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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 #25 : Adding Multi Digit Decimals

Solve:

$\begin{array}{r}\overset{\ ~}{2} \overset{\ ~}{6.}\overset{\ ~}{6}1\\ + \overset{\ ~ }{1}\overset{\ ~ }{3.}\overset{ }{4} \overset{~\ }{5} \\ \hline \end{array}$

Possible Answers:

56.84

34.07

13.33

40.06

Correct answer:

40.06

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+5=6}

Your work should look something like this:

$\begin{array}{r}\overset{\ ~}{2} \overset{\ ~}{6.}\overset{\ ~}{6}1\\ + \overset{\ ~ }{1}\overset{\ ~ }{3.}\overset{ }{4} \overset{~\ }{5} \\ \hline \space{} \, \space{\, } \space{\, }6\end{array}$

Add the numbers in the tenths place:

{6+4=10}

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:

Your work should look something like this:

$\begin{array}{r}\overset{\ ~}{2} \overset{\ 1}{6.}\overset{\ ~}{6}1\\ + \overset{\ ~ }{1}\overset{\ ~ }{3.}\overset{ }{4} \overset{~\ }{5} \\ \hline \space{} \, \space{\,. }0\space{\, }6\end{array}$

Add the numbers in the ones place:

{6+3+1=10}

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:

$\begin{array}{r}\overset{\ 1}{2} \overset{\ 1}{6.}\overset{\ ~}{6}1\\ + \overset{\ ~ }{1}\overset{\ ~ }{3.}\overset{ }{4} \overset{~\ }{5} \\ \hline \space{} \, 0\space{\,. }0\space{\, }6\end{array}$

Your final answer should be: 40.06

$\begin{array}{r}\overset{\ 1}{2} \overset{\ 1}{6.}\overset{\ ~}{6}1\\ + \overset{\ ~ }{1}\overset{\ ~ }{3.}\overset{ }{4} \overset{~\ }{5} \\ \hline 4\space{} \, 0\space{\,. }0\space{\, }6\end{array}$

Report an Error

Example Question #26 : Adding Multi Digit Decimals

Solve:

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

Possible Answers:

26.33

46.42

25.44

52.59

Correct answer:

46.42

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:

{2+0=2}

Your work should look something like this:

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

Add the numbers in the tenths place:

{0+4=4}

Your work should look something like this:

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

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

Add the numbers in the ones place:

{6+0=6}

Your work should look something like this:

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

Your final answer should be: 46.42

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

Report an Error

Example Question #85 : Fluently Add, Subtract, Multiply, And Divide Multi Digit Decimals: Ccss.Math.Content.6.Ns.B.3

Solve:

$\begin{array}{r}\overset{\ ~}{1} \overset{\ ~}{2.}\overset{\ ~}{4}1\\ + \overset{\ ~ }{4}\overset{\ ~ }{8.}\overset{ }{7} \overset{~\ }{6} \\ \hline \end{array}$

Possible Answers:

15.67

48.82

61.17

35.32

Correct answer:

61.17

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:

$\begin{array}{r}\overset{\ ~}{1} \overset{\ ~}{2.}\overset{\ ~}{4}1\\ + \overset{\ ~ }{4}\overset{\ ~ }{8.}\overset{ }{7} \overset{~\ }{6} \\ \hline \space{} \, \space{\, } \space{\, }7\end{array}$

Add the numbers in the tenths place:

{4+7=11}

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:

$\begin{array}{r}\overset{\ ~}{1} \overset{\ 1}{2.}\overset{\ ~}{4}1\\ + \overset{\ ~ }{4}\overset{\ ~ }{8.}\overset{ }{7} \overset{~\ }{6} \\ \hline \space{} \, \space{\,. }1\space{\, }7\end{array}$

Add the numbers in the ones place:

{2+8+1=11}

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:

$\begin{array}{r}\overset{\ 1}{1} \overset{\ 1}{2.}\overset{\ ~}{4}1\\ + \overset{\ ~ }{4}\overset{\ ~ }{8.}\overset{ }{7} \overset{~\ }{6} \\ \hline \space{} \, 1\space{\,. }1\space{\, }7\end{array}$

Your final answer should be: 61.17

$\begin{array}{r}\overset{\ 1}{1} \overset{\ 1}{2.}\overset{\ ~}{4}1\\ + \overset{\ ~ }{4}\overset{\ ~ }{8.}\overset{ }{7} \overset{~\ }{6} \\ \hline 6\space{} \, 1\space{\,. }1\space{\, }7\end{array}$

Report an Error

Example Question #28 : Adding Multi Digit Decimals

Solve:

$\begin{array}{r}\overset{\ ~}{4} \overset{\ ~}{6.}\overset{\ ~}{0}1\\ + \overset{\ ~ }{3}\overset{\ ~ }{4.}\overset{ }{6} \overset{~\ }{5} \\ \hline \end{array}$

Possible Answers:

80.66

45.34

19.38

19.14

Correct answer:

80.66

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+5=6}

Your work should look something like this:

$\begin{array}{r}\overset{\ ~}{4} \overset{\ ~}{6.}\overset{\ ~}{0}1\\ + \overset{\ ~ }{3}\overset{\ ~ }{4.}\overset{ }{6} \overset{~\ }{5} \\ \hline \space{} \, \space{\, } \space{\, }6\end{array}$

Add the numbers in the tenths place:

{0+6=6}

Your work should look something like this:

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

$\begin{array}{r}\overset{\ ~}{4} \overset{\ ~}{6.}\overset{\ ~}{0}1\\ + \overset{\ ~ }{3}\overset{\ ~ }{4.}\overset{ }{6} \overset{~\ }{5} \\ \hline \space{} \, \space{\,. }6\space{\, }6\end{array}$

Add the numbers in the ones place:

{6+4+1=11}

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:

$\begin{array}{r}\overset{\ 1}{4} \overset{\ ~}{6.}\overset{\ ~}{0}1\\ + \overset{\ ~ }{3}\overset{\ ~ }{4.}\overset{ }{6} \overset{~\ }{5} \\ \hline \space{} \, 0\space{\,. }6\space{\, }6\end{array}$

Your final answer should be: 80.66

$\begin{array}{r}\overset{\ 1}{4} \overset{\ ~}{6.}\overset{\ ~}{0}1\\ + \overset{\ ~ }{3}\overset{\ ~ }{4.}\overset{ }{6} \overset{~\ }{5} \\ \hline 8\space{} \, 0\space{\,. }6\space{\, }6\end{array}$

Report an Error

Example Question #21 : Adding Multi Digit Decimals

Solve:

$\begin{array}{r}\overset{\ ~}{3} \overset{\ ~}{3.}\overset{\ ~}{0}6\\ + \overset{\ ~ }{4}\overset{\ ~ }{5.}\overset{ }{4} \overset{~\ }{7} \\ \hline \end{array}$

Possible Answers:

58.82

78.53

15.65

26.63

Correct answer:

78.53

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+7=13}

Because this sum is greater than 9, we write the 3 from the ones place and carry the 1 from the tens place over to the left. Your work should look something like this:

$\begin{array}{r}\overset{\ ~}{3} \overset{\ ~}{3.}\overset{\ 1}{0}6\\ + \overset{\ ~ }{4}\overset{\ ~ }{5.}\overset{ }{4} \overset{~\ }{7} \\ \hline \space{} \, \space{\, } \space{\, }3\end{array}$

Add the numbers in the tenths place:

{0+4+1=5}

Your work should look something like this:

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

$\begin{array}{r}\overset{\ ~}{3} \overset{\ ~}{3.}\overset{\ 1}{0}6\\ + \overset{\ ~ }{4}\overset{\ ~ }{5.}\overset{ }{4} \overset{~\ }{7} \\ \hline \space{} \, \space{\,. }5\space{\, }3\end{array}$

Add the numbers in the ones place:

{3+5=8}

Your work should look something like this:

$\begin{array}{r}\overset{\ ~}{3} \overset{\ ~}{3.}\overset{\ 1}{0}6\\ + \overset{\ ~ }{4}\overset{\ ~ }{5.}\overset{ }{4} \overset{~\ }{7} \\ \hline \space{} \, 8\space{\,. }5\space{\, }3\end{array}$

Your final answer should be: 78.53

$\begin{array}{r}\overset{\ ~}{3} \overset{\ ~}{3.}\overset{\ 1}{0}6\\ + \overset{\ ~ }{4}\overset{\ ~ }{5.}\overset{ }{4} \overset{~\ }{7} \\ \hline 7\space{} \, 8\space{\,. }5\space{\, }3\end{array}$

Report an Error

Example Question #22 : Adding Multi Digit Decimals

Solve:

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

Possible Answers:

59.06

51.79

20.84

37.84

Correct answer:

59.06

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:

{2+4=6}

Your work should look something like this:

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

Add the numbers in the tenths place:

{2+8=10}

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:

Your work should look something like this:

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

Add the numbers in the ones place:

{0+8+1=9}

Your work should look something like this:

$\begin{array}{r}\overset{\ ~}{3} \overset{\ 1}{0.}\overset{\ ~}{2}2\\ + \overset{\ ~ }{2}\overset{\ ~ }{8.}\overset{ }{8} \overset{~\ }{4} \\ \hline \space{} \, 9\space{\,. }0\space{\, }6\end{array}$

Your final answer should be: 59.06

$\begin{array}{r}\overset{\ ~}{3} \overset{\ 1}{0.}\overset{\ ~}{2}2\\ + \overset{\ ~ }{2}\overset{\ ~ }{8.}\overset{ }{8} \overset{~\ }{4} \\ \hline 5\space{} \, 9\space{\,. }0\space{\, }6\end{array}$

Report an Error

Example Question #31 : Adding Multi Digit Decimals

Solve:

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

Possible Answers:

65.46

57.45

51.83

47.78

Correct answer:

65.46

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:

{3+3=6}

Your work should look something like this:

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

Add the numbers in the tenths place:

{1+3=4}

Your work should look something like this:

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

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

Add the numbers in the ones place:

{4+1=5}

Your work should look something like this:

$\begin{array}{r}\overset{\ ~}{2} \overset{\ ~}{4.}\overset{\ ~}{1}3\\ + \overset{\ ~ }{4}\overset{\ ~ }{1.}\overset{ }{3} \overset{~\ }{3} \\ \hline \space{} \, 5\space{\,. }4\space{\, }6\end{array}$

Your final answer should be: 65.46

$\begin{array}{r}\overset{\ ~}{2} \overset{\ ~}{4.}\overset{\ ~}{1}3\\ + \overset{\ ~ }{4}\overset{\ ~ }{1.}\overset{ }{3} \overset{~\ }{3} \\ \hline 6\space{} \, 5\space{\,. }4\space{\, }6\end{array}$

Report an Error

Example Question #31 : Adding Multi Digit Decimals

Solve:

$\begin{array}{r}\overset{\ ~}{2} \overset{\ ~}{2.}\overset{\ ~}{5}0\\ + \overset{\ ~ }{2}\overset{\ ~ }{5.}\overset{ }{4} \overset{~\ }{8} \\ \hline \end{array}$

Possible Answers:

37.73

14.56

26.3

47.98

Correct answer:

47.98

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+8=8}

Your work should look something like this:

$\begin{array}{r}\overset{\ ~}{2} \overset{\ ~}{2.}\overset{\ ~}{5}0\\ + \overset{\ ~ }{2}\overset{\ ~ }{5.}\overset{ }{4} \overset{~\ }{8} \\ \hline \space{} \, \space{\, } \space{\, }8\end{array}$

Add the numbers in the tenths place:

{5+4=9}

Your work should look something like this:

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

$\begin{array}{r}\overset{\ ~}{2} \overset{\ ~}{2.}\overset{\ ~}{5}0\\ + \overset{\ ~ }{2}\overset{\ ~ }{5.}\overset{ }{4} \overset{~\ }{8} \\ \hline \space{} \, \space{\,. }9\space{\, }8\end{array}$

Add the numbers in the ones place:

{2+5=7}

Your work should look something like this:

$\begin{array}{r}\overset{\ ~}{2} \overset{\ ~}{2.}\overset{\ ~}{5}0\\ + \overset{\ ~ }{2}\overset{\ ~ }{5.}\overset{ }{4} \overset{~\ }{8} \\ \hline \space{} \, 7\space{\,. }9\space{\, }8\end{array}$

Your final answer should be: 47.98

$\begin{array}{r}\overset{\ ~}{2} \overset{\ ~}{2.}\overset{\ ~}{5}0\\ + \overset{\ ~ }{2}\overset{\ ~ }{5.}\overset{ }{4} \overset{~\ }{8} \\ \hline 4\space{} \, 7\space{\,. }9\space{\, }8\end{array}$

Report an Error

Example Question #33 : Adding Multi Digit Decimals

Solve:

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

Possible Answers:

46.74

18.79

51.5

46.13

Correct answer:

51.5

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:

{4+6=10}

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:

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

Add the numbers in the tenths place:

{7+7+1=14}

Because this sum is greater than 9, we write the 5 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.

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

Add the numbers in the ones place:

{0+0+1=1}

Your work should look something like this:

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

Your final answer should be: 51.50

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

Report an Error

Example Question #32 : Adding Multi Digit Decimals

Solve:

$\begin{array}{r}\overset{\ ~}{4} \overset{\ ~}{2.}\overset{\ ~}{5}5\\ + \overset{\ ~ }{4}\overset{\ ~ }{6.}\overset{ }{2} \overset{~\ }{8} \\ \hline \end{array}$

Possible Answers:

88.83

37.79

18.03

Correct answer:

88.83

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:

{5+8=13}

Because this sum is greater than 9, we write the 3 from the ones place and carry the 1 from the tens place over to the left. Your work should look something like this:

$\begin{array}{r}\overset{\ ~}{4} \overset{\ ~}{2.}\overset{\ 1}{5}5\\ + \overset{\ ~ }{4}\overset{\ ~ }{6.}\overset{ }{2} \overset{~\ }{8} \\ \hline \space{} \, \space{\, } \space{\, }3\end{array}$

Add the numbers in the tenths place:

{5+2+1=8}

Your work should look something like this:

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

$\begin{array}{r}\overset{\ ~}{4} \overset{\ ~}{2.}\overset{\ 1}{5}5\\ + \overset{\ ~ }{4}\overset{\ ~ }{6.}\overset{ }{2} \overset{~\ }{8} \\ \hline \space{} \, \space{\,. }8\space{\, }3\end{array}$

Add the numbers in the ones place:

{2+6=8}

Your work should look something like this:

$\begin{array}{r}\overset{\ ~}{4} \overset{\ ~}{2.}\overset{\ 1}{5}5\\ + \overset{\ ~ }{4}\overset{\ ~ }{6.}\overset{ }{2} \overset{~\ }{8} \\ \hline \space{} \, 8\space{\,. }8\space{\, }3\end{array}$

Your final answer should be: 88.83

$\begin{array}{r}\overset{\ ~}{4} \overset{\ ~}{2.}\overset{\ 1}{5}5\\ + \overset{\ ~ }{4}\overset{\ ~ }{6.}\overset{ }{2} \overset{~\ }{8} \\ \hline 8\space{} \, 8\space{\,. }8\space{\, }3\end{array}$

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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

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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 #25 : Adding Multi Digit Decimals

Example Question #26 : Adding Multi Digit Decimals

Example Question #85 : Fluently Add, Subtract, Multiply, And Divide Multi Digit Decimals: Ccss.Math.Content.6.Ns.B.3

Example Question #28 : Adding Multi Digit Decimals

Example Question #21 : Adding Multi Digit Decimals

Example Question #22 : Adding Multi Digit Decimals

Example Question #31 : Adding Multi Digit Decimals

Example Question #31 : Adding Multi Digit Decimals

Example Question #33 : Adding Multi Digit Decimals

Example Question #32 : Adding Multi Digit Decimals

All Common Core: 6th Grade Math Resources

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