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Common Core: 8th Grade Math : Expressions & Equations

Study concepts, example questions & explanations for Common Core: 8th Grade Math

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All Common Core: 8th Grade Math Resources

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Example Questions

Example Question #61 : Expressions & Equations

Solve and leave your answer in scientific notation:

$(3\times10^7)\times(3\times10^4)$

Possible Answers:

$6\times10^{11}$

$9\times10^{11}$

$6\times10^{28}$

Correct answer:

$9\times10^{11}$

Explanation:

The first step to solving this problem is to combine like terms:

$(3\times3)\times(10^7\times10^4)$

Next, we can solve our two separate multiplication problems starting with the expression on the left:

$3\times3=9$

In order to solve the next expression, we need to recall our exponent rules from a previous lesson:

$10^7\times10^4$

When our base numbers are equal to each other, like in this problem, we can add our exponents together using the following formula:

$a^m\times a^n=a^{(m+n)}$

Let's apply this rule to our problem:

$10^{7}\times 10^{4}=10^{(7+4)}$

$10^7\times10^4=10^{11}$

The question asked us to leave our answer in scientific notation; thus, $9\times10^{11}$ is the correct answer.

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Example Question #62 : Expressions & Equations

Solve and leave your answer in scientific notation:

$(9\times10^2)\times(1\times10^4)$

Possible Answers:

$9\times10^6$

$10\times10^8$

$9\times10^8$

$10\times10^6$

Correct answer:

$9\times10^6$

Explanation:

The first step to solving this problem is to combine like terms:

$(9\times1)\times(10^2\times10^4)$

Next, we can solve our two separate multiplication problems starting with the expression on the left:

$9\times1=9$

In order to solve the next expression, we need to recall our exponent rules from a previous lesson:

$10^2\times10^4$

When our base numbers are equal to each other, like in this problem, we can add our exponents together using the following formula:

$a^m\times a^n=a^{(m+n)}$

Let's apply this rule to our problem:

$10^{2}\times 10^{4}=10^{(2+4)}$

$10^2\times10^4=10^6$

The question asked us to leave our answer in scientific notation; thus, $9\times10^6$ is the correct answer.

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Example Question #63 : Expressions & Equations

Solve and leave your answer in scientific notation:

$(4\times10^3)\times(2\times10^8)$

Possible Answers:

$8\times10^{5}$

$8\times10^{11}$

$6\times10^{11}$

Correct answer:

$8\times10^{11}$

Explanation:

The first step to solving this problem is to combine like terms:

$(4\times2)\times(10^3\times10^8)$

Next, we can solve our two separate multiplication problems starting with the expression on the left:

$4\times2=8$

In order to solve the next expression, we need to recall our exponent rules from a previous lesson:

$10^3\times10^8$

When our base numbers are equal to each other, like in this problem, we can add our exponents together using the following formula:

$a^m\times a^n=a^{(m+n)}$

Let's apply this rule to our problem:

$10^{3}\times 10^{8}=10^{(3+8)}$

$10^3\times10^8=10^{11}$

The question asked us to leave our answer in scientific notation; thus, $8\times10^{11}$ is the correct answer.

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Example Question #64 : Expressions & Equations

Solve and leave your answer in scientific notation:

$(3\times10^2)\times(2\times10^2)$

Possible Answers:

$6\times10^4$

$5\times10^4$

$5\times10^2$

Correct answer:

$6\times10^4$

Explanation:

The first step to solving this problem is to combine like terms:

$(3\times2)\times(10^2\times10^2)$

Next, we can solve our two separate multiplication problems starting with the expression on the left:

$3\times2=6$

In order to solve the next expression, we need to recall our exponent rules from a previous lesson:

$10^2\times10^2$

When our base numbers are equal to each other, like in this problem, we can add our exponents together using the following formula:

$a^m\times a^n=a^{(m+n)}$

Let's apply this rule to our problem:

$10^{2}\times 10^{2}=10^{(2+2)}$

$10^2\times10^2=10^4$

The question asked us to leave our answer in scientific notation; thus, $6\times10^4$ is the correct answer.

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Example Question #65 : Expressions & Equations

Solve and leave your answer in scientific notation:

$(2\times10^6)\times(4\times10^3)$

Possible Answers:

$6\times10^{18}$

$6\times10^9$

$8\times10^{18}$

$8\times10^9$

Correct answer:

$8\times10^9$

Explanation:

The first step to solving this problem is to combine like terms:

$(2\times4)\times(10^6\times10^3)$

Next, we can solve our two separate multiplication problems starting with the expression on the left:

$2\times4=8$

In order to solve the next expression, we need to recall our exponent rules from a previous lesson:

$10^6\times10^3$

When our base numbers are equal to each other, like in this problem, we can add our exponents together using the following formula:

$a^m\times a^n=a^{(m+n)}$

Let's apply this rule to our problem:

$10^{6}\times 10^{3}=10^{(6+3)}$

$10^6\times10^3=10^9$

The question asked us to leave our answer in scientific notation; thus, $8\times10^9$ is the correct answer.

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Example Question #63 : Expressions & Equations

What is the slope of the line that passes through the points (3,4) and (5,13) ?

Possible Answers:

-9/2

13/4

2/9

-4/3

9/2

Correct answer:

9/2

Explanation:

The slope of a line is sometimes referred to as "rise over run." This is because the formula for slope is the change in y-value (rise) divided by the change in x-value (run). Therefore, if you are given two points, $(x_{1},y_{1})$ and $(x_{2},y_{2})$ , the slope of their line can be found using the following formula: $slope=(y_{1}-y_{2})/(x_{1}-x_{2})$

This gives us (13-4)/(5-3)=9/2 .

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Example Question #1 : Graph Proportional Relationships, Interpreting The Unit Rate As The Slope: Ccss.Math.Content.8.Ee.B.5

Given points (1,2) and (-1,3) , what is the slope of the line connecting them?

Possible Answers:

$-\frac{1}{2}$

$\frac{1}{2}$

$-\frac{1}{4}$

Correct answer:

$-\frac{1}{2}$

Explanation:

Write the slope formula. Plug in the points and solve.

$m= \frac{y_2-y_1}{x_2-x_1}= \frac{3-2}{-1-1}= -\frac{1}{2}$

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Example Question #2 : Graph Proportional Relationships, Interpreting The Unit Rate As The Slope: Ccss.Math.Content.8.Ee.B.5

What is the slope of the line connecting the points $(2,\sqrt2)$ and (1,2) ?

Possible Answers:

$\sqrt2 -2$

$-\sqrt2+1$

$-\sqrt2-2$

$2-\sqrt2$

$-1-\sqrt2$

Correct answer:

$\sqrt2 -2$

Explanation:

Write the slope formula. Plug in the point, and simplify.

$m=\frac{y_2-y_1}{x_2-x_1}= \frac{2-\sqrt2}{1-2}=\frac{2-\sqrt2}{-1}= -(2-\sqrt2) = \sqrt2-2$

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Example Question #66 : Expressions & Equations

What is the slope of a line with an -intercept is and another -intercept of ?

Possible Answers:

$\infty$

Correct answer:

Explanation:

The -intercept is the value when y=0 .

Therefore, since the two -intercepts are and , the points are (4,0) and (6,0) .

Write the slope formula, plug in the values, and solve.

$m=\frac{y_2-y_1}{x_2-x_1} = \frac{0-0}{6-4}= \frac{0}{2} =0$

The slope is zero.

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Example Question #1 : How To Find The Slope Of A Line

Given the points (4, 3) and (8, 9) , find the slope of the line.

Possible Answers:

$\frac{-3}{4}$

$\frac{2}{3}$

$\frac{3}{2}$

$\frac{-6}{4}$

$\frac{4}{3}$

Correct answer:

$\frac{3}{2}$

Explanation:

The formula for the slope of a line is $\frac{y_2-y_1}{x_2-x_1}$ .

We then plug in the points given: $\frac{9-3}{8-4}=\frac{6}{4}$ which is then reduced to $\frac{3}{2}$ .

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All Common Core: 8th Grade Math Resources

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Common Core: 8th Grade Math : Expressions & Equations

Study concepts, example questions & explanations for Common Core: 8th Grade Math

All Common Core: 8th Grade Math Resources

Example Questions

Example Question #61 : Expressions & Equations

Example Question #62 : Expressions & Equations

Example Question #63 : Expressions & Equations

Example Question #64 : Expressions & Equations

Example Question #65 : Expressions & Equations

Example Question #63 : Expressions & Equations

Example Question #1 : Graph Proportional Relationships, Interpreting The Unit Rate As The Slope: Ccss.Math.Content.8.Ee.B.5

Example Question #2 : Graph Proportional Relationships, Interpreting The Unit Rate As The Slope: Ccss.Math.Content.8.Ee.B.5

Example Question #66 : Expressions & Equations

Example Question #1 : How To Find The Slope Of A Line

All Common Core: 8th Grade Math Resources

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