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ISEE Middle Level Math : Algebraic Concepts

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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 : Equations

$8\cdot \left ( 2\cdot 5 \right ) \div \left ( 4\cdot 1 \right )=$

Possible Answers:

Correct answer:

Explanation:

First solve the parentheses.

$8 * 10 \div 4=$

Then solve from left to right since multiplication and division are interchangeable:

$80\div 4=20$

The answer is 20.

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Example Question #2 : Equations

$3 \frac{2}{6} \ast 2\frac{3}{4}=$

Possible Answers:

$9 \frac{1}{6}$

$22\frac{1}{6}$

Correct answer:

$9 \frac{1}{6}$

Explanation:

First, convert each mixed number into an improper fraction.

$\frac{20}{6}\ast \frac{11}{4}$

Then, reduce where possible and multiply.

Finally, convert your answer into a mixed-number fraction.

$\frac{55}{6}=9 {\frac{1}{6}}$

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Example Question #827 : Concepts

$11 \frac{1}{4} \div 5\frac{2}{5}=$

Possible Answers:

$2 \frac{1}{12}$

$2\frac{1}{18}$

Correct answer:

$2 \frac{1}{12}$

Explanation:

First, convert each mixed number into an improper fraction and flip the second fraction. Then, change the operation to multiplication:

$\frac{45}{4} \ast \frac{5}{27}=$

Reduce where possible and multiply. Convert your answer into a mixed fraction.

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Example Question #211 : Algebraic Concepts

$8^{3}\div 2^{2}=$

Possible Answers:

128

Correct answer:

128

Explanation:

First find the exponent value for each number:

$8^{3}\div 2^{2}=512 \div 4=$

Then divide accordingly. The answer is 128.

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Example Question #3 : Equations

11+39=12+28+2a

Possible Answers:

2.5

Correct answer:

Explanation:

First follow order of operations and solve on each side.

11+39=12+28+2a

50=40+2a

Then, subtract 40 from each side to leave only the variable:

50-40=40+2a-40

10=2a

Finally, divide both sides by 2.

$10\div 2=2a\div 2$

The answer is 5=a

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Example Question #212 : Algebraic Concepts

13 + 27=12+3+ 5a

Possible Answers:

5.5

Correct answer:

Explanation:

First solve with order of operations on each side:

13 + 27=12+3+ 5a

40 = 15+5a

Then subtract 15 from each side:

40-15=15+ 5a-15

25=5a

Finally, divide each side by 5:

$25\div 5=5a\div 5$

5=a

The answer is 5.

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Example Question #11 : Equations

$7 \ast \left ( 3\ast 5 \right )\div \left ( 25\div 5 \right )=$

Possible Answers:

Correct answer:

Explanation:

Solve inside the parentheses first:

$7 \ast (15) \div (5)=$

Follow order of operations to solve:

$105 \div 5=21$

The answer is 21.

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Example Question #213 : Algebraic Concepts

Melissa is going on a road trip to her mother's house in another state. On a full tank of gas, she can travel 230 miles. At least how many times will she need to fill up her gas tank if her mother lives 950 miles away?

Possible Answers:

Correct answer:

Explanation:

Divide the total distance (950) by the number of miles per full tank of gas (230).

$950\div 230=4.1$

Therefore, she will have to fill up her tank with gas at least 5 times.

Answer is at least 5 times.

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Example Question #214 : Algebraic Concepts

$12a + 2a -18= 3(6) + 2(5\ast 2)$

Possible Answers:

Correct answer:

Explanation:

First solve what is inside parentheses and follow the order of operations:

$12a + 2a -18= 3(6) + 2(5\ast 2)$

14a-18= 18+ 2(10)

14a -18= 18+20

14a-18=38

Then, add 18 to each side:

14a=56

Finally, divide each side my 14:

$14a \div 14= 56\div 14$

a=4

The answer is 4.

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Example Question #215 : Algebraic Concepts

$3\frac{3}{9} \div 5\frac{1}{5}=$

Possible Answers:

$1\frac{3}{4}$

$\frac{117}{75}$

$1\frac{1}{2}$

$\frac{25}{39}$

Correct answer:

$\frac{25}{39}$

Explanation:

First, convert each fraction into an improper fraction.

$\frac{30}{9} \div \frac{26}{5}=$

Then, change the operation to multiplication and flip the second fraction.

$\frac{30}{9} \ast \frac{5}{26}=$

Reduce and multiply.

$\frac{30}{9}\ast \frac{5}{26}=\frac{10}{3}\ast \frac{5}{26}=\frac{5}{3}\ast \frac{5}{13}=\frac{25}{39}$

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All ISEE Middle Level Math Resources

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ISEE Middle Level Math : Algebraic Concepts

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

All ISEE Middle Level Math Resources

Example Questions

Example Question #1 : Equations

Example Question #2 : Equations

Example Question #827 : Concepts

Example Question #211 : Algebraic Concepts

Example Question #3 : Equations

Example Question #212 : Algebraic Concepts

Example Question #11 : Equations

Example Question #213 : Algebraic Concepts

Example Question #214 : Algebraic Concepts

Example Question #215 : Algebraic Concepts

All ISEE Middle Level Math Resources

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