Common Core: 2nd Grade Math : Common Core Math: Grade 2

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

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Example Questions

Example Question #1051 : Number & Operations In Base Ten

Solve:

\(\displaystyle \frac{\begin{array}[b]{r}67\\ -\ 33\end{array}}{\space }\)

Possible Answers:

\(\displaystyle 33\)

\(\displaystyle 34\)

\(\displaystyle 32\)

\(\displaystyle 31\)

Correct answer:

\(\displaystyle 34\)

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:

\(\displaystyle \frac{\begin{array}[b]{r}6{\color{Red} 7}\\ -\ 3{\color{Red} 3}\end{array}}{\ \ \ \ \ {\color{Red} 4} }\)

 

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

\(\displaystyle \frac{\begin{array}[b]{r}{\color{Red} 6}7\\ -\ {\color{Red} 3}3\end{array}}{\ \ \ \ {\color{Red} 3}4}\)

Your final answer should be \(\displaystyle 34\)

Example Question #1052 : Common Core Math: Grade 2

Solve:

\(\displaystyle \frac{\begin{array}[b]{r}35\\ -\ 19\end{array}}{\space }\)

Possible Answers:

\(\displaystyle 14\)

\(\displaystyle 15\)

\(\displaystyle 13\)

\(\displaystyle 16\)

Correct answer:

\(\displaystyle 16\)

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:

\(\displaystyle \frac{\begin{array}[b]{r}5\\ -\ 9\end{array}}{\space }\)

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 \(\displaystyle 5\) since \(\displaystyle 5\) is the smaller number. In this case, we are going to look to the \(\displaystyle 3\). We only ever need to take \(\displaystyle 1\) away from the number to the left. For this problem, that will leave us with a \(\displaystyle 2\) to replace the \(\displaystyle 3\). So far, your work should look something like this:

\(\displaystyle \frac{\begin{array}[b]{r}^{2} \not35\\ -\ 19\end{array}}{\space }\)

Remember, we've borrowed \(\displaystyle 1\) from the tens place, and one ten is equal to \(\displaystyle 10\). We now add that \(\displaystyle 10\) to the digit in the ones place, \(\displaystyle 5+10=15\). Your work should look something like this:

\(\displaystyle \frac{\begin{array}[b]{r}^{2} \not3\ ^{15}\not5\\ -\ 1 \ \ \ \ \ 9\end{array}}{\space }\)

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

\(\displaystyle \frac{\begin{array}[b]{r}15\\ -\ 9\end{array}}{\ \ \ 6}\)

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

\(\displaystyle \frac{\begin{array}[b]{r}2\\ -\ 1\end{array}}{\ \ \ 1}\)

Your final answer should be \(\displaystyle 16\)

\(\displaystyle \frac{\begin{array}[b]{r}^{2} \not3\ ^{15}\not5\\ -\ 1 \ \ \ \ \ 9\end{array}}{\ \ \ 1\ \ \ \ \ 6}\)

Example Question #1052 : Number & Operations In Base Ten

Solve:

\(\displaystyle \frac{\begin{array}[b]{r}55\\ -\ 36\end{array}}{\space }\)

Possible Answers:

\(\displaystyle 17\)

\(\displaystyle 18\)

\(\displaystyle 19\)

\(\displaystyle 20\)

Correct answer:

\(\displaystyle 19\)

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:

\(\displaystyle \frac{\begin{array}[b]{r}5\\ -\ 6\end{array}}{\space }\)

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 \(\displaystyle 6\) away from \(\displaystyle 5\) since \(\displaystyle 5\) is the smaller number. In this case, we are going to look to the \(\displaystyle 5\). We only ever need to take \(\displaystyle 1\) away from the number to the left. For this problem, that will leave us with a \(\displaystyle 4\) to replace the \(\displaystyle 5\). So far, your work should look something like this:

\(\displaystyle \frac{\begin{array}[b]{r}^{4} \not55\\ -\ 36\end{array}}{\space }\)

Remember, we've borrowed \(\displaystyle 1\) from the tens place, and one ten is equal to \(\displaystyle 10\). We now add that \(\displaystyle 10\) to the digit in the ones place, \(\displaystyle 5+10=15\). Your work should look something like this:

\(\displaystyle \frac{\begin{array}[b]{r}^{4} \not5\ ^{15}\not5\\ -\ 3 \ \ \ \ \ 6\end{array}}{\space }\)

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

\(\displaystyle \frac{\begin{array}[b]{r}15\\ -\ 6\end{array}}{\ \ \ 9}\)

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

\(\displaystyle \frac{\begin{array}[b]{r}4\\ -\ 3\end{array}}{\ \ \ 1}\)

Your final answer should be \(\displaystyle 19\)

\(\displaystyle \frac{\begin{array}[b]{r}^{4} \not5\ ^{15}\not5\\ -\ 3 \ \ \ \ \ 6\end{array}}{\ \ \ 1\ \ \ \ \ \ 9}\)

Example Question #1054 : Common Core Math: Grade 2

Solve:

\(\displaystyle \frac{\begin{array}[b]{r}85\\ -\ 18\end{array}}{\space }\)

Possible Answers:

\(\displaystyle 67\)

\(\displaystyle 68\)

\(\displaystyle 69\)

\(\displaystyle 66\)

Correct answer:

\(\displaystyle 67\)

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:

\(\displaystyle \frac{\begin{array}[b]{r}5\\ -\ 8\end{array}}{\space }\)

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 \(\displaystyle 8\) away from \(\displaystyle 5\) since \(\displaystyle 5\) is the smaller number. In this case, we are going to look to the \(\displaystyle 8\). We only ever need to take \(\displaystyle 1\) away from the number to the left. For this problem, that will leave us with a \(\displaystyle 7\) to replace the \(\displaystyle 8\). So far, your work should look something like this:

\(\displaystyle \frac{\begin{array}[b]{r}^{7} \not85\\ -\ 18\end{array}}{\space }\)

Remember, we've borrowed \(\displaystyle 1\) from the tens place, and one ten is equal to \(\displaystyle 10\). We now add that \(\displaystyle 10\) to the digit in the ones place, \(\displaystyle 5+10=15\). Your work should look something like this:

\(\displaystyle \frac{\begin{array}[b]{r}^{7} \not8\ ^{15}\not5\\ -\ 1 \ \ \ \ \ 8\end{array}}{\space }\)

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

\(\displaystyle \frac{\begin{array}[b]{r}15\\ -\ 8\end{array}}{\ \ \ 7}\)

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

\(\displaystyle \frac{\begin{array}[b]{r}7\\ -\ 1\end{array}}{\ \ \ 6}\)

Your final answer should be \(\displaystyle 67\)

\(\displaystyle \frac{\begin{array}[b]{r}^{7} \not8\ ^{15}\not5\\ -\ 1 \ \ \ \ \ 8\end{array}}{\ \ \ \ 6\ \ \ \ \ 7 }\)

Example Question #1053 : Number & Operations In Base Ten

Solve:

\(\displaystyle \frac{\begin{array}[b]{r}81\\ -\ 12\end{array}}{\space }\)

Possible Answers:

\(\displaystyle 69\)

\(\displaystyle 68\)

\(\displaystyle 66\)

\(\displaystyle 67\)

Correct answer:

\(\displaystyle 69\)

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:

\(\displaystyle \frac{\begin{array}[b]{r}1\\ -\ 2\end{array}}{\space }\)

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 \(\displaystyle 2\) away from \(\displaystyle 1\) since \(\displaystyle 1\) 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 an \(\displaystyle 7\) to replace the \(\displaystyle 8\). So far, your work should look something like this:

\(\displaystyle \frac{\begin{array}[b]{r}^{7} \not81\\ -\ 12\end{array}}{\space }\)

Remember, we've borrowed \(\displaystyle 1\) from the tens place, and one ten is equal to \(\displaystyle 10\). We now add that \(\displaystyle 10\) to the digit in the ones place, \(\displaystyle 1+10=11\). Your work should look something like this:

\(\displaystyle \frac{\begin{array}[b]{r}^{7} \not8\ ^{11}\not1\\ -\ 1 \ \ \ \ \ 2\end{array}}{\space }\)

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

\(\displaystyle \frac{\begin{array}[b]{r}11\\ -\ 2\end{array}}{\ \ \ 9}\)

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

\(\displaystyle \frac{\begin{array}[b]{r}7\\ -\ 1\end{array}}{\ \ \ 6}\)

Your final answer should be \(\displaystyle 69\)

\(\displaystyle \frac{\begin{array}[b]{r}^{7} \not8\ ^{11}\not1\\ -\ 1 \ \ \ \ \ 2\end{array}}{\ \ \ \ 6\ \ \ \ \ 9 }\)

Example Question #1056 : Common Core Math: Grade 2

Solve:

\(\displaystyle \frac{\begin{array}[b]{r}21\\ -\ 17\end{array}}{\space }\)

Possible Answers:

\(\displaystyle 5\)

\(\displaystyle 4\)

\(\displaystyle 6\)

\(\displaystyle 7\)

Correct answer:

\(\displaystyle 4\)

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:

\(\displaystyle \frac{\begin{array}[b]{r}1\\ -\ 7\end{array}}{\space }\)

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 \(\displaystyle 7\) away from \(\displaystyle 1\) since \(\displaystyle 1\) is the smaller number. In this case, we are going to look to the \(\displaystyle 2\). We only ever need to take \(\displaystyle 1\) away from the number to the left. For this problem, that will leave us with a \(\displaystyle 1\) to replace the \(\displaystyle 2\). So far, your work should look something like this:

\(\displaystyle \frac{\begin{array}[b]{r}^{1} \not21\\ -\ 17\end{array}}{\space }\)

Remember, we've borrowed \(\displaystyle 1\) from the tens place, and one ten is equal to \(\displaystyle 10\). We now add that \(\displaystyle 10\) to the digit in the ones place, \(\displaystyle 1+10=11\). Your work should look something like this:

\(\displaystyle \frac{\begin{array}[b]{r}^{1} \not2\ ^{11}\not1\\ -\ 1 \ \ \ \ \ 7\end{array}}{\space }\)

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

\(\displaystyle \frac{\begin{array}[b]{r}11\\ -\ 7\end{array}}{\ \ \ 4}\)

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

\(\displaystyle \frac{\begin{array}[b]{r}1\\ -\ 1\end{array}}{\ \ \ 0}\)

Your final answer should be \(\displaystyle 4\)

\(\displaystyle \frac{\begin{array}[b]{r}^{1} \not2\ ^{11}\not1\\ -\ 1 \ \ \ \ \ 7\end{array}}{\ \ \ \ \ \ \ \ \ \ \ 4}\)

Example Question #1052 : Number & Operations In Base Ten

Solve:

\(\displaystyle \frac{\begin{array}[b]{r}36\\ -\ 18\end{array}}{\space }\)

Possible Answers:

\(\displaystyle 19\)

\(\displaystyle 18\)

\(\displaystyle 17\)

\(\displaystyle 20\)

Correct answer:

\(\displaystyle 18\)

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:

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

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 \(\displaystyle 8\) away from \(\displaystyle 6\) since \(\displaystyle 6\) is the smaller number. In this case, we are going to look to the \(\displaystyle 3\). We only ever need to take \(\displaystyle 1\) away from the number to the left. For this problem, that will leave us with a \(\displaystyle 2\) to replace the \(\displaystyle 3\). So far, your work should look something like this:

\(\displaystyle \frac{\begin{array}[b]{r}^{2} \not36\\ -\ 18\end{array}}{\space }\)

Remember, we've borrowed \(\displaystyle 1\) from the tens place, and one ten is equal to \(\displaystyle 10\). We now add that \(\displaystyle 10\) to the digit in the ones place, \(\displaystyle 6+10=16\). Your work should look something like this:

\(\displaystyle \frac{\begin{array}[b]{r}^{2} \not3\ ^{16}\not6\\ -\ 1 \ \ \ \ \ 8\end{array}}{\space }\)

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

\(\displaystyle \frac{\begin{array}[b]{r}16\\ -\ 8\end{array}}{\ \ \ 8}\)

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

\(\displaystyle \frac{\begin{array}[b]{r}2\\ -\ 1\end{array}}{\ \ \ 1}\)

Your final answer should be \(\displaystyle 18\)

\(\displaystyle \frac{\begin{array}[b]{r}^{2} \not3\ ^{16}\not6\\ -\ 1 \ \ \ \ \ 8\end{array}}{\ \ \ 1\ \ \ \ \ 8}\)

Example Question #41 : Add And Subtract Within 100: Ccss.Math.Content.2.Nbt.B.5

Solve:

\(\displaystyle \frac{\begin{array}[b]{r}15\\ -\ 10\end{array}}{\space }\)

Possible Answers:

\(\displaystyle 8\)

\(\displaystyle 7\)

\(\displaystyle 6\)

\(\displaystyle 5\)

Correct answer:

\(\displaystyle 5\)

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:

\(\displaystyle \frac{\begin{array}[b]{r}1{\color{Red} 5}\\ -\ 1{\color{Red} 0}\end{array}}{\ \ \ \ \ {\color{Red} 5} }\)

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

\(\displaystyle \frac{\begin{array}[b]{r}{\color{Red} 1}5\\ -\ {\color{Red} 1}0\end{array}}{\ \ \ \ {\color{Red} 0}5}\)

Your final answer should be \(\displaystyle 5\)

Example Question #41 : Add And Subtract Within 100: Ccss.Math.Content.2.Nbt.B.5

Solve:

\(\displaystyle \frac{\begin{array}[b]{r}37\\ -\ 11\end{array}}{\space }\)

Possible Answers:

\(\displaystyle 27\)

\(\displaystyle 28\)

\(\displaystyle 29\)

\(\displaystyle 26\)

Correct answer:

\(\displaystyle 26\)

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:

\(\displaystyle \frac{\begin{array}[b]{r}3{\color{Red} 7}\\ -\ 1{\color{Red} 1}\end{array}}{\ \ \ \ \ {\color{Red} 6} }\)

 

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

\(\displaystyle \frac{\begin{array}[b]{r}{\color{Red} 3}7\\ -\ {\color{Red} 1}1\end{array}}{\ \ \ \ {\color{Red} 2}6}\)

Your final answer should be \(\displaystyle 26\)

Example Question #41 : Add And Subtract Within 100: Ccss.Math.Content.2.Nbt.B.5

Solve:

\(\displaystyle \frac{\begin{array}[b]{r}58\\ -\ 30\end{array}}{\space }\)

Possible Answers:

\(\displaystyle 25\)

\(\displaystyle 26\)

\(\displaystyle 27\)

\(\displaystyle 28\)

Correct answer:

\(\displaystyle 28\)

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:

\(\displaystyle \frac{\begin{array}[b]{r}5{\color{Red} 8}\\ -\ 3{\color{Red} 0}\end{array}}{\ \ \ \ \ {\color{Red} 8} }\)

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

\(\displaystyle \frac{\begin{array}[b]{r}{\color{Red} 5}8\\ -\ {\color{Red} 3}0\end{array}}{\ \ \ \ {\color{Red} 2}8}\)

Your final answer should be \(\displaystyle 28\)

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