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Common Core: 6th Grade Math : The Number System

Study concepts, example questions & explanations for Common Core: 6th Grade Math

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All Common Core: 6th Grade Math Resources

6 Diagnostic Tests 186 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #75 : Adding Multi Digit Decimals

Solve:

$\begin{array}{r}\overset{\ ~}{1} \overset{\ ~}{4.}\overset{\ ~}{0}0\\ + \overset{\ ~ }{1}\overset{\ ~ }{7.}\overset{ }{1} \overset{~\ }{0} \\ \hline \end{array}$

Possible Answers:

57.55

30.05

31.1

11.86

Correct answer:

31.1

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:

{0+0=0}

Your work should look something like this:

$\begin{array}{r}\overset{\ ~}{1} \overset{\ ~}{4.}\overset{\ ~}{0}0\\ + \overset{\ ~ }{1}\overset{\ ~ }{7.}\overset{ }{1} \overset{~\ }{0} \\ \hline \space{} \, \space{\, } \space{\, }0\end{array}$

Add the numbers in the tenths place:

{0+1=1}

Your work should look something like this:

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

$\begin{array}{r}\overset{\ ~}{1} \overset{\ ~}{4.}\overset{\ ~}{0}0\\ + \overset{\ ~ }{1}\overset{\ ~ }{7.}\overset{ }{1} \overset{~\ }{0} \\ \hline \space{} \, \space{\,. }1\space{\, }0\end{array}$

Add the numbers in the ones place:

{4+7+1=12}

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:

$\begin{array}{r}\overset{\ 1}{1} \overset{\ ~}{4.}\overset{\ ~}{0}0\\ + \overset{\ ~ }{1}\overset{\ ~ }{7.}\overset{ }{1} \overset{~\ }{0} \\ \hline \space{} \, 1\space{\,. }1\space{\, }0\end{array}$

Your final answer should be: 31.10

$\begin{array}{r}\overset{\ 1}{1} \overset{\ ~}{4.}\overset{\ ~}{0}0\\ + \overset{\ ~ }{1}\overset{\ ~ }{7.}\overset{ }{1} \overset{~\ }{0} \\ \hline 3\space{} \, 1\space{\,. }1\space{\, }0\end{array}$

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Example Question #76 : Adding Multi Digit Decimals

Solve:

$\begin{array}{r}\overset{\ ~}{2} \overset{\ ~}{6.}\overset{\ ~}{1}6\\ + \overset{\ ~ }{3}\overset{\ ~ }{6.}\overset{ }{8} \overset{~\ }{8} \\ \hline \end{array}$

Possible Answers:

63.04

15.57

47.79

55.81

Correct answer:

63.04

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:

{6+8=14}

Because this sum is greater than 9, we write the 4 from the ones place and carry the 1 from the tens place over to the left. Your work should look something like this:

$\begin{array}{r}\overset{\ ~}{2} \overset{\ ~}{6.}\overset{\ 1}{1}6\\ + \overset{\ ~ }{3}\overset{\ ~ }{6.}\overset{ }{8} \overset{~\ }{8} \\ \hline \space{} \, \space{\, } \space{\, }4\end{array}$

Add the numbers in the tenths place:

{1+8+1=9}

Because this sum is greater than 9, we write the 0 from the ones place and carry the 1 from the tens place over to the left. Your work should look something like this:

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

$\begin{array}{r}\overset{\ ~}{2} \overset{\ 1}{6.}\overset{\ 1}{1}6\\ + \overset{\ ~ }{3}\overset{\ ~ }{6.}\overset{ }{8} \overset{~\ }{8} \\ \hline \space{} \, \space{\,. }0\space{\, }4\end{array}$

Add the numbers in the ones place:

{6+6+1=13}

Because this sum is greater than 9, we write the 2 from the ones place and carry the 1 from the tens place over to the left. Your work should look something like this:

$\begin{array}{r}\overset{\ 1}{2} \overset{\ 1}{6.}\overset{\ 1}{1}6\\ + \overset{\ ~ }{3}\overset{\ ~ }{6.}\overset{ }{8} \overset{~\ }{8} \\ \hline \space{} \, 3\space{\,. }0\space{\, }4\end{array}$

Your final answer should be: 63.04

$\begin{array}{r}\overset{\ 1}{2} \overset{\ 1}{6.}\overset{\ 1}{1}6\\ + \overset{\ ~ }{3}\overset{\ ~ }{6.}\overset{ }{8} \overset{~\ }{8} \\ \hline 6\space{} \, 3\space{\,. }0\space{\, }4\end{array}$

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Example Question #77 : Adding Multi Digit Decimals

Solve:

$\begin{array}{r}\overset{\ ~}{2} \overset{\ ~}{0.}\overset{\ ~}{1}1\\ + \overset{\ ~ }{2}\overset{\ ~ }{5.}\overset{ }{4} \overset{~\ }{6} \\ \hline \end{array}$

Possible Answers:

24.71

45.57

10.22

56.56

Correct answer:

45.57

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:

{1+6=7}

Your work should look something like this:

$\begin{array}{r}\overset{\ ~}{2} \overset{\ ~}{0.}\overset{\ ~}{1}1\\ + \overset{\ ~ }{2}\overset{\ ~ }{5.}\overset{ }{4} \overset{~\ }{6} \\ \hline \space{} \, \space{\, } \space{\, }7\end{array}$

Add the numbers in the tenths place:

{1+4=5}

Your work should look something like this:

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

$\begin{array}{r}\overset{\ ~}{2} \overset{\ ~}{0.}\overset{\ ~}{1}1\\ + \overset{\ ~ }{2}\overset{\ ~ }{5.}\overset{ }{4} \overset{~\ }{6} \\ \hline \space{} \, \space{\,. }5\space{\, }7\end{array}$

Add the numbers in the ones place:

{0+5=5}

Your work should look something like this:

$\begin{array}{r}\overset{\ ~}{2} \overset{\ ~}{0.}\overset{\ ~}{1}1\\ + \overset{\ ~ }{2}\overset{\ ~ }{5.}\overset{ }{4} \overset{~\ }{6} \\ \hline \space{} \, 5\space{\,. }5\space{\, }7\end{array}$

Your final answer should be: 45.57

$\begin{array}{r}\overset{\ ~}{2} \overset{\ ~}{0.}\overset{\ ~}{1}1\\ + \overset{\ ~ }{2}\overset{\ ~ }{5.}\overset{ }{4} \overset{~\ }{6} \\ \hline 4\space{} \, 5\space{\,. }5\space{\, }7\end{array}$

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Example Question #1 : Subtracting Multi Digit Decimals

Find the difference.

7.26-5.83=

Possible Answers:

1.43

2.43

1.53

1.33

1.48

Correct answer:

1.43

Explanation:

Finding a difference means to subtract.

In the hundredths column, we can easily subtract 6-3=3 .

In the tenths column we must borrow from the 7 (making it 6) and also making the 2 a 12. Now we can subtract 12-8=4 .

Finally in the ones column we can subtract 6-5=1 .

Thus the final answer is 1.43.

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Example Question #141 : Fluently Add, Subtract, Multiply, And Divide Multi Digit Decimals: Ccss.Math.Content.6.Ns.B.3

Elliot bought coffee drinks from a famous coffee shop. The first two drinks cost him $\$8.91$ and he paid a total of $\$12.35$ . How much did the third drink cost?

Possible Answers:

$\$4.36$

$\$3.23$

$\$2.78$

$\$3.44$

Correct answer:

$\$3.44$

Explanation:

To find the cost of the third drink, you must subtract the total cost by the cost of the two drinks.

$$12.35 - $8.91 = \$3.44$

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Example Question #1 : Subtracting Multi Digit Decimals

5.89 - 3.98 =

Possible Answers:

2.10

1.89

2.01

1.91

Correct answer:

1.91

Explanation:

5.89 - 3.98 =

We first subtract the hundredths place: 9-8 = 1

Then the tenths place: Since is less than , we have to borrow from the , the becomes a and the becomes : 18 - 9 = 9

Then the ones place: 4-3 = 1

So the final answer is 1.91 .

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Example Question #2 : Subtracting Multi Digit Decimals

11.85 - 8.94 =

Possible Answers:

2.87

3.01

2.91

2.85

Correct answer:

2.91

Explanation:

11.85 - 8.94 =

We first subtract the hundredths place: 5 - 4 = 1

Then the tenths place: Since is less than , we have to borrow from the , the becomes a and the becomes : 18 - 9 = 9

Then the ones place: 0-8 , since the is less than , we have to borrow from the , the becomes is the tens place, and the becomes in the ones place:

10-8 = 2

So the final answer is 2.91 .

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Example Question #1 : Problem Solving

What is 3.2-0.2 ?

Possible Answers:

1.0

2.0

3.0

1.2

3.4

Correct answer:

3.0

Explanation:

0.2 removed from 3.2 results in the whole integer 3.0 .

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Example Question #2 : Problem Solving

Subtract: 1-0.009

Possible Answers:

0.0091

0.0991

0.991

0.9991

0.91

Correct answer:

0.991

Explanation:

Rewrite 1-0.009 adding the correct number of placeholders and evaluate.

1.000-0.009=0.991

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Example Question #4 : Subtracting Multi Digit Decimals

Menu 1

The above is a menu at the concession stand at a drive-in movie. The stand also offers a special "Meal Deal": a hamburger or a hot dog, a medium order of fries, and a medium soda for $\$ 8$ .

Randy orders two Meal Deals - a hamburger Meal Deal for himself and a hot dog Meal Deal for his friend Denise. How much more would he have paid for the items separately?

(Ignore tax)

Possible Answers:

$\$3.24$

$\$1.74$

$\$2.74$

$\$2.24$

Correct answer:

$\$2.24$

Explanation:

The two Meal Deals cost $\$ 8 \times 2 = \$16$ .

Purchased separately, the hamburger would have cost $4.89; the hot dog, $4.39; each of the two medium orders of fries, $2.79; and each of the two medium sodas, $1.69. The total price of the items, purchased separately, would have been

$\$4.89$

4.39

2.79

1.69

$\underline{1.69}$

$\$18.24$

The difference between this and the $16 paid for the food is

$\$18.24 - \$16 .00 = \$2.24$

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Common Core: 6th Grade Math : The Number System

Study concepts, example questions & explanations for Common Core: 6th Grade Math

All Common Core: 6th Grade Math Resources

Example Questions

Example Question #75 : Adding Multi Digit Decimals

Example Question #76 : Adding Multi Digit Decimals

Example Question #77 : Adding Multi Digit Decimals

Example Question #1 : Subtracting Multi Digit Decimals

Example Question #141 : Fluently Add, Subtract, Multiply, And Divide Multi Digit Decimals: Ccss.Math.Content.6.Ns.B.3

Example Question #1 : Subtracting Multi Digit Decimals

Example Question #2 : Subtracting Multi Digit Decimals

Example Question #1 : Problem Solving

Example Question #2 : Problem Solving

Example Question #4 : Subtracting Multi Digit Decimals

All Common Core: 6th Grade Math Resources

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