ISEE Middle Level Math : How to find the part from the whole with percentage

Study concepts, example questions & explanations for ISEE Middle Level Math

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Example Questions

Example Question #893 : Numbers And Operations

What is \displaystyle 17 \frac{1}{2} \% of \displaystyle 17 \frac{1}{2} ?

Possible Answers:

\displaystyle 30 \frac{5}{8}

\displaystyle 306 \frac{1}{4}

\displaystyle 100

\displaystyle 1

\displaystyle 3\frac{1}{16}

Correct answer:

\displaystyle 3\frac{1}{16}

Explanation:

\displaystyle 17 \frac{1}{2} \% of \displaystyle 17 \frac{1}{2}  can be rewritten as 

\displaystyle \frac{17 \frac{1}{2} }{100} \times 17 \frac{1}{2}

\displaystyle = \frac{35}{2} \times \frac{1}{100} \times \frac{35}{2}

\displaystyle = \frac{35 \times 1 \times 35}{2 \times 100 \times 2}

\displaystyle = \frac{1,225}{400} = \frac{1,225 \div 25}{400\div 25} = \frac{49}{16} = 3 \frac{1}{16}

Example Question #41 : How To Find The Part From The Whole With Percentage

What is 1,800% of 0.00018?

Possible Answers:

\displaystyle 0.0001

\displaystyle 0.00324

\displaystyle 10,000

\displaystyle 0.324

\displaystyle 1,000,000

Correct answer:

\displaystyle 0.00324

Explanation:

1,800% of 0.00018 is equal to

\displaystyle \frac{1,800}{100} \times 0.00018 = 18 \times 0.00018 = 0.00324.

Example Question #42 : How To Find The Part From The Whole With Percentage

What is 1.11% percent of 1.11?

Possible Answers:

\displaystyle 0.012321

\displaystyle 100

\displaystyle 1

\displaystyle 0.12321

\displaystyle 0.0012321

Correct answer:

\displaystyle 0.012321

Explanation:

Taking 1.11% percent of a number is the same as multiplying it by 0.0111, so

1.11% percent of 1.11 is equal to

\displaystyle 0.0111 \times 1.11 = 0.012321.

Example Question #901 : Numbers And Operations

If \displaystyle 0.2 is \displaystyle 20\% of \displaystyle x, what is the value of \displaystyle 5x + 1?

Possible Answers:

\displaystyle 4

\displaystyle 5

\displaystyle 7

\displaystyle 6

Correct answer:

\displaystyle 6

Explanation:

If \displaystyle 0.2 is \displaystyle 20\% of \displaystyle x, that means that \displaystyle x=1. When we plug 1 into \displaystyle 5x+1, the result is \displaystyle 6.

Example Question #43 : How To Find The Part From The Whole With Percentage

King Middle School has 320 students enrolled in the 7th grade.  Sixty percent of the 7th graders at King are girls.  How many 7th grade girls are enrolled at King Middle School?

Possible Answers:

\displaystyle 150

\displaystyle 200

\displaystyle 170

\displaystyle 192

Correct answer:

\displaystyle 192

Explanation:

When given the quantity of the whole, you can determine a part using a percentage by converting the percentage to a decimal and multiplying the whole by that decimal.  

\displaystyle 320\times0.60=192

Example Question #44 : How To Find The Part From The Whole With Percentage

What is 60% of 300?

Possible Answers:

\displaystyle 180

\displaystyle 60

\displaystyle 1800

\displaystyle 18

Correct answer:

\displaystyle 180

Explanation:

Substitute in the proportion:

\displaystyle \frac{part}{whole} = \frac{x}{300}

\displaystyle \frac{percent}{100} = \frac{60}{100}

 

\displaystyle \frac{x}{300} = \frac{60}{100}

 

Cross multiply:

\displaystyle 18,000 = 100x

\displaystyle x = 180

Example Question #45 : How To Find The Part From The Whole With Percentage

What number is 85% of 560?

Possible Answers:

\displaystyle 85

\displaystyle 475

\displaystyle 476

\displaystyle 376

Correct answer:

\displaystyle 476

Explanation:

To determine the number that is 85% of 560, convert the percentage to a decimal:

\displaystyle 85\%=\frac{85}{100}=0.85

Then multiply:

\displaystyle 560 \times 0.85 = 476

The correct answer is \displaystyle 476

Example Question #233 : Percentage

What is \displaystyle 30\% of \displaystyle 150 ? 

Possible Answers:

\displaystyle 30

\displaystyle 60

\displaystyle 55

\displaystyle 120

\displaystyle 45

Correct answer:

\displaystyle 45

Explanation:

To find a percentage of a whole, we will first write the percentage as a fraction.  We know that all percentages can be written as a number over 100.  So,

\displaystyle 30\% = \frac{30}{100}

Now, we will multiply the fraction by the whole number.  We get

\displaystyle \frac{30}{100} \cdot 150

Now, we can simplify/multiply.  

 

We write 150 as a fraction over 1.

\displaystyle \frac{30}{100} \cdot \frac{150}{1}

We can cancel out the zero in 150 and the zero in 100.  

\displaystyle \frac{30}{10} \cdot \frac{15}{1}

We can cancel out the zero in 30 and the zero in 10.

\displaystyle \frac{3}{1} \cdot \frac{15}{1}

Now, we can multiply.  

\displaystyle \frac{3 \cdot 15}{1 \cdot 1}

\displaystyle \frac{45}{1}

\displaystyle 45

 

Therefore, \displaystyle 30\% of \displaystyle 150 is \displaystyle 45.

 

Example Question #82 : Percentages

What is the sale price of a product that costs \displaystyle \$500 if the sale is \displaystyle 40\% off the original price?

Possible Answers:

\displaystyle \$540

\displaystyle \$200

\displaystyle \$800

\displaystyle \$300

\displaystyle \$700

Correct answer:

\displaystyle \$300

Explanation:

First, find \displaystyle 40\% of \displaystyle \$500:

\displaystyle 0.4\cdot \$500=\$200

Then, subtract this value from the whole:

\displaystyle \$500-\$200=\$300

Example Question #234 : Percentage

What is \displaystyle 30\% of \displaystyle 270?

Possible Answers:

\displaystyle 100

\displaystyle 27

\displaystyle 240

\displaystyle 81

\displaystyle 75

Correct answer:

\displaystyle 81

Explanation:

To find a percentage of a whole, we will multiply the percentage by the whole number.  So,

\displaystyle 30\% of \displaystyle 270

can be written as

\displaystyle 30\% \cdot 270

We know that a percentage can be written as a fraction over 100.  So, 

\displaystyle \frac{30}{100} \cdot 270

Now, we can solve.  

\displaystyle \frac{30}{100} \cdot \frac{270}{1}

We can cancel out the zero in 30 and the zero in 100.

\displaystyle \frac{3}{10} \cdot \frac{270}{1}

We can cancel out the zero in 10 and the zero in 270.

\displaystyle \frac{3}{1} \cdot \frac{27}{1}

Now, we multiply.

\displaystyle \frac{3 \cdot 27}{1 \cdot 1}

\displaystyle \frac{81}{1}

\displaystyle 81

 

Therefore, \displaystyle 30\% of \displaystyle 270 is \displaystyle 81.

 

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