Common Core: 5th Grade Math : Common Core Math: Grade 5

Study concepts, example questions & explanations for Common Core: 5th Grade Math

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Example Questions

Example Question #1 : Add Decimals

Add: 

\(\displaystyle \frac{\begin{array}[b]{r}.35\\ +\ .13\end{array}}{\ \ \ \ }\)

Possible Answers:

\(\displaystyle .22\)

\(\displaystyle .4\)

\(\displaystyle .48\)

\(\displaystyle .12\)

Correct answer:

\(\displaystyle .48\)

Explanation:

When we add decimals, we can treat it like a normal addition problem, we just need to remember out decimal: 

\(\displaystyle \frac{\begin{array}[b]{r}.35\\ +\ .13\end{array}}{\ \ \ \ }\)

       \(\displaystyle .48\)

Example Question #2 : Add Decimals

Add:

\(\displaystyle \frac{\begin{array}[b]{r}.51\\ +\ .11\end{array}}{\ \ \ \ }\)

Possible Answers:

\(\displaystyle .62\)

\(\displaystyle 4\)

\(\displaystyle .40\)

\(\displaystyle .6\)

Correct answer:

\(\displaystyle .62\)

Explanation:

Adding decimals is just like adding regular numbers, you just must remember to bring down your decimal point: 

\(\displaystyle \frac{\begin{array}[b]{r}.51\\ +\ .11\end{array}}{\ \ \ \ }\)

       \(\displaystyle .62\)

Example Question #3 : Add Decimals

Add:

\(\displaystyle \frac{\begin{array}[b]{r}.24\\ +\ .05\end{array}}{\ \ \ \ }\)

Possible Answers:

\(\displaystyle .29\)

\(\displaystyle .01\)

\(\displaystyle 1\)

\(\displaystyle 29\)

Correct answer:

\(\displaystyle .29\)

Explanation:

Adding decimals is like adding regular numbers, you just need to remember your decimal:

\(\displaystyle \frac{\begin{array}[b]{r}.24\\ +\ .05\end{array}}{\ \ \ \ }\)

       \(\displaystyle .29\)

Example Question #4 : Add Decimals

\(\displaystyle \frac{\begin{array}[b]{r}7.17\\ +\ 2.24\end{array}}{\ \ \ \ }\)

Possible Answers:

\(\displaystyle 9.31\)

\(\displaystyle 9.41\)

\(\displaystyle 10.31\)

\(\displaystyle 5.13\)

Correct answer:

\(\displaystyle 9.41\)

Explanation:

Adding decimals is just like adding whole numbers. But, you must remember your decimal in your answer.

You start adding on the far right which in this case is the hundredths place. \(\displaystyle 7+4=11\). We have to carry a \(\displaystyle 1\) from the sum \(\displaystyle 11\) above the tenths place and place the other \(\displaystyle 1\) below the hundredths place. Screen shot 2020 09 11 at 11.53.18 am

Next, add the tenths place. Screen shot 2020 09 11 at 11.53.23 am

The decimal will be carried down and remain between the tenths place and the ones place. Screen shot 2020 09 11 at 11.53.27 am

The final addition portion is the ones place. Screen shot 2020 09 11 at 11.53.32 am

The final answer is \(\displaystyle 9.41\)

Example Question #4 : Add Decimals

\(\displaystyle \frac{\begin{array}[b]{r}3.64\\ +\ 2.26\end{array}}{\ \ \ \ }\)

Possible Answers:

\(\displaystyle 5.90\)

\(\displaystyle 5.80\)

\(\displaystyle 5.11\)

\(\displaystyle 5.810\)

Correct answer:

\(\displaystyle 5.90\)

Explanation:

Adding decimals is just like adding whole numbers. But, you must remember your decimal in your answer.

You start adding on the far right which in this case is the hundredths place. \(\displaystyle 4+6=10\). We have to carry a \(\displaystyle 1\) from the sum \(\displaystyle 10\) above the tenths place and place the \(\displaystyle 0\) below the hundredths place. Screen shot 2020 09 11 at 12.07.59 pm

Next, add the tenths place. Screen shot 2020 09 11 at 12.08.04 pm

The decimal will be carried down and remain between the tenths place and the ones place. Screen shot 2020 09 11 at 12.08.07 pm

The final addition portion is the ones place. Screen shot 2020 09 11 at 12.08.12 pm

The final answer is \(\displaystyle 5.90\)

Example Question #6 : Add Decimals

\(\displaystyle \frac{\begin{array}[b]{r}0.84\\ +\ 0.64\end{array}}{\ \ \ \ }\)

Possible Answers:

\(\displaystyle 1.48\)

\(\displaystyle 14.8\)

\(\displaystyle 0.148\)

\(\displaystyle 0.128\)

\(\displaystyle 1.28\)

Correct answer:

\(\displaystyle 1.48\)

Explanation:

Adding decimals is just like adding whole numbers. But, you must remember your decimal in your answer.

You start adding on the far right which in this case is the hundredths place. Screen shot 2020 09 11 at 12.41.27 pm

Next, add the tenths place. \(\displaystyle 8+6=14\). We have to carry a \(\displaystyle 1\) from the sum \(\displaystyle 14\) above the ones place and place the \(\displaystyle 4\) below the tenths place. Screen shot 2020 09 11 at 12.41.31 pm

The decimal will be carried down and remain between the tenths place and the ones place. Screen shot 2020 09 11 at 12.41.34 pm

The final addition portion is the ones place. Screen shot 2020 09 11 at 12.41.38 pm

The final answer is \(\displaystyle 1.48\)

Example Question #7 : Add Decimals

\(\displaystyle \frac{\begin{array}[b]{r}8.13\\ +\ 2.34\end{array}}{\ \ \ \ }\)

Possible Answers:

\(\displaystyle 11.47\)

\(\displaystyle 114.7\)

\(\displaystyle 1.47\)

\(\displaystyle 1.147\)

Correct answer:

\(\displaystyle 11.47\)

Explanation:

Adding decimals is just like adding whole numbers. But, you must remember your decimal in your answer.

You start adding on the far right which in this case is the hundredths place. Screen shot 2020 09 11 at 1.02.37 pm

Next, add the tenths place. Screen shot 2020 09 11 at 1.02.41 pm

The decimal will be carried down and remain between the tenths place and the ones place. Screen shot 2020 09 11 at 1.02.45 pm

The final addition portion is the ones place. \(\displaystyle 8+3=11\). The first \(\displaystyle 1\) in \(\displaystyle 11\) will be carried into the tens place. Screen shot 2020 09 11 at 1.02.49 pm

The final answer is \(\displaystyle 11.47\)

Example Question #371 : Fractions

\(\displaystyle \frac{1}{4}+\frac{1}{2}\)

Possible Answers:

\(\displaystyle \frac{1}{3}\)

\(\displaystyle \frac{3}{4}\)

\(\displaystyle \frac{2}{6}\)

\(\displaystyle \frac{1}{2}\)

\(\displaystyle \frac{2}{4}\)

Correct answer:

\(\displaystyle \frac{3}{4}\)

Explanation:

\(\displaystyle \frac{1}{4}+\frac{1}{2}\)

In order to solve this problem, we first have to find common denominators. 

\(\displaystyle \frac{1}{2}\times\frac{2}{2}=\frac{2}{4}\)

Now that we have common denominators, we can add the fractions. Remember, when we add and subtract fractions, we only add or subtract the numerator. 

\(\displaystyle \frac{1}{4}+\frac{2}{4}=\frac{3}{4}\)

Example Question #1 : Add Fractions With Unlike Denominators

\(\displaystyle \frac{1}{5}+\frac{1}{2}\)

Possible Answers:

\(\displaystyle \frac{7}{20}\)

\(\displaystyle \frac{1}{7}\)

\(\displaystyle \frac{8}{10}\)

\(\displaystyle \frac{2}{7}\)

\(\displaystyle \frac{7}{10}\)

Correct answer:

\(\displaystyle \frac{7}{10}\)

Explanation:

\(\displaystyle \frac{1}{5}+\frac{1}{2}\)

In order to solve this problem, we first have to find common denominators. 

\(\displaystyle \frac{1}{5}\times\frac{2}{2}=\frac{2}{10}\)

\(\displaystyle \frac{1}{2}\times \frac{5}{5}=\frac{5}{10}\)

Now that we have common denominators, we can add the fractions. Remember, when we add and subtract fractions, we only add or subtract the numerator. 

\(\displaystyle \frac{2}{10}+\frac{5}{10}=\frac{7}{10}\)

Example Question #372 : Fractions

\(\displaystyle \frac{1}{3}+\frac{2}{5}\)

Possible Answers:

\(\displaystyle \frac{3}{8}\)

\(\displaystyle \frac{11}{15}\)

\(\displaystyle \frac{15}{11}\)

\(\displaystyle \frac{2}{8}\)

\(\displaystyle \frac{11}{30}\)

Correct answer:

\(\displaystyle \frac{11}{15}\)

Explanation:

\(\displaystyle \frac{1}{3}+\frac{2}{5}\)

In order to solve this problem, we first have to find common denominators. 

\(\displaystyle \frac{1}{3}\times\frac{5}5{}=\frac{5}{15}\)

\(\displaystyle \frac{2}{5}\times\frac{3}{3}=\frac{6}{15}\)

Now that we have common denominators, we can add the fractions. Remember, when we add and subtract fractions, we only add or subtract the numerator. 

\(\displaystyle \frac{5}{15}+\frac{6}{15}=\frac{11}{15}\)

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