Common Core: 2nd Grade Math : Number & Operations in Base Ten

Study concepts, example questions & explanations for Common Core: 2nd Grade Math

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Example Questions

Example Question #1 : Add Up To Four Two Digit Numbers: Ccss.Math.Content.2.Nbt.B.6

Solve:

\(\displaystyle \frac{\begin{array}[b]{r}36\\20\\25\\ +\ 12\end{array}}{\space }\)

 

Possible Answers:

\(\displaystyle 93\)

\(\displaystyle 91\)

\(\displaystyle 94\)

\(\displaystyle 92\)

Correct answer:

\(\displaystyle 93\)

Explanation:

When we add with multi-digit numbers, we start with the numbers in the ones place, and then move to the left. 

9 1

Let's add the digits in the ones place:

\(\displaystyle 6+0+5+2=13\)

Because the sum is greater than \(\displaystyle 9\), we have to carry the \(\displaystyle 1\) to the tens place. So far, your work should look like the following: 

9 2

Next, we add the numbers in the tens position, including the \(\displaystyle 1\) that was carried over:

9 3

Let's add the digits in the tens place:

\(\displaystyle 1+3+2+2+1=9\)

Your final answer should be \(\displaystyle 93\)

9 4

Example Question #1072 : Number & Operations In Base Ten

Solve:

\(\displaystyle \frac{\begin{array}[b]{r}89\\30\\56\\ +\ 11\end{array}}{\space }\)

Possible Answers:

\(\displaystyle 184\)

\(\displaystyle 183\)

\(\displaystyle 186\)

\(\displaystyle 185\)

Correct answer:

\(\displaystyle 186\)

Explanation:

When we add with multi-digit numbers, we start with the numbers in the ones place, and then move to the left. 

10 1

Let's add the digits in the ones place:

\(\displaystyle 9+0+6+1=16\)

Because the sum is greater than \(\displaystyle 9\), we have to carry the \(\displaystyle 1\) to the tens place. So far, your work should look like the following: 

10 2

Next, we add the numbers in the tens position, including the \(\displaystyle 1\) that was carried over:

10 3

Let's add the digits in the tens place:

\(\displaystyle 1+8+3+5+1=18\)

Your final answer should be \(\displaystyle 186\)


10 4

Example Question #1073 : Number & Operations In Base Ten

Solve:

\(\displaystyle \frac{\begin{array}[b]{r}97\\13\\98\\ +\ 15\end{array}}{\space }\)

Possible Answers:

\(\displaystyle 226\)

\(\displaystyle 225\)

\(\displaystyle 223\)

\(\displaystyle 224\)

Correct answer:

\(\displaystyle 223\)

Explanation:

When we add with multi-digit numbers, we start with the numbers in the ones place, and then move to the left. 

11 1

Let's add the digits in the ones place:

\(\displaystyle 7+3+8+5=23\)

Because the sum is greater than \(\displaystyle 9\), we have to carry the \(\displaystyle 2\) to the tens place. So far, your work should look like the following: 

11 2

Next, we add the numbers in the tens position, including the \(\displaystyle 2\) that was carried over:

11 3

Let's add the digits in the tens place:

\(\displaystyle 2+8+1+9+1=22\)

Your final answer should be \(\displaystyle 223\)

11 4

Example Question #4 : Add Up To Four Two Digit Numbers: Ccss.Math.Content.2.Nbt.B.6

Solve:

\(\displaystyle \frac{\begin{array}[b]{r}81\\39\\82\\ +\ 91\end{array}}{\space }\)

Possible Answers:

\(\displaystyle 295\)

\(\displaystyle 293\)

\(\displaystyle 294\)

\(\displaystyle 296\)

Correct answer:

\(\displaystyle 293\)

Explanation:

When we add with multi-digit numbers, we start with the numbers in the ones place, and then move to the left. 

12 1

Let's add the digits in the ones place:

\(\displaystyle 1+9+2+1=13\)

Because the sum is greater than \(\displaystyle 9\), we have to carry the \(\displaystyle 1\) to the tens place. So far, your work should look like the following: 

12 2

Next, we add the numbers in the tens position, including the \(\displaystyle 1\) that was carried over:

12 3

Let's add the digits in the tens place:

\(\displaystyle 1+8+3+8+9=29\)

Your final answer should be \(\displaystyle 293\)

12 4

Example Question #1074 : Number & Operations In Base Ten

Solve the following:

\(\displaystyle \frac{\begin{array}[b]{r}87\\30\\97\\ +\ 64\end{array}}{\space }\)

Possible Answers:

\(\displaystyle 278\)

\(\displaystyle 277\)

\(\displaystyle 276\)

\(\displaystyle 275\)

Correct answer:

\(\displaystyle 278\)

Explanation:

When we add with multi-digit numbers, we start with the numbers in the ones place, and then move to the left. 

1 1

Let's add the digits in the ones place:

\(\displaystyle 7+0+7+4=18\)

Because the sum is greater than \(\displaystyle 9\), we have to carry the \(\displaystyle 1\) to the tens place. So far, your work should look like the following: 

1 2

Next, we add the numbers in the tens position, including the \(\displaystyle 1\) that was carried over:

1 3

Let's add the digits in the tens place:

\(\displaystyle 1+8+3+9+6=27\)

Your final answer should be \(\displaystyle 278\)

1 4

Example Question #1075 : Number & Operations In Base Ten

Solve:

   46

   64

   58

+ 14

Possible Answers:

\(\displaystyle 184\)

\(\displaystyle 185\)

\(\displaystyle 182\)

\(\displaystyle 183\)

Correct answer:

\(\displaystyle 182\)

Explanation:

When we add with multi-digit numbers, we start with the numbers in the ones place, and then move to the left. 

2 1

Let's add the digits in the ones place:

\(\displaystyle 6+4+8+4=22\)

Because the sum is greater than \(\displaystyle 9\), we have to carry the \(\displaystyle 2\) to the tens place. So far, your work should look like the following: 

2 2

Next, we add the numbers in the tens position, including the \(\displaystyle 2\) that was carried over:

2 3

Let's add the digits in the tens place:

\(\displaystyle 2+4+6+5+1=18\)

Your final answer should be \(\displaystyle 182\)

2 4

Example Question #1 : Add And Subtract Within 1000: Ccss.Math.Content.2.Nbt.B.7

Solve the following:

\(\displaystyle \frac{\begin{array}[b]{r}920\\ -\ 290\end{array}}{\space }\)

Possible Answers:

\(\displaystyle 630\)

\(\displaystyle 632\)

\(\displaystyle 631\)

\(\displaystyle 634\)

Correct answer:

\(\displaystyle 630\)

Explanation:

When we subtract multi-digit numbers, we start with the digits in the ones place and move to the left. 

Let's look at the numbers in the ones place:

\(\displaystyle \frac{\begin{array}[b]{r}0\\ -\ 0\end{array}}{\ \ \ 0 }\)

Next, let's look at the numbers in the tens place:

\(\displaystyle \frac{\begin{array}[b]{r}2\\ -\ 9\end{array}}{\ \ \ }\)

When the top number is smaller than the bottom number, we have to borrow from the number to the left because we can't take \(\displaystyle 9\) away from \(\displaystyle 2\) since \(\displaystyle 2\) is the smaller number. In this case, we are going to look to the \(\displaystyle 9\). We only ever need to take \(\displaystyle 1\) away from the number to the left. For this problem, that will leave us with a \(\displaystyle 8\) to replace the \(\displaystyle 9\). So far, your work should look something like this:

\(\displaystyle \frac{\begin{array}[b]{r}^{8} \not920\\ -\ 290\end{array}}{\space }\)

Remember, we've borrowed \(\displaystyle 1\) from the hundreds place, so we can put a \(\displaystyle 1\) in front of the number in the tens place. So far, your work should look something like this:

\(\displaystyle \frac{\begin{array}[b]{r}^{8} \not9\ ^{12}\not2\ \ \ \ \ 0\\ -\ 2 \ \ \ \ \ 9\ \ \ \ \ 0\end{array}}{\space }\)

Now, we can subtract the numbers in the tens place:

\(\displaystyle \frac{\begin{array}[b]{r}12\\ -\ 9\end{array}}{\ \ \ 3}\)

Next, we can subtract the numbers in the hundreds place:

\(\displaystyle \frac{\begin{array}[b]{r}8\\ -\ 2\end{array}}{\ \ \ 6}\)

Your final answer should be \(\displaystyle 630\)

\(\displaystyle \frac{\begin{array}[b]{r}^{8} \not9\ ^{12}\not2\ \ \ \ \ 0\\ -\ 2 \ \ \ \ \ 9\ \ \ \ \ 0\end{array}}{\ \ \ 6 \ \ \ \ \ 3\ \ \ \ \ 0}\)

Example Question #1071 : Number & Operations In Base Ten

Solve the following:

\(\displaystyle \frac{\begin{array}[b]{r}169\\ +\ 323\end{array}}{\space }\)

Possible Answers:

\(\displaystyle 494\)

\(\displaystyle 493\)

\(\displaystyle 492\)

\(\displaystyle 495\)

Correct answer:

\(\displaystyle 492\)

Explanation:

When we add with multi-digit numbers, we start with the numbers in the ones place, and then move to the left to the tens place, followed by the hundreds place. 

Add the numbers in the ones place:

\(\displaystyle 9+3=12\)

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

\(\displaystyle \frac{\begin{array}[b]{r}1^{{\color{Red} 1}}6\ 9\\ +\ 3\ 2\ 3\end{array}}{\ \ \ \ \ \ \ \ 2 }\)

Add the numbers in the tens place, including the \(\displaystyle 1\) that was carried over:

\(\displaystyle 1+6+2=9\)

Add the numbers in the hundreds place:

\(\displaystyle 1+3=4\)

Your final answer should be \(\displaystyle 492:\)

\(\displaystyle \frac{\begin{array}[b]{r}169\\ +\ 323\end{array}}{\ \ \ 492 }\)

Example Question #1071 : Number & Operations In Base Ten

Solve the following:

\(\displaystyle \frac{\begin{array}[b]{r}432\\ +\ 100\end{array}}{ }\)

Possible Answers:

\(\displaystyle 332\)

\(\displaystyle 532\)

\(\displaystyle 500\)

\(\displaystyle 300\)

\(\displaystyle 442\)

Correct answer:

\(\displaystyle 532\)

Explanation:

When adding any number by \(\displaystyle 100\) the only number that will change in your answer is the hundreds place. 

\(\displaystyle 2+0=2\)

\(\displaystyle 3+0=3\)

\(\displaystyle 4+1=5\)

\(\displaystyle \frac{\begin{array}[b]{r}432\\ +\ 100\end{array}}{\ \ \ \space 532}\)

Example Question #1072 : Number & Operations In Base Ten

\(\displaystyle \frac{\begin{array}[b]{r}349\\ +\ 100\end{array}}{?}\)

Possible Answers:

\(\displaystyle 400\)

\(\displaystyle 449\)

\(\displaystyle 359\)

\(\displaystyle 200\)

\(\displaystyle 249\)

Correct answer:

\(\displaystyle 449\)

Explanation:

When adding any number by \(\displaystyle 100\) the only number that will change in your answer is the hundreds place. 

\(\displaystyle 9+0=9\)

\(\displaystyle 4+0=4\)

\(\displaystyle 3+1=4\)

\(\displaystyle \frac{\begin{array}[b]{r}349\\ +\ 100\end{array}}{\ \ \ \space449}\)

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