ISEE Middle Level Math : How to find the solution to an equation

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

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Example Questions

Example Question #526 : Algebraic Concepts

Multiply:

\(\displaystyle y^{99}*y^{11}=\)

Possible Answers:

\(\displaystyle y^{110}\)

\(\displaystyle y^{88}\)

\(\displaystyle 110\)

\(\displaystyle y^{100}\)

Correct answer:

\(\displaystyle y^{110}\)

Explanation:

To solve, add the exponents and leave the base the same:

\(\displaystyle y^{99}*y^{11}=y^{110}\)

Answer:

\(\displaystyle y^{110}\)

Example Question #527 : Algebraic Concepts

Which of the following phrases can be written as the algebraic expression \(\displaystyle 5 (75 - x )\)?

Possible Answers:

Five mutiplied by the difference of a number and seventy-five

Five mutiplied by the difference of seventy-five and a number

The product of five and a number subtracted from seventy-five

Seventy-five subtracted from the product of five and a number

The correct answer is not given among the other responses.

Correct answer:

Five mutiplied by the difference of seventy-five and a number

Explanation:

\(\displaystyle 5 (75 - x )\) is five multiplied by the expression \(\displaystyle 75-x\).

\(\displaystyle 75-x\) is the difference of seventy-five and a number.

Subsequently, \(\displaystyle 5 (75 - x )\) is "five multiplied by the difference of seventy-five and a number".

Example Question #528 : Algebraic Concepts

Which of the following statements demonstrates the inverse property of multiplication? 

Possible Answers:

\(\displaystyle 8.4 \times 5.3 = 5.3 \times 8.4\)

None of the other answer choices contain the correct response.

\(\displaystyle 8.4 \times 0 = 0\)

\(\displaystyle 8.4 \times 1 = 8.4\)

\(\displaystyle 8.4 \times\left ( 5.3 \times 4.8 \right )= \left (8.4 \times 5.3 \right ) \times 4.8\)

Correct answer:

None of the other answer choices contain the correct response.

Explanation:

The inverse property of multiplication states that for every real number, a number exists, called the multiplicative inverse, such that the number and its inverse have product 1. Of the statements given, none demonstrate this property.

Example Question #529 : Algebraic Concepts

\(\displaystyle 4^{3}*2^{3}=\)

Possible Answers:

\(\displaystyle 521\)

\(\displaystyle 512\)

\(\displaystyle 251\)

\(\displaystyle 215\)

Correct answer:

\(\displaystyle 512\)

Explanation:

First take care of the exponents:

\(\displaystyle 4^{3}=64\)

\(\displaystyle 2^{3}=8\)

Then multiply:

\(\displaystyle 64*8=512\)

Answer: \(\displaystyle 512\)

Example Question #321 : How To Find The Solution To An Equation

\(\displaystyle 5^{2}*7^{2}=\)

Possible Answers:

\(\displaystyle 1275\)

\(\displaystyle 1200\)

\(\displaystyle 1225\)

\(\displaystyle 1250\)

Correct answer:

\(\displaystyle 1225\)

Explanation:

First square both numbers:

\(\displaystyle 5^{2}=25\)

\(\displaystyle 7^{2}=49\)

Then multiply those squares together:

\(\displaystyle 25*49=1225\)

Answer: \(\displaystyle 1225\)

Example Question #322 : How To Find The Solution To An Equation

Solve for \(\displaystyle x\):

\(\displaystyle 5x=650\)

Possible Answers:

\(\displaystyle 165\)

\(\displaystyle 155\)

\(\displaystyle 130\)

\(\displaystyle 140\)

Correct answer:

\(\displaystyle 130\)

Explanation:

To solve, divide by 5 on each side:

\(\displaystyle 5x\div 5=650\div 5\)

\(\displaystyle x=130\)

Answer: \(\displaystyle 130\)

Example Question #323 : How To Find The Solution To An Equation

Solve for \(\displaystyle t\):

\(\displaystyle 12t=540\)

Possible Answers:

\(\displaystyle 54\)

\(\displaystyle 528\)

\(\displaystyle 552\)

\(\displaystyle 45\)

Correct answer:

\(\displaystyle 45\)

Explanation:

To solve, divide by 12 on each side:

\(\displaystyle 12t\div 12=540\div 12\)

\(\displaystyle t=45\)

Answer: \(\displaystyle 45\)

Example Question #324 : How To Find The Solution To An Equation

 

\(\displaystyle \sqrt{144}*\sqrt{81}=\)

Possible Answers:

\(\displaystyle 111\)

\(\displaystyle 109\)

\(\displaystyle 108\)

\(\displaystyle 110\)

Correct answer:

\(\displaystyle 108\)

Explanation:

First take the square roots:

\(\displaystyle \sqrt{144}=12\)

\(\displaystyle \sqrt{81}=9\)

Then multiply:

\(\displaystyle 12*9=108\)

Answer: \(\displaystyle 108\)

Example Question #325 : How To Find The Solution To An Equation

 

\(\displaystyle \sqrt{64}*\sqrt{169}=\)

Possible Answers:

\(\displaystyle 105\)

\(\displaystyle 104\)

\(\displaystyle 102\)

\(\displaystyle 103\)

Correct answer:

\(\displaystyle 104\)

Explanation:

First, find the square roots:

\(\displaystyle \sqrt{64}=8\)

\(\displaystyle \sqrt{169}=13\)

Then multiply those square roots together:

\(\displaystyle 8*13=104\)

Answer: \(\displaystyle 104\)

 

Example Question #2652 : Isee Middle Level (Grades 7 8) Mathematics Achievement

If \(\displaystyle f=4x+1\) and \(\displaystyle x=3\), then what is the value of the expression below?

\(\displaystyle 3f+9\cdot \frac{4}{3} \right\)

 

Possible Answers:

\(\displaystyle 41\)

\(\displaystyle 61\)

\(\displaystyle 51\)

\(\displaystyle 39\)

Correct answer:

\(\displaystyle 51\)

Explanation:

If \(\displaystyle f=4x+1\) and \(\displaystyle x=3\) and we need to solve for \(\displaystyle f\), the first step is to plug \(\displaystyle 3\) in for \(\displaystyle x\). This results in:

 \(\displaystyle f=4\cdot 3+1\)

\(\displaystyle f=12+1\)

\(\displaystyle f=13\)

Now that we know that \(\displaystyle f=13\), we can plug \(\displaystyle 13\) in for \(\displaystyle f\) into the expression below:

\(\displaystyle 3f+9\cdot \frac{4}{3} \right\)

\(\displaystyle 3\cdot13+\frac{36}{3}\)

\(\displaystyle 39+12\)

\(\displaystyle 51\)

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