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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 #1441 : Isee Middle Level (Grades 7 8) Mathematics Achievement

Divide the following:

$\frac{8}{9} \div \frac{1}{4}$

Possible Answers:

$\frac{8}{3}$

$\frac{2}{3}$

$\frac{32}{9}$

$\frac{4}{9}$

Correct answer:

$\frac{32}{9}$

Explanation:

To divide, we will multiply the first fraction by the reciprocal of the second fraction. To find the reciprocal, the numerator becomes the denominator, and the denominator becomes the numerator (in other words, we will flip the fraction).

We get

$\frac{8}{9} \div \frac{1}{4}$

$\frac{8}{9} \cdot \frac{4}{1}$

$\frac{8 \cdot 4}{9 \cdot 1}$

$\frac{32}{9}$

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Example Question #1441 : Isee Middle Level (Grades 7 8) Mathematics Achievement

Divide the following:

$\frac{4}{5} \div \frac{1}{2}$

Possible Answers:

$\frac{5}{8}$

$\frac{2}{10}$

$\frac{2}{5}$

$\frac{4}{10}$

$\frac{8}{5}$

Correct answer:

$\frac{8}{5}$

Explanation:

To divide fractions, we will take the first fraction and multiply it by the reciprocal of the second fraction.

To find the reciprocal, the numerator will become the denominator, and the denominator will become the numerator. In other words, we will flip the fraction.

So, we get

$\frac{4}{5} \div \frac{1}{2}$

$\frac{4}{5} \cdot \frac{2}{1}$

$\frac{4 \cdot 2}{5 \cdot 1}$

$\frac{8}{5}$

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Example Question #414 : Fractions

Divide the following:

$\frac{8}{9} \div \frac{1}{2}$

Possible Answers:

$\frac{8}{4.5}$

$\frac{4}{9}$

$\frac{1}{2}$

$\frac{16}{9}$

$\frac{8}{18}$

Correct answer:

$\frac{16}{9}$

Explanation:

To divide fractions, we will take the first fraction and multiply it by the reciprocal of the second fraction. To find the reciprocal, the numerator will become the denominator, and the denominator will become the numerator. In other words, we will flip the fraction. So, we get

$\frac{8}{9} \div \frac{1}{2}$

$\frac{8}{9} \cdot \frac{2}{1}$

$\frac{8 \cdot 2}{9 \cdot 1}$

$\frac{16}{9}$

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Example Question #415 : Fractions

Divide the following:

$\frac{9}{10} \div \frac{1}{2}$

Possible Answers:

$\frac{3}{5}$

$\frac{9}{20}$

$\frac{4}{5}$

$\frac{9}{5}$

Correct answer:

$\frac{9}{5}$

Explanation:

To divide fractions, we will take the first fraction and multiply it by the reciprocal of the second fraction. To find the reciprocal of a fraction, the numerator will become the denominator, and the denominator will become the numerator. In other words, we will flip the fraction.

So, we get

$\frac{9}{10} \div \frac{1}{2}$

$\frac{9}{10} \cdot \frac{2}{1}$

$\frac{9 \cdot 2}{10 \cdot 1}$

$\frac{18}{10}$

$\frac{9}{5}$

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Example Question #561 : Numbers And Operations

Divide the following:

$\frac{6}{8} \div \frac{1}{2}$

Possible Answers:

$\frac{1}{2}$

$\frac{3}{8}$

$\frac{3}{4}$

$\frac{6}{8}$

$\frac{3}{2}$

Correct answer:

$\frac{3}{2}$

Explanation:

So, we get

$\frac{6}{8} \div \frac{1}{2}$

$\frac{6}{8} \cdot \frac{2}{1}$

$\frac{6 \cdot 2}{8 \cdot 1}$

$\frac{12}{8}$

$\frac{6}{4}$

$\frac{3}{2}$

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Example Question #1 : Distributive Property

Which of the following expressions is equivalent to the expression below?

-7 (x - 9)

Possible Answers:

-7x - 9

63x

-7x + 63

-7x+9

-7x - 63

Correct answer:

-7x + 63

Explanation:

First, we can distribute the into the parentheses.

-7 (x - 9) = (-7 * x) - (-7*9)

Now we can simplify the terms.

(-7*x)-(-7*9)= -7 x - (-63)

Subtracting a negative is the same as adding a positive.

-7x-(-63)= -7x+63

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Example Question #1 : How To Find The Distributive Property

$3\left ( 4+5 \right )=$

Possible Answers:

Correct answer:

Explanation:

Using the distributive property, multiply 3 times each of the numbers in parentheses, then add both products:

3*4=12

3*5=15

12+15=27

The answer is 27.

Alternatively, add the two terms inside the parentheses and then multiply the sum by 3:

3(4+5)=3(9)=27

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Example Question #2 : Distributive Property

$\frac{5(3+4)}{5}=$

Possible Answers:

2.4

Correct answer:

Explanation:

First, using the distributive property, multiply 5 times each number in parenthesis, then add the products.

5*3=15

5*4=20

15+20=35

Finally, divide the numerator by the denominator.

$\frac{35}{5}=7$

The answer is 7.

Alternatively, first cancel the 5s and then add the terms in the parentheses:

$\frac{5(3+4)}{5}=(3+4)=7$

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Example Question #1 : How To Find The Distributive Property

Simplify the expression: 9 (y-6)

Possible Answers:

9y-54

9y-6

9y-15

y-15

y-54

Correct answer:

9y-54

Explanation:

Apply the distributive property:

9 (y-6)

$=9 \cdot y-9 \cdot 6$

=9 y-54

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Example Question #2 : How To Find The Distributive Property

Simplify the expression: 9y - 3y + 5y

Possible Answers:

-135y

11y

17y

$-135y^{3}$

Correct answer:

11y

Explanation:

Apply the distributive property:

9y - 3y + 5y

$= \left (9- 3 + 5 \right ) y$

$= \left (6 + 5 \right ) y$

= 11y

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All ISEE Middle Level Math Resources

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

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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 #1441 : Isee Middle Level (Grades 7 8) Mathematics Achievement

Example Question #1441 : Isee Middle Level (Grades 7 8) Mathematics Achievement

Example Question #414 : Fractions

Example Question #415 : Fractions

Example Question #561 : Numbers And Operations

Example Question #1 : Distributive Property

Example Question #1 : How To Find The Distributive Property

Example Question #2 : Distributive Property

Example Question #1 : How To Find The Distributive Property

Example Question #2 : How To Find The Distributive Property

All ISEE Middle Level Math Resources

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