ISEE Middle Level Math : ISEE Middle Level (grades 7-8) Mathematics Achievement

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

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Example Questions

Example Question #241 : Percentage

What is \displaystyle 20\% of \displaystyle 50 ?

Possible Answers:

\displaystyle 30

\displaystyle 20

\displaystyle 10

\displaystyle 15

\displaystyle 40

Correct answer:

\displaystyle 10

Explanation:

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

So, in the problem

\displaystyle 20\% of \displaystyle 50

we can write it as

\displaystyle 20\% \cdot 50

 

Now, to multiply, we need to write \displaystyle 20\% as a fraction.  A percentage can be rewritten as the number over 100.  So, we get

\displaystyle \frac{20}{100} \cdot 50

 

Now, we need to write \displaystyle 50 as a fraction.  Any whole number can be written as a fraction by simply writing it over 1.  So, we get

\displaystyle \frac{20}{100} \cdot \frac{50}{1}

 

Before we multiply, we can simplify the fractions to make things easier.  The zero in 20 can cancel a zero in 100.  We get

\displaystyle \frac{2}{10} \cdot \frac{50}{1}

 

The zero in 10 can cancel the zero in 50.  We get

\displaystyle \frac{2}{1} \cdot \frac{5}{1}

 

Now, we can multiply.  To multiply fractions, we will multiply straight across.  We get

\displaystyle \frac{2 \cdot 5}{1 \cdot 1}

\displaystyle \frac{10}{1}

\displaystyle 10

 

Therefore, \displaystyle 20\% of \displaystyle 50 is \displaystyle 10.

Example Question #51 : How To Find The Part From The Whole With Percentage

What is \displaystyle 10\% of \displaystyle 40 ?

Possible Answers:

\displaystyle 10

\displaystyle 4

\displaystyle 30

\displaystyle 15

\displaystyle 8

Correct answer:

\displaystyle 4

Explanation:

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

So, given the problem 

\displaystyle 10\% of \displaystyle 40

we can write it as

\displaystyle 10\% \cdot 40

To multiply a percentage, we will re-write the percentage as a fraction.  We know that percentages can be written as that number over 100.  So, we get

\displaystyle \frac{10}{100} \cdot 40

Now, we will write 40 as a fraction.  We know that whole numbers can be written as that number over 1.  So, we get

\displaystyle \frac{10}{100} \cdot \frac{40}{1}

 

Now, before we multiply, we will simplify to make things easier.  The zero in 10 and a zero in 100 can be cancelled.  We get

\displaystyle \frac{1}{10} \cdot \frac{40}{1}

The zero in 10 can be cancelled with the zero in 40.  We get

\displaystyle \frac{1}{1} \cdot \frac{4}{1}

 

Now, we will multiply straight across. 

\displaystyle \frac{1 \cdot 4}{1 \cdot 1}

\displaystyle \frac{4}{1}

\displaystyle 4

 

Therefore,  \displaystyle 10\% of \displaystyle 40 is \displaystyle 4.

Example Question #53 : How To Find The Part From The Whole With Percentage

What is \displaystyle 15\% of \displaystyle 30 ?

Possible Answers:

\displaystyle 2

\displaystyle 5.5

\displaystyle 8

\displaystyle 15

\displaystyle 4.5

Correct answer:

\displaystyle 4.5

Explanation:

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

So, in the problem

\displaystyle 15\% of \displaystyle 30

we can write it as

\displaystyle 15\% \cdot 30

 

Now, we will write the percentage as a fraction.  To do that, we write the number over 100.  So,

\displaystyle \frac{15}{100} \cdot 30

To multiply, we also need to write 30 as a fraction.  To do that, we write the whole number over 1.  So,

\displaystyle \frac{15}{100} \cdot \frac{30}{1}

Now, before we multiply, we will simplify to make things easier.  The zero in 100 can cancel the zero in 30.  So,

\displaystyle \frac{15}{10} \cdot \frac{3}{1}

Now, we will multiply straight across.  We get

\displaystyle \frac{15 \cdot 3}{10}

\displaystyle \frac{45}{10}

\displaystyle 4.5

 

Therefore, \displaystyle 15\% of \displaystyle 30 is \displaystyle 4.5.

 

Example Question #54 : How To Find The Part From The Whole With Percentage

What is \displaystyle 70\% of \displaystyle 150 ? 

Possible Answers:

\displaystyle 120

\displaystyle 100

\displaystyle 105

\displaystyle 70

\displaystyle 143

Correct answer:

\displaystyle 105

Explanation:

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

\displaystyle 70\% of \displaystyle 150

we can write it as

\displaystyle 70\% \cdot 150

 

Now, we will write 70% as a fraction.  We know that a percentage can be written as the number over 100.  So, we get

\displaystyle \frac{70}{100} \cdot 150

Now, we will write 150 as a fraction.  To write a whole number as a fraction, we will write the number over 1.  We get

\displaystyle \frac{70}{100} \cdot \frac{150}{1}

Now, before we multiply, we can simplify to make things easier.  

The zero in 70 can cancel a zero in 100.  So,

\displaystyle \frac{7}{10} \cdot \frac{150}{1}

The zero in 10 can cancel the zero in 150.  So,

\displaystyle \frac{7}{1} \cdot \frac{15}{1}

Now, we can multiply straight across. We get

\displaystyle \frac{7 \cdot 15}{1 \cdot 1}

\displaystyle \frac{105}{1}

\displaystyle 105

 

Therefore, \displaystyle 70\% of \displaystyle 150 is \displaystyle 105.

Example Question #61 : How To Find The Part From The Whole With Percentage

What is \displaystyle 20\% of \displaystyle 80 ? 

Possible Answers:

\displaystyle 15

\displaystyle 24

\displaystyle 16

\displaystyle 60

\displaystyle 20

Correct answer:

\displaystyle 16

Explanation:

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

So, 

\displaystyle 20\% of \displaystyle 80

can be written as

\displaystyle 20\% \cdot 80

Now, we will write 20% as a fraction.  We know that percentages can be written as the number over 100.  So,

\displaystyle \frac{20}{100} \cdot 80

Now, we will write 80 as a fraction.  We know that whole numbers can be written as the number over 1.  So,

\displaystyle \frac{20}{100} \cdot \frac{80}{1}

Now, we can simplify before multiplying to make things easier.  The zero in 20 can cancel a zero in 100. So,

\displaystyle \frac{2}{10} \cdot \frac{80}{1}

The zero in 10 can cancel the zero in 80.  So,

\displaystyle \frac{2}{1} \cdot \frac{8}{1}

Now, we can multiply straight across.  We get

\displaystyle \frac{2 \cdot 8}{1 \cdot 1}

\displaystyle \frac{16}{1}

\displaystyle 16

 

Therefore, \displaystyle 20\% of \displaystyle 80 is \displaystyle 16.

Example Question #911 : Numbers And Operations

What is \displaystyle 25\% of \displaystyle 500?

Possible Answers:

\displaystyle 125

\displaystyle 100

\displaystyle 475

\displaystyle 25

Correct answer:

\displaystyle 125

Explanation:

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

So, in the problem

\displaystyle 25\% of \displaystyle 500

we can write it as

\displaystyle 25\% \cdot 500

Now, we can write \displaystyle 25\% as a fraction.  We know that percentages can be written as fractions over 100.  So, we get

\displaystyle \frac{25}{100} \cdot 500

Now, we will write \displaystyle 500 as a fraction.  We know that whole numbers can be written as fractions over 1.  So, we get

\displaystyle \frac{25}{100} \cdot \frac{500}{1}

Now, before we multiply, we can simplify to make things easier.  The zeros in 100 can cancel the zeros in 500.  So, we get

\displaystyle \frac{25}{1} \cdot \frac{5}{1}

Now, we can multiply straight across.  We get

\displaystyle \frac{25 \cdot 5}{1 \cdot 1}

\displaystyle \frac{125}{1}

\displaystyle 125

 

Therefore, \displaystyle 25\% of \displaystyle 500 is \displaystyle 125.

Example Question #1801 : Isee Middle Level (Grades 7 8) Mathematics Achievement

What is \displaystyle 30\% of \displaystyle 250 ? 

Possible Answers:

\displaystyle 85

\displaystyle 75

\displaystyle 125

\displaystyle 220

\displaystyle 30

Correct answer:

\displaystyle 75

Explanation:

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

\displaystyle 30\% of \displaystyle 250

we can re-write it like

\displaystyle 30\% \cdot 250

Now, we can multiply.  First, we will write the percentage as a fraction.  We know that percentages can be written as fractions over 100.  So, we get

\displaystyle \frac{30}{100} \cdot 250

Now, we will write 250 as a fraction.  We know that whole numbers can be written as fractions over 1.  So, we get

\displaystyle \frac{30}{100} \cdot \frac{250}{1}

Now, before we multiply, we will simplify to make things easier. The zero in 30 and the zero in 100 can cancel.  So, we get

\displaystyle \frac{3}{10} \cdot \frac{250}{1}

Now, the zero in 10 can cancel the zero in 250.  So, we get

\displaystyle \frac{3}{1} \cdot \frac{25}{1}

Now, we can multiply straight across.  We get

\displaystyle \frac{3 \cdot 25}{1 \cdot 1}

\displaystyle \frac{75}{1}

\displaystyle 75

 

Therefore, \displaystyle 30\% of \displaystyle 250  is \displaystyle 75.

Example Question #921 : Numbers And Operations

What is \displaystyle 40\% of \displaystyle 80 ? 

Possible Answers:

\displaystyle 30

\displaystyle 32

\displaystyle 28

\displaystyle 40

\displaystyle 36

Correct answer:

\displaystyle 32

Explanation:

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

So, given the problem

\displaystyle 40\% of \displaystyle 80

we can re-write it as

\displaystyle 40\% \cdot 80

Now, to multiply, we will write both numbers as fractions.  So, to write \displaystyle 40\% as a fraction, we know percentages can be written as fractions over 100.  So, we get

\displaystyle \frac{40}{100} \cdot 80

Now, to write \displaystyle 80 as a fraction, we know whole numbers can be written as fractions over 1.  So, we get

\displaystyle \frac{40}{100} \cdot \frac{80}{1}

Now, before we multiply, we will simplify to make things easier.  The zero in \displaystyle 40 can cancel a zero in \displaystyle 100. So, we get

\displaystyle \frac{4}{10} \cdot \frac{80}{1}

Now, the zero in \displaystyle 10 can cancel the zero in \displaystyle 80.  So, we get

\displaystyle \frac{4}{1} \cdot \frac{8}{1}

Now, we can multiply straight across.  We get

\displaystyle \frac{4 \cdot 8}{1 \cdot 1}

\displaystyle \frac{32}{1}

\displaystyle 32

 

Therefore,  \displaystyle 40\% of \displaystyle 80 is \displaystyle 32.

Example Question #921 : Numbers And Operations

What is \displaystyle 10\% of \displaystyle 90 ?

Possible Answers:

\displaystyle 30

\displaystyle 10

\displaystyle 80

\displaystyle 9

\displaystyle 20

Correct answer:

\displaystyle 9

Explanation:

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

\displaystyle 10\% of \displaystyle 90

we can write 

\displaystyle 10\% \cdot 90

Now, we will write \displaystyle 10\% as a fraction.  We know that percentages can be written as fractions over 100.  So, we get

\displaystyle \frac{10}{100} \cdot 90

Now, we will write \displaystyle 90 as a fraction.  We know that whole numbers can be written as fractions over 1.  So, we get

\displaystyle \frac{10}{100} \cdot \frac{90}{1}

Now, before we multiply, we will simplify to make things easier.  The zero in 10 can cancel a zero in 100.  So, we get

\displaystyle \frac{1}{10} \cdot \frac{90}{1}

The zero in 10 can cancel the zero in 90.  So, we get

\displaystyle \frac{1}{1} \cdot \frac{9}{1}

Now, we can multiply straight across.  We get

\displaystyle \frac{1 \cdot 9}{1 \cdot 1}

\displaystyle \frac{9}{1}

\displaystyle 9

 

Therefore, \displaystyle 10\% of \displaystyle 90 is \displaystyle 9.

Example Question #61 : How To Find The Part From The Whole With Percentage

Find \displaystyle 45\% of \displaystyle 200.

Possible Answers:

\displaystyle 90

\displaystyle 24

\displaystyle 110

\displaystyle 155

\displaystyle 76

Correct answer:

\displaystyle 90

Explanation:

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

\displaystyle 45\% of \displaystyle 200

we can re-write it like this

\displaystyle 45\% \cdot 200

Now, to multiply, we will first write \displaystyle 45\% as a fraction.  We know that percentages can be written as fractions over 100.  So, we can write

\displaystyle \frac{45}{100} \cdot 200

Now, we will write \displaystyle 200 as a fraction.  We know that whole numbers can be written as fractions over 1.  So, we get

\displaystyle \frac{45}{100} \cdot \frac{200}{1}

Now, we can simplify before we multiply to make things easier.  The zeros in 100 can cancel the zeros in 200.  So, we get

\displaystyle \frac{45}{1} \cdot \frac{2}{1}

Now, we can multiply straight across.  We get

\displaystyle \frac{45 \cdot 2}{1 \cdot 1}

\displaystyle \frac{90}{1}

\displaystyle 90

 

Therefore,  \displaystyle 45\% of \displaystyle 200 is \displaystyle 90.

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