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6th Grade Math › Grade 6

Questions 1 - 10
1

Select the expression that is equal to

Explanation

To solve this problem we need to use the distributive property. This property is used to multiply a term outside of a set of parentheses by each of the terms in the parentheses.

Now we have

This expression is simplified because we cannot add to because has a variable attached to it.

2

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 in length and occupies an area of . How wide is this particular site?

Explanation

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

Substitute in the given values in the equation and solve for .

Divide both sides by

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

Find the reciprocal of

Simplify and rewrite.

Multiply and solve.

Reduce.

The width of the fracking site is

3

A large crate in the shape of a rectangular prism has dimensions 5 feet by 4 feet by 12 feet. Give its volume in cubic yards.

Explanation

Divide each dimension by 3 to convert feet to yards, then multiply the three dimensions together:

4

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

4

Explanation

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:

4

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

Substitute in our side lengths.

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 .

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

or

5

Select the expression that is equal to

Explanation

To solve this problem we need to use the distributive property. This property is used to multiply a term outside of a set of parentheses by each of the terms in the parentheses.

Now we have

This expression is simplified because we cannot add to because has a variable attached to it.

6

Select the expression that is equal to

Explanation

To solve this problem we need to use the distributive property. This property is used to multiply a term outside of a set of parentheses by each of the terms in the parentheses.

Now we have

This expression is simplified because we cannot add to because has a variable attached to it.

7

Solve:

Explanation

When we add with multi-digit numbers with decimals, we start with the numbers furthest to the right and work our way towards the left.

Add the numbers in the hundredths place:

Your work should look something like this:

Add the numbers in the tenths place:

Because this sum is greater than 9, we write the 1 from the ones place and carry the 1 from the tens place over to the left. Your work should look something like this:

Your work should look something like this:

*Notice that the decimal moves directly down when we are adding decimal numbers.

Add the numbers in the ones place including the one carried over:

Your work should look something like this:

Add the numbers in the tens place:

Your final answer should be:

8

Select the expression that is equal to

Explanation

To solve this problem we need to use the distributive property. This property is used to multiply a term outside of a set of parentheses by each of the terms in the parentheses.

Now we have

This expression is simplified because we cannot add to because has a variable attached to it.

9

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

4

Explanation

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:

4

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

Substitute in our side lengths.

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 .

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

or

10

On a particular November day, it is and sunny in Tucson, Arizona. On the eastern side of the United States, it is and sleeting in New Castle, Pennsylvania. How many degrees warmer is it in Tucson than New Castle?

Explanation

There are several ways that we could solve this problem. First, we can say that the temperature in New Castle is below zero and in Tucson it is above zero; therefore we can say:

Also, we can solve this problem by using a number line. New Castle’s temperature is units away from zero and Tucson’s is units away.

Temp1

We can see that Tucson is warmer than New Castle.

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