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ISEE Middle Level Math : Numbers and Operations

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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 #1061 : Ssat Middle Level Quantitative (Math)

Stephanie needs to drive 357.5 $\displaystyle 357.5$ miles to meet her family at their vacation home. If she drives at $\displaystyle 55$ miles per hour, how many hours will it take Stephanie to arrive?

Possible Answers:

$\displaystyle 6$

$\displaystyle 5$

6.5 $\displaystyle 6.5$

7.5 $\displaystyle 7.5$

5.5 $\displaystyle 5.5$

Correct answer:

6.5 $\displaystyle 6.5$

Explanation:

Divide: $357.5 \div 55= 6.5$ $\displaystyle 357.5 \div 55= 6.5$

Answer: It will take Stephanie 6.5 $\displaystyle 6.5$ hours to arrive.

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Example Question #32 : How To Find The Part From The Whole

Eighteen dollars must be shared among $\displaystyle 6$ friends. How much money will each friend receive?

Possible Answers:

$\displaystyle 6$

$\displaystyle 5$

$\displaystyle 7$

$\displaystyle 3$

$\displaystyle 4$

Correct answer:

$\displaystyle 3$

Explanation:

Divide: $18\div 6=3$ $\displaystyle 18\div 6=3$

Answer: Each friend will receive $\$3.00$ $\displaystyle \$3.00$.

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Example Question #73 : Numbers And Operations

You bought $\displaystyle 25$ pieces of fruit including $\displaystyle 12$ apples, $\displaystyle 3$ oranges, and $\displaystyle x$ pineapples. How many pineapples did you buy?

Possible Answers:

$\displaystyle 12$

$\displaystyle 3$

$\displaystyle 9$

$\displaystyle 10$

$\displaystyle 25$

Correct answer:

$\displaystyle 10$

Explanation:

You know that you bought $\displaystyle 25$ fruit and you have three kinds; apples, oranges, and pineapples.

If $\displaystyle 12$ are apples and $\displaystyle 3$ are oranges, the rest would be pineapples.

So you must subtract those values from the total and that will be the number of pineapples.

$\displaystyle 25-12-3=10$ so you bought $\displaystyle 10$ pineapples.

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Example Question #74 : Numbers And Operations

You and you friends make $\$25$ $\displaystyle \$25$ doing some yard work. If you have four friends and you need to split the revenue evenly, how much do you make?

Possible Answers:

$\$5$ $\displaystyle \$5$

$\$12.50$ $\displaystyle \$12.50$

$\$5.50$ $\displaystyle \$5.50$

$\$10.00$ $\displaystyle \$10.00$

$\$6.25$ $\displaystyle \$6.25$

Correct answer:

$\$5$ $\displaystyle \$5$

Explanation:

Since there are five of people to split it (you and four friends) you must divide the $\$25$ $\displaystyle \$25$ by $\displaystyle 5$ which is,

$\frac{\$25}{5}=\frac{5\cdot \$5}{5}=\$5$ $\displaystyle \frac{\$25}{5}=\frac{5\cdot \$5}{5}=\$5$.

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Example Question #75 : Numbers And Operations

Find $\frac{2}{3}$ $\displaystyle \frac{2}{3}$ of $\displaystyle 60$.

Possible Answers:

$\displaystyle 10$

$\displaystyle 20$

$\displaystyle 50$

$\displaystyle 30$

$\displaystyle 40$

Correct answer:

$\displaystyle 40$

Explanation:

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

$\frac{2}{3} \cdot 60$ $\displaystyle \frac{2}{3} \cdot 60$

$\frac{120}{3}$ $\displaystyle \frac{120}{3}$

$\displaystyle 40$

Therefore, $\frac{2}{3}$ $\displaystyle \frac{2}{3}$ of $\displaystyle 60$ is $\displaystyle 40$.

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Example Question #31 : Whole And Part

What is $\frac{1}{6}$ $\displaystyle \frac{1}{6}$ of $\displaystyle 72$?

Possible Answers:

$\displaystyle 18$

$\displaystyle 66$

$\displaystyle 32$

$\displaystyle 12$

$\displaystyle 6$

Correct answer:

$\displaystyle 12$

Explanation:

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

$\frac{1}{6} \cdot 72$ $\displaystyle \frac{1}{6} \cdot 72$

Now, we can solve.

$\frac{1}{6} \cdot \frac{72}{1}$ $\displaystyle \frac{1}{6} \cdot \frac{72}{1}$

$\frac{1 \cdot 72}{6 \cdot 1}$ $\displaystyle \frac{1 \cdot 72}{6 \cdot 1}$

$\frac{72}{6}$ $\displaystyle \frac{72}{6}$

We can simplify this, and we get

$\displaystyle 12$

Therefore, $\frac{1}{6}$ $\displaystyle \frac{1}{6}$ of $\displaystyle 72$ is $\displaystyle 12$.

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Example Question #71 : Numbers And Operations

Which of the following numbers yields a remainder of 7 when divided by 9?

Possible Answers:

108 $\displaystyle 108$

106 $\displaystyle 106$

104 $\displaystyle 104$

110 $\displaystyle 110$

Correct answer:

106 $\displaystyle 106$

Explanation:

We can test each of the numbers in tun by dividing each by 9:

$104 \div 9 = 11 \textrm{ R }5$ $\displaystyle 104 \div 9 = 11 \textrm{ R }5$

$106 \div 9 = 11 \textrm{ R }7$ $\displaystyle 106 \div 9 = 11 \textrm{ R }7$

$108 \div 9 = 12\textrm{ R }0$ $\displaystyle 108 \div 9 = 12\textrm{ R }0$

$110 \div 9 = 12 \textrm{ R }2$ $\displaystyle 110 \div 9 = 12 \textrm{ R }2$

106 is the correct choice.

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Example Question #78 : Numbers And Operations

Find $\frac{1}{3}$ $\displaystyle \frac{1}{3}$ of $\displaystyle 45$.

Possible Answers:

$\displaystyle 15$

$\displaystyle 21$

$\displaystyle 42$

$\displaystyle 13$

$\frac{1}{3}$ $\displaystyle \frac{1}{3}$

Correct answer:

$\displaystyle 15$

Explanation:

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

$\frac{1}{3}$ $\displaystyle \frac{1}{3}$ of $\displaystyle 45$

can be written as

$\frac{1}{3} \cdot 45$ $\displaystyle \frac{1}{3} \cdot 45$

Now, we can multiply.

$\frac{1}{3} \cdot \frac{45}{1}$ $\displaystyle \frac{1}{3} \cdot \frac{45}{1}$

$\frac{1 \cdot 45}{3 \cdot1}$ $\displaystyle \frac{1 \cdot 45}{3 \cdot1}$

$\frac{45}{3}$ $\displaystyle \frac{45}{3}$

$\displaystyle 15$

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Example Question #72 : Numbers And Operations

Add in modulo 13 arithmetic:

9+8+7+6 $\displaystyle 9+8+7+6$

Possible Answers:

$\displaystyle 8$

$\displaystyle 6$

$\displaystyle 4$

$\displaystyle 10$

Correct answer:

$\displaystyle 4$

Explanation:

To add numbers in modulo 13 arithmetic, we can add, divide by 13 and note the remainder:

$\displaystyle 9+8+7+6 = 30$

$30 \div 13 =2 \textrm{ R }4$ $\displaystyle 30 \div 13 =2 \textrm{ R }4$

The remainder is 4, so

$9+8+7+6 \equiv 4$ $\displaystyle 9+8+7+6 \equiv 4$ modulo 13.

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Example Question #73 : Numbers And Operations

Subtract in modulo 13 arithmetic:

5 - 11 $\displaystyle 5 - 11$

Possible Answers:

$\displaystyle 5$

$\displaystyle 7$

$\displaystyle 6$

$\displaystyle 8$

Correct answer:

$\displaystyle 7$

Explanation:

To subtract two numbers in modulo 13 arithmetic, we can simply subtract first:

$\displaystyle 5 - 11 = 5+ (-11) = - (11-5) = -6$

Since the number is negative, add 13:

$\displaystyle -6+ 13 = + (13-6) = 7$

$5 - 11 \equiv 7$ $\displaystyle 5 - 11 \equiv 7$ in modulo 13 arithmetic.

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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 #1061 : Ssat Middle Level Quantitative (Math)

Example Question #32 : How To Find The Part From The Whole

Example Question #73 : Numbers And Operations

Example Question #74 : Numbers And Operations

Example Question #75 : Numbers And Operations

Example Question #31 : Whole And Part

Example Question #71 : Numbers And Operations

Example Question #78 : Numbers And Operations

Example Question #72 : Numbers And Operations

Example Question #73 : Numbers And Operations

All ISEE Middle Level Math Resources

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