MAP 6th Grade Math - MAP 6th Grade Math

Card 0 of 48

Question

Find the range of this set of numbers:

Answer

First order the numbers from least to greatest:

Then subtract the smallest number from the largest number:

Answer:

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Question

Find the mean of the data set provided:

Answer

In order to answer this question correctly, we need to recall the definition of mean:

Mean: The mean of a data set is the average of the numbers in a data set.

In order to calculate the mean we must first add up all of the numbers in the data set:

Next, we need to divide by the number of addends, or the number of numbers in the data set:

$\frac{72}{15}=4.8$

The mean for this data set is

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Question

Find the median of the data set provided:

Answer

In order to answer this question correctly, we need to recall the definition of median:

Median: The median of a data set is the middle value, when the data set is ordered from least to greatest.

In order to find the median, we need to first organize the data from least to greatest:

Next, we can solve for the median by finding the middlemost number in our data:

$26,26,26,27,28,28,28,29,30,{\color{Red} 30,30},31,32,33,34,34,34,34,35,36$

The median for this data set is

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Question

What is the area of the right triangle in the following figure?

Answer

There are several different ways to solve for the area of a right triangle. In this lesson, we will transform the right triangle into a rectangle, use the the simpler formula for area of a rectangle to solve for the new figure's area, and divide this area in half in order to solve for the area of the original figure.

First, let's transform the triangle into a rectangle:

Second, let's remember that the formula for area of a rectangle is as follows:

$A=l\times w$

Substitute in our side lengths.

$A=13\times 9$

Last, notice that our triangle is exactly half the size of the rectangle that we made. This means that in order to solve for the area of the triangle we will need to take half of the area of the rectangle, or divide it by .

$117\div 2= 58.5\textup{ in}^2$

Thus, the area formula for a right triangle is as follows:

$A=\frac{1}{2}(l\times w)$ or $A=\frac{l\times w}{2}$

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Question

What is the volume of the rectangular prism in the following figure?

Answer

The formula used to find volume of a rectangular prism is as follows:

$A=l\times w\times h$

Substitute our side lengths:

$A=3\frac{1}{2}\times4\times10$

$A=140\textup{ cm}^3$

Remember, volume is always written with cubic units because volume is how many cubic units can fit inside of a figure.

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Question

Hydraulic fracturing is a process used by gas companies to rupture and collects pockets of gas trapped within pockets of shale rock. A particular shale fracking site is $\frac{1}{6}\textup{ miles}$ in length and occupies an area of $\frac{5}{8}\textup{ miles}^2$ . How wide is this particular site?

Answer

In order to solve this question, we need to first recall how to find the area of a rectangle.

$\text{Area}=\text{Length} \times \text{Width}$

Substitute in the given values in the equation and solve for $\text{Width}$ .

$\frac{5}{8}\ miles^2=\frac{1}{6}\ miles\times Width$

Divide both sides by $\frac{1}{6}\ miles$

$\frac{\frac{5}{8}\ miles^2}{\frac{1}{6}\ miles}=\frac{\frac{1}{6}\ miles \times Width}{\frac{1}{6}\ miles}$

Dividing by a fraction is the same as multiplying by its inverse or reciprocal.

Find the reciprocal of $\frac{1}{6}\ miles$

$\frac{1}{6}\ miles\rightarrow \frac{6}{1}\ miles$

Simplify and rewrite.

$Width=\frac{6}{1} \times \frac{5}{8}$

Multiply and solve.

$Width=\frac{30}{8}$

Reduce.

$Width=3\tfrac{3}{4}\ miles$

The width of the fracking site is $3\tfrac{3}{4}\ miles$

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Question

Candidate A receives votes for every vote that candidate B receives. At the end of the election candidate B has votes. How many votes did candidate A get?

Answer

In order to solve this problem we need to create a ratio with the given information. It says that for every votes cast for candidate A, candidate B got vote. We can write the following ratio.

$A:B\rightarrow\frac{A}{B}$

Now substitute in the given numbers.

$3:1\rightarrow \frac{3}{1}$

We know that candidate B received votes. Write a new ratio.

$A:900\rightarrow\frac{A}{900}$

Now, use the original relationship to create a proportion and solve for the number of votes that candidate A received.

$\frac{3}{1}=\frac{A}{900}$

Cross multiply and solve for .

Simplify and solve.

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Question

Use the distributive property to express the sum as the multiple of a sum of two whole numbers with no common factor.

Answer

The distributive property can be used to rewrite an expression. When we use this property we will identify and pull out the greatest common factor of each of the addends. Then we can create a quantity that represents the sum of two whole numbers with no common factor multiplied by their greatest common factor.

In this case, the greatest common factor shared by each number is:

$\text{GCF}=4$

After we reduce each addend by the greatest common factor we can rewrite the expression:

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Question

Which value for would make the inequality below true?

Answer

We can use substitution to determine which value of makes the inequality true.

$54>8\textup { TRUE}$

$54>10\textup{ TRUE}$

$54>12\textup { TRUE}$

$54>14\textup { TRUE}$

Because we are looking for a value of that makes the expression less than , all of our choices are correct.

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Question

Find the range of this set of numbers:

Answer

First order the numbers from least to greatest:

Then subtract the smallest number from the largest number:

Answer:

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Question

Find the mean of the data set provided:

Answer

In order to answer this question correctly, we need to recall the definition of mean:

Mean: The mean of a data set is the average of the numbers in a data set.

In order to calculate the mean we must first add up all of the numbers in the data set:

Next, we need to divide by the number of addends, or the number of numbers in the data set:

$\frac{72}{15}=4.8$

The mean for this data set is

Compare your answer with the correct one above

Question

Find the median of the data set provided:

Answer

In order to answer this question correctly, we need to recall the definition of median:

Median: The median of a data set is the middle value, when the data set is ordered from least to greatest.

In order to find the median, we need to first organize the data from least to greatest:

Next, we can solve for the median by finding the middlemost number in our data:

$26,26,26,27,28,28,28,29,30,{\color{Red} 30,30},31,32,33,34,34,34,34,35,36$

The median for this data set is

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Question

What is the area of the right triangle in the following figure?

Answer

There are several different ways to solve for the area of a right triangle. In this lesson, we will transform the right triangle into a rectangle, use the the simpler formula for area of a rectangle to solve for the new figure's area, and divide this area in half in order to solve for the area of the original figure.

First, let's transform the triangle into a rectangle:

Second, let's remember that the formula for area of a rectangle is as follows:

$A=l\times w$

Substitute in our side lengths.

$A=13\times 9$

Last, notice that our triangle is exactly half the size of the rectangle that we made. This means that in order to solve for the area of the triangle we will need to take half of the area of the rectangle, or divide it by .

$117\div 2= 58.5\textup{ in}^2$

Thus, the area formula for a right triangle is as follows:

$A=\frac{1}{2}(l\times w)$ or $A=\frac{l\times w}{2}$

Compare your answer with the correct one above

Question

What is the volume of the rectangular prism in the following figure?

Answer

The formula used to find volume of a rectangular prism is as follows:

$A=l\times w\times h$

Substitute our side lengths:

$A=3\frac{1}{2}\times4\times10$

$A=140\textup{ cm}^3$

Remember, volume is always written with cubic units because volume is how many cubic units can fit inside of a figure.

Compare your answer with the correct one above

Question

Hydraulic fracturing is a process used by gas companies to rupture and collects pockets of gas trapped within pockets of shale rock. A particular shale fracking site is $\frac{1}{6}\textup{ miles}$ in length and occupies an area of $\frac{5}{8}\textup{ miles}^2$ . How wide is this particular site?

Answer

In order to solve this question, we need to first recall how to find the area of a rectangle.

$\text{Area}=\text{Length} \times \text{Width}$

Substitute in the given values in the equation and solve for $\text{Width}$ .

$\frac{5}{8}\ miles^2=\frac{1}{6}\ miles\times Width$

Divide both sides by $\frac{1}{6}\ miles$

$\frac{\frac{5}{8}\ miles^2}{\frac{1}{6}\ miles}=\frac{\frac{1}{6}\ miles \times Width}{\frac{1}{6}\ miles}$

Dividing by a fraction is the same as multiplying by its inverse or reciprocal.

Find the reciprocal of $\frac{1}{6}\ miles$

$\frac{1}{6}\ miles\rightarrow \frac{6}{1}\ miles$

Simplify and rewrite.

$Width=\frac{6}{1} \times \frac{5}{8}$

Multiply and solve.

$Width=\frac{30}{8}$

Reduce.

$Width=3\tfrac{3}{4}\ miles$

The width of the fracking site is $3\tfrac{3}{4}\ miles$

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Question

What is the area of the right triangle in the following figure?

Answer

There are several different ways to solve for the area of a right triangle. In this lesson, we will transform the right triangle into a rectangle, use the the simpler formula for area of a rectangle to solve for the new figure's area, and divide this area in half in order to solve for the area of the original figure.

First, let's transform the triangle into a rectangle:

Second, let's remember that the formula for area of a rectangle is as follows:

$A=l\times w$

Substitute in our side lengths.

$A=13\times 9$

Last, notice that our triangle is exactly half the size of the rectangle that we made. This means that in order to solve for the area of the triangle we will need to take half of the area of the rectangle, or divide it by .

$117\div 2= 58.5\textup{ in}^2$

Thus, the area formula for a right triangle is as follows:

$A=\frac{1}{2}(l\times w)$ or $A=\frac{l\times w}{2}$

Compare your answer with the correct one above

Question

What is the volume of the rectangular prism in the following figure?

Answer

The formula used to find volume of a rectangular prism is as follows:

$A=l\times w\times h$

Substitute our side lengths:

$A=3\frac{1}{2}\times4\times10$

$A=140\textup{ cm}^3$

Remember, volume is always written with cubic units because volume is how many cubic units can fit inside of a figure.

Compare your answer with the correct one above

Question

Hydraulic fracturing is a process used by gas companies to rupture and collects pockets of gas trapped within pockets of shale rock. A particular shale fracking site is $\frac{1}{6}\textup{ miles}$ in length and occupies an area of $\frac{5}{8}\textup{ miles}^2$ . How wide is this particular site?

Answer

In order to solve this question, we need to first recall how to find the area of a rectangle.

$\text{Area}=\text{Length} \times \text{Width}$

Substitute in the given values in the equation and solve for $\text{Width}$ .

$\frac{5}{8}\ miles^2=\frac{1}{6}\ miles\times Width$

Divide both sides by $\frac{1}{6}\ miles$

$\frac{\frac{5}{8}\ miles^2}{\frac{1}{6}\ miles}=\frac{\frac{1}{6}\ miles \times Width}{\frac{1}{6}\ miles}$

Dividing by a fraction is the same as multiplying by its inverse or reciprocal.

Find the reciprocal of $\frac{1}{6}\ miles$

$\frac{1}{6}\ miles\rightarrow \frac{6}{1}\ miles$

Simplify and rewrite.

$Width=\frac{6}{1} \times \frac{5}{8}$

Multiply and solve.

$Width=\frac{30}{8}$

Reduce.

$Width=3\tfrac{3}{4}\ miles$

The width of the fracking site is $3\tfrac{3}{4}\ miles$

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Question

Find the range of this set of numbers:

Answer

First order the numbers from least to greatest:

Then subtract the smallest number from the largest number:

Answer:

Compare your answer with the correct one above

Question

Find the mean of the data set provided:

Answer

In order to answer this question correctly, we need to recall the definition of mean:

Mean: The mean of a data set is the average of the numbers in a data set.

In order to calculate the mean we must first add up all of the numbers in the data set:

Next, we need to divide by the number of addends, or the number of numbers in the data set:

$\frac{72}{15}=4.8$

The mean for this data set is

Compare your answer with the correct one above

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