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6th Grade Math › Grade 6

Questions 1 - 10

On a particular November day, it is $65^\circ F$ and sunny in Tucson, Arizona. On the eastern side of the United States, it is $-23^\circ F$ and sleeting in New Castle, Pennsylvania. How many degrees warmer is it in Tucson than New Castle?

$88^\circ F$

$87^\circ F$

$78^\circ F$

$98^\circ F$

$97^\circ F$

Explanation

There are several ways that we could solve this problem. First, we can say that the temperature in New Castle is $23^\circ F$ below zero and in Tucson it is $65^\circ F$ above zero; therefore we can say:

$23+65=88^\circ F$

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 $88^\circ F$ warmer than New Castle.

Menu 1

The above is a menu at the concession stand at a drive-in movie.

Gary wants to order two hamburgers and two small orders of fries. He wants to order two sodas of the same size. If he has just a twenty-dollar bill on hand, what is the largest size soda of which he can order two?

Gary can afford two large sodas

Gary can afford two medium sodas, but not two large sodas

Gary can afford two small sodas, but not two medium or large sodas

Gary cannot afford two sodas

Explanation

The easiest way to think of this is to note that Gary seems to be ordering for two people, himself and a friend. He has $20, so half of this will be for himself and half for his friend - and half of $20 is $10.

Each hamburger costs $4.89, and each small order of fries costs $2.29. This leaves

$\$10 - ($4.89 + $2.29) = $10 - $7.18 = \$2.82$

to spend on a soda for each person. This will enable to him to buy both himself and his friend a large soda.

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?

$3\tfrac{3}{4}\textup{ miles}$

$3\tfrac{1}{3}\textup{ miles}$

$4\tfrac{1}{4}\textup{ miles}$

$3\tfrac{5}{7}\textup{ miles}$

$5\tfrac{3}{4}\textup{ miles}$

Explanation

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

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.

$8 \frac{8}{9 } \textrm{ yd}^{3}$

$7 \frac{2}{9 } \textrm{ yd}^{3}$

$10 \textrm{ yd}^{3}$

$80 \textrm{ yd}^{3}$

$90\textrm{ yd}^{3}$

Explanation

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

$V = \frac{5}{3} \cdot \frac{4}{3} \cdot \frac{12}{3}$

$V = \frac{5}{3} \cdot \frac{4}{3} \cdot \frac{4}{1}$

$V = \frac{80}{9 } = 8 \frac{8}{9 } \textrm{ yd}^{3}$

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.

$6\times7=42$

$6\times x=6x$

Now we have

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

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.

$3\times8=24$

$3\times x=3x$

Now we have

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

Solve:

${0.84{\overline{\smash{)}1.59708}}}$

Explanation

The first thing that we want to do when dividing decimals is to turn the divisor into a whole number. We do this by moving the decimal place to the right:

${0.84\rightarrow 84}$

If we move the decimal over two places in the divisor, we must also move the decimal over two places in the dividend:

${1.59708\rightarrow 159.708}$

The new division problem should look as follows:

$\ \ \ \ .\84{\overline{\smash{)}159.708}}$

*Notice how we've already placed the decimal in our answer. When we divide decimals, we place the decimal directly above the decimal in the dividend, but only after we've completed the first two steps of moving the decimal point in the divisor and dividend.

Now we can divide like normal:

$\ \ \ \ .\84{\overline{\smash{)}159.708}}$

Think: how many times can 84 go into 159

84 can go into 159 one time times so we write a 1 over the 9 in the dividend:

$\begin{array}{rl} \underline{ \phantom{000} 1.~\phantom{~~0} } \[-3pt]84\ )159.708\ \end{array}$

Next, we multiply 1 and 84 and write that product underneath the 159 and subtract:

$\begin{array}{rl} \underline{ \phantom{000}1.~\phantom{~~0} } \[-3pt] 84) \ 159.708\ \underline{-84\phantom{~000}} \75\phantom{~000} \end{array}$

Now we bring down the 7 from the dividend to make the 75 into a 757.

Think: how many times can 84 go into 757?

84 can go into 757 nine times so we write a 9 above the 7 in the dividend:

$\begin{array}{rl} \underline{ \phantom{000}1.9\phantom{00} } \[-3pt]84) \ 159.708\ \underline{-84\phantom{~000}} \ 757\phantom{~00} \end{array}$

Next, we multiply 9 and 84 and write that product underneath the 757 and subtract:

$\begin{array}{rl} \underline{ \phantom{000}1.9 \phantom{00} } \[-3pt]84) \ 159.708 \ \underline{-84\phantom{~000}} \ 757 \phantom{~00} \ \underline{-756\phantom{~00}} \1\phantom{~00} \end{array}$

Now we bring down the 0 from the dividend to make the 1 into a 10.

Think: how many times can 84 go into 10?

84 can go into 10 zero so we write a 0 above the 0 in the dividend:

$\begin{array}{rl} \underline{ \phantom{000}1.90 \phantom{0} } \[-3pt]84) \ 159.708 \ \underline{-84\phantom{~000}} \ 757\phantom{~00} \ \underline{-756\phantom{~00}} \ 10 \phantom{~0} \end{array}$

Next, we multiply 0 and 84 and write that product underneath the 10 and subtract:

$\begin{array}{rl} \underline{ \phantom{000}1.90 \phantom{0} } \[-3pt]84) \ 159.708 \ \underline{-84\phantom{~000}} \ 757\phantom{~00} \ \underline{-756\phantom{~00}} \ 10 \phantom{~0} \ \underline{-0\phantom{~0}} \10 \phantom{~0} \end{array}$

Now we bring down the 8 from the dividend to make the 10 into a 108.

Think: how many times can 84 go into 108?

84 can go into 108 one time so we write a 1 above the 8 in the dividend:

$\begin{array}{rl} \underline{ \phantom{000}1.901 } \[-3pt]84) \ 159.708 \ \underline{-84\phantom{~000}} \ 757\phantom{~00} \ \underline{-756\phantom{~00}} \ 10 \phantom{~0} \ \underline{-0\phantom{~0}} \108 \phantom{~} \end{array}$

Next, we multiply 1 and 84 and write that product underneath the 108 and subtract:

Notice our remainder is 24 so our answer is 1.901R24.

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.

$12\times7=84$

$12\times x=12x$

Now we have

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

Select the description that best describes the distribution of the data shown in the provided dot plot.

Right skewed

Left skewed

Symmetric

Explanation

In order to answer this question correctly, we need to define our answer options:

Symmetric: A symmetric distribution will have a middle, or center, and each side from the middle will look fairly similar. Many symmetrical distributions are bell shaped, with the middle being tall, and the two sides thinning out.

Left skewed: A left skewed distribution will have most of the data on the right side of the number line.

Right skewed: A right skewed distribution will have most of the data on the left side of the number line.

The data shown in the number plot is mostly on the left side; thus, right skewed is the correct answer.

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.

$10\times4=40$