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ISEE Middle Level Math : Algebraic Concepts

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 #2 : Equations

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

Possible Answers:

$\displaystyle 24$

$\displaystyle 20$

$\displaystyle 32$

$\displaystyle 14$

Correct answer:

$\displaystyle 20$

Explanation:

First solve the parentheses.

$8 * 10 \div 4=$ $\displaystyle 8 * 10 \div 4=$

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

$80\div 4=20$ $\displaystyle 80\div 4=20$

The answer is 20.

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Example Question #3 : Equations

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

Possible Answers:

$22\frac{1}{6}$ $\displaystyle 22\frac{1}{6}$

$\displaystyle 9$

$\displaystyle 3$

$9 \frac{1}{6}$ $\displaystyle 9 \frac{1}{6}$

Correct answer:

$9 \frac{1}{6}$ $\displaystyle 9 \frac{1}{6}$

Explanation:

First, convert each mixed number into an improper fraction.

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

Then, reduce where possible and multiply.

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

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

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Example Question #1 : How To Find The Solution To An Equation

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

Possible Answers:

$\displaystyle 3$

$\displaystyle 2$

$2\frac{1}{18}$ $\displaystyle 2\frac{1}{18}$

$\displaystyle 8$

$2 \frac{1}{12}$ $\displaystyle 2 \frac{1}{12}$

Correct answer:

$2 \frac{1}{12}$ $\displaystyle 2 \frac{1}{12}$

Explanation:

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

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

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

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Example Question #2 : How To Find The Solution To An Equation

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

Possible Answers:

$\displaystyle 12$

$\displaystyle 34$

128 $\displaystyle 128$

$\displaystyle 23$

Correct answer:

128 $\displaystyle 128$

Explanation:

First find the exponent value for each number:

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

Then divide accordingly. The answer is 128.

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Example Question #1 : Equations

$\displaystyle 11+39=12+28+2a$

Possible Answers:

$\displaystyle 20$

2.5 $\displaystyle 2.5$

$\displaystyle 4$

$\displaystyle 10$

$\displaystyle 5$

Correct answer:

$\displaystyle 5$

Explanation:

First follow order of operations and solve on each side.

$\displaystyle 11+39=12+28+2a$

$\displaystyle 50=40+2a$

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

$\displaystyle 50-40=40+2a-40$

10=2a $\displaystyle 10=2a$

Finally, divide both sides by 2.

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

The answer is 5=a $\displaystyle 5=a$

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Example Question #1 : How To Find The Solution To An Equation

$\displaystyle 13 + 27=12+3+ 5a$

Possible Answers:

$\displaystyle 5$

5.5 $\displaystyle 5.5$

$\displaystyle 6$

$\displaystyle 3$

Correct answer:

$\displaystyle 5$

Explanation:

First solve with order of operations on each side:

$\displaystyle 13 + 27=12+3+ 5a$

$\displaystyle 40 = 15+5a$

Then subtract 15 from each side:

$\displaystyle 40-15=15+ 5a-15$

25=5a $\displaystyle 25=5a$

Finally, divide each side by 5:

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

5=a $\displaystyle 5=a$

The answer is 5.

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Example Question #211 : Algebraic Concepts

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

Possible Answers:

$\displaystyle 21$

$\displaystyle 25$

$\displaystyle 10$

$\displaystyle 15$

Correct answer:

$\displaystyle 21$

Explanation:

Solve inside the parentheses first:

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

Follow order of operations to solve:

$105 \div 5=21$ $\displaystyle 105 \div 5=21$

The answer is 21.

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Example Question #212 : 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:

$\displaystyle 4$

$\displaystyle 3$

$\displaystyle 6$

$\displaystyle 5$

Correct answer:

$\displaystyle 5$

Explanation:

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

$950\div 230=4.1$ $\displaystyle 950\div 230=4.1$

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 #213 : Algebraic Concepts

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

Possible Answers:

$\displaystyle 14$

$\displaystyle 4$

$\displaystyle 7$

$\displaystyle 28$

Correct answer:

$\displaystyle 4$

Explanation:

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

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

$\displaystyle 14a-18= 18+ 2(10)$

$\displaystyle 14a -18= 18+20$

$\displaystyle 14a-18=38$

Then, add 18 to each side:

$\displaystyle 14a - 18 +18= 38 +18$

14a=56 $\displaystyle 14a=56$

Finally, divide each side my 14:

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

a=4 $\displaystyle a=4$

The answer is 4.

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Example Question #214 : Algebraic Concepts

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

Possible Answers:

$1\frac{1}{2}$ $\displaystyle 1\frac{1}{2}$

$\frac{25}{39}$ $\displaystyle \frac{25}{39}$

$1\frac{3}{4}$ $\displaystyle 1\frac{3}{4}$

$\frac{117}{75}$ $\displaystyle \frac{117}{75}$

Correct answer:

$\frac{25}{39}$ $\displaystyle \frac{25}{39}$

Explanation:

First, convert each fraction into an improper fraction.

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

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

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

Reduce and multiply.

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

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All ISEE Middle Level Math Resources

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

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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 #2 : Equations

Example Question #3 : Equations

Example Question #1 : How To Find The Solution To An Equation

Example Question #2 : How To Find The Solution To An Equation

Example Question #1 : Equations

Example Question #1 : How To Find The Solution To An Equation

Example Question #211 : Algebraic Concepts

Example Question #212 : Algebraic Concepts

Example Question #213 : Algebraic Concepts

Example Question #214 : Algebraic Concepts

All ISEE Middle Level Math Resources

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