

## Solving Percent Problems: part and whole given exercise

Would you like to apply the knowledge you’ve learned? You can review and practice it with the tasks for the video Solving Percent Problems: part and whole given.
• ### 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 $x$

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.

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 $60\%$.

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

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