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 #251 : Percentage

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

Possible Answers:

\(\displaystyle 105\)

\(\displaystyle 70\)

\(\displaystyle 115\)

\(\displaystyle 100\)

\(\displaystyle 120\)

Correct answer:

\(\displaystyle 105\)

Explanation:

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

So, 

\(\displaystyle 70\%\) of \(\displaystyle 150\)

can be written as 

\(\displaystyle 70\% \cdot 150\)

Now, we will write \(\displaystyle 70\%\) as a fraction.  We know that percentages can be written as fractions over 100.  So, we get

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

Now, we will write \(\displaystyle 150\) as a fraction.  We know that whole numbers can be written as fractions over 1.  So, we get

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

Now, we will simplify before we multiply to make things easier.  The zero in 70 can cancel a zero in 100.  So, we get

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

Now, the zero in 10 can cancel the zero in 150.  So, we get

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

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 #253 : Percentage

What is \(\displaystyle 25\%\) of \(\displaystyle 300\) ? 

Possible Answers:

\(\displaystyle 75\)

\(\displaystyle 25\)

\(\displaystyle 125\)

\(\displaystyle 225\)

\(\displaystyle 50\)

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

\(\displaystyle 25\%\) of \(\displaystyle 300\)

we can re-write it as

\(\displaystyle 25\% \cdot 300\)

Now, to multiply, we will write 25% as a fraction.  We know percentages can be written as fractions over 100.  So, we get

\(\displaystyle \frac{25}{100} \cdot 300\)

Now, we will write 300 as a fraction.  We know whole numbers can be written as fractions over 1.  So, we get

\(\displaystyle \frac{25}{100} \cdot \frac{300}{1}\)

Now, before we multiply, we can simplify to make things easier.  The zeros in 100 can cancel the zeros in 300.  So, we get

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

Now, we can multiply straight across.  We get

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

\(\displaystyle \frac{75}{1}\)

\(\displaystyle 75\)

 

Therefore,  \(\displaystyle 25\%\) of \(\displaystyle 300\) is \(\displaystyle 75\).

Example Question #254 : Percentage

What is \(\displaystyle 25\%\) of \(\displaystyle 400\) ? 

Possible Answers:

\(\displaystyle 100\)

\(\displaystyle 225\)

\(\displaystyle 375\)

\(\displaystyle 150\)

\(\displaystyle 250\)

Correct answer:

\(\displaystyle 100\)

Explanation:

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

\(\displaystyle 25\%\) of \(\displaystyle 400\)

can be written as

\(\displaystyle 25\% \cdot 400\)

Now, to multiply, we will write \(\displaystyle 25\%\) as a fraction. We know that percentages can be written as fractions over 100.  So,

\(\displaystyle \frac{25}{100} \cdot 400\)

Now, we will write \(\displaystyle 400\) as a fraction.  We know that whole numbers can be written as fractions over 1.  So,

\(\displaystyle \frac{25}{100} \cdot \frac{400}{1}\)

Now, before we multiply, we will simplify to make things easier.  The zeros in 100 can cancel the zeros in 400.  So,

\(\displaystyle \frac{25}{1} \cdot \frac{4}{1}\)

Now, we can multiply straight across.  We get

\(\displaystyle \frac{25 \cdot 4}{1 \cdot 1}\)

\(\displaystyle \frac{100}{1}\)

\(\displaystyle 100\)

 

Therefore, \(\displaystyle 25\%\) of \(\displaystyle 400\) is \(\displaystyle 100\).

Example Question #62 : How To Find The Part From The Whole With Percentage

What is \(\displaystyle 80\%\) of \(\displaystyle 250\) ? 

Possible Answers:

\(\displaystyle 150\)

\(\displaystyle 80\)

\(\displaystyle 225\)

\(\displaystyle 170\)

\(\displaystyle 200\)

Correct answer:

\(\displaystyle 200\)

Explanation:

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

 

So, given the problem

\(\displaystyle 80\%\) of \(\displaystyle 250\)

 

We can re-write it as

\(\displaystyle 80\% \cdot 250\)

 

Now, we will write 80% as a fraction.  We know that percentages can be written as fractions over 100.  So, we get

\(\displaystyle \frac{80}{100} \cdot 250\) 

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

\(\displaystyle \frac{80}{100} \cdot \frac{250}{1}\) 

Now, we will simplify before we multiply to make things easier.  The zero in 80 can cancel a zero in 100.  So, we get

\(\displaystyle \frac{8}{10} \cdot \frac{250}{1}\)

 The zero in 10 can cancel the zero in 250.  We get

\(\displaystyle \frac{8}{1} \cdot \frac{25}{1}\) 

Now, we can multiply straight across.  We get

\(\displaystyle \frac{8 \cdot 25}{1 \cdot 1}\)

\(\displaystyle \frac{200}{1}\)

\(\displaystyle 200\)

 

Therefore, \(\displaystyle 80\%\) of \(\displaystyle 250\) is \(\displaystyle 200\).

Example Question #71 : How To Find The Part From The Whole With Percentage

What is \(\displaystyle 60\%\) of \(\displaystyle 120\) ?

Possible Answers:

\(\displaystyle 82\)

\(\displaystyle 72\)

\(\displaystyle 60\)

\(\displaystyle 70\)

\(\displaystyle 80\)

Correct answer:

\(\displaystyle 72\)

Explanation:

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

\(\displaystyle 60\% \cdot 120\)

 

\(\displaystyle \frac{60}{100} \cdot 120\)

 

\(\displaystyle \frac{60}{100} \cdot \frac{120}{1}\)

 

\(\displaystyle \frac{6}{10} \cdot \frac{120}{1}\)

 

\(\displaystyle \frac{6}{1} \cdot \frac{12}{1}\)

 

\(\displaystyle \frac{6 \cdot 12}{1 \cdot 1}\)

 

\(\displaystyle \frac{72}{1}\)

 

\(\displaystyle 72\)

 

Therefore,  \(\displaystyle 60\%\) of \(\displaystyle 120\) is \(\displaystyle 72\).

Example Question #72 : How To Find The Part From The Whole With Percentage

Find \(\displaystyle 60\%\) of \(\displaystyle 180\).

Possible Answers:

\(\displaystyle 98\)

\(\displaystyle 120\)

\(\displaystyle 115\)

\(\displaystyle 108\)

\(\displaystyle 112\)

Correct answer:

\(\displaystyle 108\)

Explanation:

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

\(\displaystyle 60\% \cdot 180\)

 

\(\displaystyle \frac{60}{100} \cdot 180\)

 

\(\displaystyle \frac{60}{100} \cdot \frac{180}{1}\)

 

The zeros can cancel.  We get

\(\displaystyle \frac{6}{10} \cdot \frac{180}{1}\)

 

\(\displaystyle \frac{6}{1} \cdot \frac{18}{1}\)

 

\(\displaystyle \frac{6 \cdot 18}{1 \cdot 1}\)

 

\(\displaystyle \frac{108}{1}\)

 

\(\displaystyle 108\)

Example Question #73 : How To Find The Part From The Whole With Percentage

What is \(\displaystyle 20\%\) of \(\displaystyle 240\) ? 

Possible Answers:

\(\displaystyle 56\)

\(\displaystyle 4.8\)

\(\displaystyle 78\)

\(\displaystyle 220\)

\(\displaystyle 48\)

Correct answer:

\(\displaystyle 48\)

Explanation:

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

So, we get

\(\displaystyle 20\% \cdot 240\)

 

\(\displaystyle \frac{20}{100} \cdot 240\)

 

\(\displaystyle \frac{20}{100} \cdot \frac{240}{1}\)

 

The zeros can cancel out.  We get

\(\displaystyle \frac{2}{10} \cdot \frac{240}{1}\)

 

\(\displaystyle \frac{2}{1} \cdot \frac{24}{1}\)

 

\(\displaystyle \frac{2 \cdot 24}{1 \cdot 1}\)

 

\(\displaystyle \frac{48}{1}\)

 

\(\displaystyle 48\)

 

Therefore, \(\displaystyle 20\%\) of \(\displaystyle 240\) is \(\displaystyle 48\).

Example Question #74 : How To Find The Part From The Whole With Percentage

Find \(\displaystyle 30\%\) of \(\displaystyle 250\).

Possible Answers:

\(\displaystyle 30\)

\(\displaystyle 75\)

\(\displaystyle 220\)

\(\displaystyle 65\)

\(\displaystyle 110\)

Correct answer:

\(\displaystyle 75\)

Explanation:

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

\(\displaystyle 30\% \cdot 250\)

 

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

 

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

 

We can cancel the zeros to simplify.  We get

 

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

 

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

 

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

 

\(\displaystyle \frac{75}{1}\)

 

\(\displaystyle 75\)

 

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

Example Question #75 : How To Find The Part From The Whole With Percentage

What is \(\displaystyle 60\%\) of \(\displaystyle 350\) ?

Possible Answers:

\(\displaystyle 290\)

\(\displaystyle 210\)

\(\displaystyle 190\)

\(\displaystyle 270\)

\(\displaystyle 240\)

Correct answer:

\(\displaystyle 210\)

Explanation:

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

\(\displaystyle 60\% \cdot 350\)

 

\(\displaystyle \frac{60}{100} \cdot 350\)

 

\(\displaystyle \frac{60}{100} \cdot \frac{350}{1}\)

 

Now, we can cancel out the zeros.  We get

 

\(\displaystyle \frac{6}{10} \cdot \frac{350}{1}\)

 

\(\displaystyle \frac{6}{1} \cdot \frac{35}{1}\)

 

\(\displaystyle \frac{6 \cdot 35}{1 \cdot 1}\)

 

\(\displaystyle \frac{210}{1}\)

 

\(\displaystyle 210\)

Example Question #76 : How To Find The Part From The Whole With Percentage

What is 35% of 200 ? 

Possible Answers:

\(\displaystyle 90\)

\(\displaystyle 70\)

\(\displaystyle 60\)

\(\displaystyle 75\)

\(\displaystyle 155\)

Correct answer:

\(\displaystyle 70\)

Explanation:

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

\(\displaystyle 35\% \cdot 200\)

 

\(\displaystyle \frac{35}{100} \cdot 200\)

 

\(\displaystyle \frac{35}{100} \cdot \frac{200}{1}\)

 

We can cancel the zeros to make things easier.

 

\(\displaystyle \frac{35}{1} \cdot \frac{2}{1}\)

 

\(\displaystyle \frac{35 \cdot 2}{1 \cdot 1}\)

 

\(\displaystyle \frac{70}{1}\)

 

\(\displaystyle 70\)

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