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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 #1572 : Grade 6

Solve:

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

Possible Answers:

58.11

57.23

69.83

54.2

Correct answer:

69.83

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:

{8+5=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:

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

Add the numbers in the tenths place:

{4+3+1=8}

Your work should look something like this:

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

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

Add the numbers in the ones place:

{8+1=9}

Your work should look something like this:

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

Your final answer should be: 69.83

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

Report an Error

Example Question #1573 : Grade 6

Solve:

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

Possible Answers:

37.35

38.84

16.73

Correct answer:

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:

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

Add the numbers in the tenths place:

{5+5=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:

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

Add the numbers in the ones place:

{2+4+1=7}

Your work should look something like this:

$\begin{array}{r}\overset{\ ~}{3} \overset{\ 1}{2.}\overset{\ ~}{5}0\\ + \overset{\ ~ }{1}\overset{\ ~ }{4.}\overset{ }{5} \overset{~\ }{0} \\ \hline \space{} \, 7\space{\,. }0\space{\, }0\end{array}$

Your final answer should be: 47.00

$\begin{array}{r}\overset{\ ~}{3} \overset{\ 1}{2.}\overset{\ ~}{5}0\\ + \overset{\ ~ }{1}\overset{\ ~ }{4.}\overset{ }{5} \overset{~\ }{0} \\ \hline 4\space{} \, 7\space{\,. }0\space{\, }0\end{array}$

Report an Error

Example Question #47 : Adding Multi Digit Decimals

Solve:

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

Possible Answers:

32.7

35.62

61.62

29.73

Correct answer:

61.62

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+6=12}

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:

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

Add the numbers in the tenths place:

{4+1+1=6}

Your work should look something like this:

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

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

Add the numbers in the ones place:

{6+5+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:

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

Your final answer should be: 61.62

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

Report an Error

Example Question #101 : Fluently Add, Subtract, Multiply, And Divide Multi Digit Decimals: Ccss.Math.Content.6.Ns.B.3

Solve:

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

Possible Answers:

20.15

82.33

52.4

41.54

Correct answer:

82.33

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+0=3}

Your work should look something like this:

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

Add the numbers in the tenths place:

{8+5=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:

Your work should look something like this:

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

Add the numbers in the ones place:

{4+7+1=12}

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:

$\begin{array}{r}\overset{\ 1}{3} \overset{\ 1}{4.}\overset{\ ~}{8}3\\ + \overset{\ ~ }{4}\overset{\ ~ }{7.}\overset{ }{5} \overset{~\ }{0} \\ \hline \space{} \, 2\space{\,. }3\space{\, }3\end{array}$

Your final answer should be: 82.33

$\begin{array}{r}\overset{\ 1}{3} \overset{\ 1}{4.}\overset{\ ~}{8}3\\ + \overset{\ ~ }{4}\overset{\ ~ }{7.}\overset{ }{5} \overset{~\ }{0} \\ \hline 8\space{} \, 2\space{\,. }3\space{\, }3\end{array}$

Report an Error

Example Question #431 : The Number System

Solve:

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

Possible Answers:

37.59

21.39

42.03

37.32

Correct answer:

42.03

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+3=3}

Your work should look something like this:

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

Add the numbers in the tenths place:

{7+3=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:

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

Add the numbers in the ones place:

{1+0+1=2}

Your work should look something like this:

$\begin{array}{r}\overset{\ ~}{3} \overset{\ 1}{1.}\overset{\ ~}{7}0\\ + \overset{\ ~ }{1}\overset{\ ~ }{0.}\overset{ }{3} \overset{~\ }{3} \\ \hline \space{} \, 2\space{\,. }0\space{\, }3\end{array}$

Your final answer should be: 42.03

$\begin{array}{r}\overset{\ ~}{3} \overset{\ 1}{1.}\overset{\ ~}{7}0\\ + \overset{\ ~ }{1}\overset{\ ~ }{0.}\overset{ }{3} \overset{~\ }{3} \\ \hline 4\space{} \, 2\space{\,. }0\space{\, }3\end{array}$

Report an Error

Example Question #50 : Adding Multi Digit Decimals

Solve:

$\begin{array}{r}\overset{\ ~}{2} \overset{\ ~}{2.}\overset{\ ~}{7}0\\ + \overset{\ ~ }{2}\overset{\ ~ }{7.}\overset{ }{5} \overset{~\ }{5} \\ \hline \end{array}$

Possible Answers:

30.97

18.54

50.25

36.48

Correct answer:

50.25

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+5=5}

Your work should look something like this:

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

Add the numbers in the tenths place:

{7+5=12}

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:

Your work should look something like this:

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

Add the numbers in the ones place:

{2+7+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:

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

Your final answer should be: 50.25

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

Report an Error

Example Question #432 : The Number System

Solve:

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

Possible Answers:

10.34

42.94

16.47

34.9

Correct answer:

34.9

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+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:

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

Add the numbers in the tenths place:

{6+2+1=9}

Your work should look something like this:

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

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

Add the numbers in the ones place:

{0+4=4}

Your work should look something like this:

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

Your final answer should be: 34.90

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

Report an Error

Example Question #51 : Adding Multi Digit Decimals

Solve:

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

Possible Answers:

40.98

12.14

59.57

57.53

Correct answer:

40.98

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:

{4+4=8}

Your work should look something like this:

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

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.

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

Add the numbers in the ones place:

{0+0=0}

Your work should look something like this:

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

Your final answer should be: 40.98

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

Report an Error

Example Question #52 : Adding Multi Digit Decimals

Solve:

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

Possible Answers:

34.91

85.07

16.45

50.77

Correct answer:

85.07

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:

{7+0=7}

Your work should look something like this:

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

Add the numbers in the tenths place:

{0+0=0}

Your work should look something like this:

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

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

Add the numbers in the ones place:

{4+1=5}

Your work should look something like this:

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

Your final answer should be: 85.07

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

Report an Error

Example Question #115 : Fluently Add, Subtract, Multiply, And Divide Multi Digit Decimals: Ccss.Math.Content.6.Ns.B.3

Solve:

$\begin{array}{r}\overset{\ ~}{3} \overset{\ ~}{3.}\overset{\ ~}{4}3\\ + \overset{\ ~ }{1}\overset{\ ~ }{8.}\overset{ }{7} \overset{~\ }{4} \\ \hline \end{array}$

Possible Answers:

28.88

52.17

48.29

12.49

Correct answer:

52.17

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:

{3+4=7}

Your work should look something like this:

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

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:

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

Add the numbers in the ones place:

{3+8+1=12}

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:

$\begin{array}{r}\overset{\ 1}{3} \overset{\ 1}{3.}\overset{\ ~}{4}3\\ + \overset{\ ~ }{1}\overset{\ ~ }{8.}\overset{ }{7} \overset{~\ }{4} \\ \hline \space{} \, 2\space{\,. }1\space{\, }7\end{array}$

Your final answer should be: 52.17

$\begin{array}{r}\overset{\ 1}{3} \overset{\ 1}{3.}\overset{\ ~}{4}3\\ + \overset{\ ~ }{1}\overset{\ ~ }{8.}\overset{ }{7} \overset{~\ }{4} \\ \hline 5\space{} \, 2\space{\,. }1\space{\, }7\end{array}$

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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 #1572 : Grade 6

Example Question #1573 : Grade 6

Example Question #47 : Adding Multi Digit Decimals

Example Question #101 : Fluently Add, Subtract, Multiply, And Divide Multi Digit Decimals: Ccss.Math.Content.6.Ns.B.3

Example Question #431 : The Number System

Example Question #50 : Adding Multi Digit Decimals

Example Question #432 : The Number System

Example Question #51 : Adding Multi Digit Decimals

Example Question #52 : Adding Multi Digit Decimals

Example Question #115 : Fluently Add, Subtract, Multiply, And Divide Multi Digit Decimals: Ccss.Math.Content.6.Ns.B.3

All Common Core: 6th Grade Math Resources

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