Common Core: 4th Grade Math : Adding Mixed Numbers

Study concepts, example questions & explanations for Common Core: 4th Grade Math

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Example Questions

Example Question #1 : Adding Mixed Numbers

\(\displaystyle 4\frac{1}{5}+1\frac{1}{5}\)

Possible Answers:

\(\displaystyle 5\frac{3}{10}\)

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

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

\(\displaystyle 5\frac{1}{10}\)

\(\displaystyle 5\frac{2}{10}\)

Correct answer:

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

Explanation:

When we add mixed numbers, we add whole numbers to whole numbers and fractions to fractions. 

\(\displaystyle 4+1=5\)

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

Remember, when we are adding fractions we must have common denominators and we only add the numerators. 

Example Question #101 : Operations With Fractions And Whole Numbers

\(\displaystyle 2\frac{5}{10}+5\frac{3}{10}\)

Possible Answers:

\(\displaystyle 7\frac{3}{5}\)

\(\displaystyle 7\frac{3}6{}\)

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

\(\displaystyle 7\frac{4}{5}\)

\(\displaystyle 7\frac{9}{10}\)

Correct answer:

\(\displaystyle 7\frac{4}{5}\)

Explanation:

When we add mixed numbers, we add whole numbers to whole numbers and fractions to fractions. 

\(\displaystyle 2+5=7\)

\(\displaystyle \frac{5}{10}+\frac{3}{10}=\frac{8}{10}\)

Remember, when we are adding fractions we must have common denominators and we only add the numerators. 

\(\displaystyle \frac{8}{10}\) can be reduced by dividing \(\displaystyle 2\) to both sides. 

\(\displaystyle \frac{8}{10}\div\frac{2}{2}=\frac{4}{5}\)

 

Example Question #2 : Adding Mixed Numbers

\(\displaystyle 3\frac{1}{5}+8\frac{2}{5}\)

Possible Answers:

\(\displaystyle 11\frac{4}{10}\)

\(\displaystyle 11\frac{3}{10}\)

\(\displaystyle 11\frac{3}{5}\)

\(\displaystyle 12\)

\(\displaystyle 11\frac{4}{5}\)

Correct answer:

\(\displaystyle 11\frac{3}{5}\)

Explanation:

When we add mixed numbers, we add whole numbers to whole numbers and fractions to fractions. 

\(\displaystyle 3+8=11\)

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

Remember, when we are adding fractions we must have common denominators and we only add the numerators. 

Example Question #2 : Adding Mixed Numbers

Solve: 

\(\displaystyle 6\frac{4}{10}+5\frac{5}{10}\)

Possible Answers:

\(\displaystyle 11\frac{8}{20}\)

\(\displaystyle 11\frac{8}{10}\)

\(\displaystyle 11\frac{9}{10}\)

\(\displaystyle 11\frac{9}{20}\)

\(\displaystyle 11\frac{4}{5}\)

Correct answer:

\(\displaystyle 11\frac{9}{10}\)

Explanation:

When we add mixed numbers, we add whole numbers to whole numbers and fractions to fractions. 

\(\displaystyle 6+5=11\)

\(\displaystyle \frac{4}{10}+\frac{5}{10}=\frac{9}{10}\)

Remember, when we are adding fractions we must have common denominators and we only add the numerators. 

Example Question #3 : Adding Mixed Numbers

\(\displaystyle 2\frac{3}{7}+9\frac{1}{7}\)

Possible Answers:

\(\displaystyle 11\)

\(\displaystyle 11\frac{3}{7}\)

\(\displaystyle 11\frac{4}{14}\)

\(\displaystyle 11\frac{3}{14}\)

\(\displaystyle 11\frac{4}{7}\)

Correct answer:

\(\displaystyle 11\frac{4}{7}\)

Explanation:

When we add mixed numbers, we add whole numbers to whole numbers and fractions to fractions. 

\(\displaystyle 2+9=11\)

\(\displaystyle \frac{3}{7}+\frac{1}{7}=\frac{4}{7}\)

Remember, when we are adding fractions we must have common denominators and we only add the numerators. 

Example Question #1422 : Ssat Middle Level Quantitative (Math)

\(\displaystyle 5\frac{3}{6}+8\frac{2}{6}\)

Possible Answers:

\(\displaystyle 13\frac{1}{2}\)

\(\displaystyle 13\frac{5}{6}\)

\(\displaystyle 13\frac{3}{6}\)

\(\displaystyle 13\)

\(\displaystyle 13\frac{5}{12}\)

Correct answer:

\(\displaystyle 13\frac{5}{6}\)

Explanation:

When we add mixed numbers, we add whole numbers to whole numbers and fractions to fractions. 

\(\displaystyle 5+8=13\)

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

Remember, when we are adding fractions we must have common denominators and we only add the numerators. 

Example Question #4 : Adding Mixed Numbers

\(\displaystyle 6\frac{1}{7}+6\frac{1}{7}\)

Possible Answers:

\(\displaystyle 6\frac{2}{7}\)

\(\displaystyle 6\)

\(\displaystyle 12\frac{2}{14}\)

\(\displaystyle 12\frac{2}{7}\)

\(\displaystyle 6\frac{2}{14}\)

Correct answer:

\(\displaystyle 12\frac{2}{7}\)

Explanation:

When we add mixed numbers, we add whole numbers to whole numbers and fractions to fractions. 

\(\displaystyle 6+6=12\)

\(\displaystyle \frac{1}{7}+\frac{1}{7}=\frac{2}{7}\)

Remember, when we are adding fractions we must have common denominators and we only add the numerators. 

Example Question #5 : Adding Mixed Numbers

\(\displaystyle 7\frac{1}{8}+5\frac{2}{8}\)

Possible Answers:

\(\displaystyle 12\frac{3}{16}\)

\(\displaystyle 12\frac{4}{16}\)

\(\displaystyle 12\frac{4}{8}\)

\(\displaystyle 12\frac{5}{8}\)

\(\displaystyle 12\frac{3}{8}\)

Correct answer:

\(\displaystyle 12\frac{3}{8}\)

Explanation:

When we add mixed numbers, we add whole numbers to whole numbers and fractions to fractions. 

\(\displaystyle 7+5=12\)

\(\displaystyle \frac{1}{8}+\frac{2}{8}=\frac{3}{8}\)

Remember, when we are adding fractions we must have common denominators and we only add the numerators. 

Example Question #1131 : Common Core Math: Grade 4

\(\displaystyle 5\frac{1}{5}+11\frac{2}{5}\)

 

Possible Answers:

\(\displaystyle 16\frac{3}{5}\)

\(\displaystyle 16\frac{2}{5}\)

\(\displaystyle 16\frac{4}{5}\)

\(\displaystyle 17\frac{2}{5}\)

\(\displaystyle 17\frac{3}{5}\)

Correct answer:

\(\displaystyle 16\frac{3}{5}\)

Explanation:

When we add mixed numbers, we add whole numbers to whole numbers and fractions to fractions. 

\(\displaystyle 5+11=16\)

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

Remember, when we are adding fractions we must have common denominators and we only add the numerators. 

Example Question #8 : Adding Mixed Numbers

\(\displaystyle 13\frac{1}{3}+7\frac{1}{3}\)

 

Possible Answers:

\(\displaystyle 21\frac{2}{3}\)

\(\displaystyle 22\frac{2}{3}\)

\(\displaystyle 19\frac{2}{3}\)

\(\displaystyle 20\frac{2}{3}\)

\(\displaystyle 18\frac{2}{3}\)

Correct answer:

\(\displaystyle 20\frac{2}{3}\)

Explanation:

When we add mixed numbers, we add whole numbers to whole numbers and fractions to fractions. 

\(\displaystyle 13+7=20\)

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

Remember, when we are adding fractions we must have common denominators and we only add the numerators. 

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