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ISEE Middle Level Math : Numbers and Operations

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

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All ISEE Middle Level Math Resources

6 Diagnostic Tests 303 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : How To Multiply Fractions

$\frac{1}{6}* \frac{1}{6}=$

Possible Answers:

$\frac{1}{6}$

$\frac{2}{12}$

$\frac{1}{12}$

$\frac{1}{36}$

Correct answer:

$\frac{1}{36}$

Explanation:

Multiply the numerators and the denominators:

$\frac{1}{6}*\frac{1}{6}=\frac{1}{36}$

Answer: $\frac{1}{36}$

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Example Question #2 : How To Multiply Fractions

What is the simplest form of the result:

$\frac{1}{x^3}\times \frac{3x}{2x^2}\times \frac{4x^4}{3}$

Possible Answers:

$\frac{2}{x}$

Correct answer:

Explanation:

In order to multiply fractions, we can simply multiply straight across:

$\frac{a}{b}\times \frac{c}{d}=\frac{ac}{bd}$

So we can write:

$\frac{1}{x^3}\times \frac{3x}{2x^2}\times \frac{4x^4}{3}=\frac{1\times 3x\times 4x^4}{x^3\times 2x^2\times 3}$

$\frac{12x^5}{6x^5}=\frac{12}{6}=2$

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Example Question #3 : How To Multiply Fractions

Simplify

$\frac{3}{5}\times \frac{2}{6}\times \frac{3}{7}$

Possible Answers:

$\frac{3}{35}$

$\frac{1}{12}$

$\frac{4}{35}$

$\frac{24}{35}$

$\frac{6}{35}$

Correct answer:

$\frac{3}{35}$

Explanation:

In order to multiply fractions, we can simply multiply straight across:

$\frac{a}{b}\times \frac{c}{d}=\frac{ac}{bd}$

So we can write:

$\frac{3}{5}\times \frac{2}{6}\times \frac{3}{7}=\frac{3\times 2\times 3}{5\times 6\times 7}$

$=\frac{18}{210}$

Divide it by the least common factor (i.e. 6) to simplify:

$\frac{18}{210}=\frac{3}{35}$

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Example Question #4 : Fractions

$\frac{1}{4}\times \frac{2}{6}-\frac{1}{8}=?$

Possible Answers:

$-\frac{1}{24}$

$\frac{1}{24}$

$\frac{2}{17}$

$\frac{1}{4}$

$\frac{45}{24}$

Correct answer:

$-\frac{1}{24}$

Explanation:

In this problem we need to follow our order of operations; in this case we need to multiply before we subtract fractions.

To multiply fractions we just need to multiply the numerator by the numerator and the denominator by the denominator. In this case $1\times 2$ (the numerators of the fractions being multiplied) and $4\times 6$ (the denominators) giving us

$\frac{2}{24}$

We then rewrite our equation.

$\frac{2}{24}-\frac{1}{8}=?$

In order to subtract fractions, we must have a common denominator. To do this we need to find a common multiple of 24 and 8. In this case, the 8 nicely goes into 24 three times, so we will only need to multiply one of our fractions to have common denominators.

To do this we must multiply one-eighth three times like this...

$\frac{3}{3}\left(-\frac{1}{8}\right)=-\frac{3}{24}$

Remember that if you are multiplying a fraction, you must multiply both the numerator and the denominator in order to obtain a multiple of your original factor.

Lastly subtract.

$\frac{2}{24}-\frac{3}{24}=-\frac{1}{24}$

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Example Question #4 : How To Multiply Fractions

Solve:

$\frac{2}{5}\times \frac{3}4=$

Possible Answers:

$\frac{3}{10}$

$\frac{6}{5}$

$\frac{5}{9}$

$\frac{8}{15}$

Correct answer:

$\frac{3}{10}$

Explanation:

$\frac{2}{5}\times \frac{3}{4}=\frac{2\times3}{5\times4}=\frac{6}{20}=\frac{3}{10}$

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Example Question #341 : Numbers And Operations

Multiply the fractions:

$\frac{2}{4}*\frac{5}{7}=$

Possible Answers:

$\frac{1}{4}$

$\frac{5}{14}$

$\frac{1}{5}$

Correct answer:

$\frac{5}{14}$

Explanation:

To multiply fractions, multiply both numerators on top and both denominators on the bottom.

$\frac{2}{4}*\frac{5}{7}=\frac{2*5}{4*7}=\frac{10}{28}$

Then, reduce to simplest form by removing any common factors:

$\frac{10}{28}=\frac{10\div2}{28\div2}=\frac{5}{14}$

Answer: $\frac{5}{14}$

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Example Question #342 : Numbers And Operations

Solve:

$\small \frac{3}{10}\times \frac{16}{15}=$

Possible Answers:

$\small \frac{8}{25}$

$\small \small \frac{9}{32}$

$\small \frac{41}{30}$

$\frac{19}{150}$

$\small \frac{19}{25}$

Correct answer:

$\small \frac{8}{25}$

Explanation:

$\small \frac{3}{10}\times \frac{16}{15}=\frac{48}{150}=\frac{8}{25}$

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Example Question #343 : Numbers And Operations

Solve for y:

$\frac{3}{2y}=\frac{6}{x}$

Possible Answers:

$\frac{x}{3}$

$\frac{1}{2}$

$\frac{x}{4}$

Correct answer:

$\frac{x}{4}$

Explanation:

In order to solve for y, cross multiplication must be used. Appyling cross multiplication, we get:

$\frac{3}{2y}=\frac{6}{x}$

12y=3x

Next, we divide each side by 12.

This results in $y=\frac{x}{4}$

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Example Question #344 : Numbers And Operations

On Monday, Marsha saw a sweater that she wanted to buy. It was 15 dollars. She went back the next day and saw that it was only 10 dollars. Which of the following is a sale that the store could have been running, explaining the reduced price on the sweater?

Possible Answers:

$\frac{2}{5}$ off

$\frac{1}{3}$ off

percent off

Correct answer:

$\frac{1}{3}$ off

Explanation:

Given that the sweater's price was reduced by 5 dollars, this is a one third reduction because one third of 15 dollars is 5 dollars. 15 dollars minus 5 dollars is equal to 10 dollars.

Thus, the correct answer is:

$\frac{1}{3}$ off

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Example Question #345 : Numbers And Operations

One dollar is equal to about 116.76 Japanese yen. For how many yen should a tourist to Japan be able to exchange $3,000 at that rate (nearest whole yen)?

Possible Answers:

$3,503 \textrm{ yen }$

$26\textrm{ yen}$

$350,280 \textrm{ yen }$

$257\textrm{ yen}$

$35,028 \textrm{ yen }$

Correct answer:

$350,280 \textrm{ yen }$

Explanation:

One dollar is equal to 116.76 yen, so multiply $3,000 by this conversion rate to get

$3,000 \times 116.76 = 350,280$ yen.

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All ISEE Middle Level Math Resources

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ISEE Middle Level Math : Numbers and Operations

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

All ISEE Middle Level Math Resources

Example Questions

Example Question #1 : How To Multiply Fractions

Example Question #2 : How To Multiply Fractions

Example Question #3 : How To Multiply Fractions

Example Question #4 : Fractions

Example Question #4 : How To Multiply Fractions

Example Question #341 : Numbers And Operations

Example Question #342 : Numbers And Operations

Example Question #343 : Numbers And Operations

Example Question #344 : Numbers And Operations

Example Question #345 : Numbers And Operations

All ISEE Middle Level Math Resources

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