Common Core: 4th Grade Math : Build fractions from unit fractions

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

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Example Questions

Example Question #1462 : Ssat Middle Level Quantitative (Math)

\(\displaystyle \frac{8}{12}\) is equal to which of the options below? 

 

Possible Answers:

\(\displaystyle \frac{4}{12}+\frac{1}{12}+\frac{4}{12}\)

\(\displaystyle \frac{1}{12}+\frac{4}{12}\)

\(\displaystyle \frac{3}{12}+\frac{2}{12}+\frac{4}{12}\)

\(\displaystyle \frac{3}{12}+\frac{1}{12}+\frac{4}{12}\)

\(\displaystyle \frac{3}{12}+\frac{1}{12}\)

Correct answer:

\(\displaystyle \frac{3}{12}+\frac{1}{12}+\frac{4}{12}\)

Explanation:

When we add fractions, we have to have common denominators and we only add the numerators. 

\(\displaystyle \frac{3}{12}+\frac{1}{12}+\frac{4}{12}=\frac{8}{12}\)

Example Question #1463 : Ssat Middle Level Quantitative (Math)

\(\displaystyle \frac{13}{14}\) is equal to which of the options below? 

Possible Answers:

\(\displaystyle \frac{7}{14}+\frac{7}{14}\)

\(\displaystyle \frac{7}{14}+\frac{5}{14}\)

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

\(\displaystyle \frac{7}{14}+\frac{6}{14}\)

\(\displaystyle \frac{7}{14}+\frac{6}{14}+\frac{1}{14}\)

Correct answer:

\(\displaystyle \frac{7}{14}+\frac{6}{14}\)

Explanation:

When we add fractions, we have to have common denominators and we only add the numerators. 

\(\displaystyle \frac{7}{14}+\frac{6}{14}=\frac{13}{14}\)

Example Question #144 : How To Add Fractions

\(\displaystyle \frac{7}{14}\) is equal to which of the options below? 

 

Possible Answers:

\(\displaystyle \frac{2}{14}+\frac{3}{14}+\frac{4}{14}\)

\(\displaystyle \frac{5}{14}+\frac{1}{14}+\frac{4}{14}\)

\(\displaystyle \frac{2}{14}+\frac{1}{14}+\frac{5}{14}\)

\(\displaystyle \frac{2}{14}+\frac{1}{14}+\frac{2}{14}\)

\(\displaystyle \frac{2}{14}+\frac{1}{14}+\frac{4}{14}\)

Correct answer:

\(\displaystyle \frac{2}{14}+\frac{1}{14}+\frac{4}{14}\)

Explanation:

When we add fractions, we have to have common denominators and we only add the numerators. 

\(\displaystyle \frac{2}{14}+\frac{1}{14}+\frac{4}{14}=\frac{7}{14}\)

Example Question #1464 : Ssat Middle Level Quantitative (Math)

\(\displaystyle \frac{5}{8}\) is equal to which of the options below? 

 

Possible Answers:

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

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

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

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

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

Correct answer:

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

Explanation:

When we add fractions, we have to have common denominators and we only add the numerators. 

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

Example Question #25 : Build Fractions From Unit Fractions

\(\displaystyle 4\frac{3}{8}\) is equal to which of the options below? 

 

Possible Answers:

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

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

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

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

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

Correct answer:

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

Explanation:

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

Don't forget, when we add fractions, we have to have common denominators and we only add the numerators. 

 

\(\displaystyle 2\frac{2}{8}+2\frac{1}{8}=4\frac{3}{8}\)

Example Question #26 : Build Fractions From Unit Fractions

\(\displaystyle 7\frac{7}{9}\) is equal to which of the options below? 

 

Possible Answers:

\(\displaystyle 3\frac{2}{9}+4\frac{5}{9}\)

\(\displaystyle 3\frac{1}{9}+4\frac{5}{9}\)

\(\displaystyle 3\frac{2}{9}+4\frac{6}{9}\)

\(\displaystyle 3\frac{2}{9}+4\frac{5}{9}+\frac{1}{9}\)

\(\displaystyle 4\frac{2}{9}+4\frac{5}{9}\)

Correct answer:

\(\displaystyle 3\frac{2}{9}+4\frac{5}{9}\)

Explanation:

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

Don't forget, when we add fractions, we have to have common denominators and we only add the numerators. 

\(\displaystyle 3\frac{2}{9}+4\frac{5}{9}=7\frac{7}{9}\)

Example Question #27 : Build Fractions From Unit Fractions

\(\displaystyle 11\frac{5}{8}\) is equal to which of the options below? 

Possible Answers:

\(\displaystyle 4\frac{1}{8}+2\frac{2}{8}+6\frac{2}{8}\)

\(\displaystyle 4\frac{1}{8}+1\frac{2}{8}+6\frac{3}{8}\)

\(\displaystyle 4\frac{1}{8}+1\frac{2}{8}+6\frac{2}{8}\)

\(\displaystyle 4\frac{2}{8}+1\frac{2}{8}+6\frac{2}{8}\)

\(\displaystyle 4\frac{1}{8}+1\frac{2}{8}+5\frac{2}{8}\)

Correct answer:

\(\displaystyle 4\frac{1}{8}+1\frac{2}{8}+6\frac{2}{8}\)

Explanation:

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

Don't forget, when we add fractions, we have to have common denominators and we only add the numerators. 

\(\displaystyle 4\frac{1}{8}+1\frac{2}{8}+6\frac{2}{8}=11\frac{5}{8}\)

Example Question #28 : Build Fractions From Unit Fractions

Which option is equal to:

\(\displaystyle 17\frac{4}{10}\) 

Possible Answers:

\(\displaystyle 11\frac{2}{10}+6\frac{2}{10}\)

\(\displaystyle 12\frac{2}{10}+6\frac{2}{10}\)

\(\displaystyle 11\frac{2}{10}+5\frac{2}{10}\)

\(\displaystyle 11\frac{1}{10}+5\frac{2}{10}\)

\(\displaystyle 11\frac{1}{10}+6\frac{2}{10}\)

Correct answer:

\(\displaystyle 11\frac{2}{10}+6\frac{2}{10}\)

Explanation:

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

Don't forget, when we add fractions, we have to have common denominators and we only add the numerators. 

\(\displaystyle 11\frac{2}{10}+6\frac{2}{10}=17\frac{4}{10}\)

Example Question #111 : Number & Operations: €”Fractions

\(\displaystyle 21\frac{7}{8}\) is equal to which of the options below? 

Possible Answers:

\(\displaystyle 7\frac{2}{8}+7\frac{1}{8}+7\frac{4}{8}\)

\(\displaystyle 9\frac{2}{8}+7\frac{1}{8}+7\frac{4}{8}\)

\(\displaystyle 7\frac{2}{8}+8\frac{1}{8}+7\frac{4}{8}\)

\(\displaystyle 7\frac{2}{8}+6\frac{1}{8}+7\frac{4}{8}\)

\(\displaystyle 7\frac{2}{8}+5\frac{1}{8}+5\frac{4}{8}\)

Correct answer:

\(\displaystyle 7\frac{2}{8}+7\frac{1}{8}+7\frac{4}{8}\)

Explanation:

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

Don't forget, when we add fractions, we have to have common denominators and we only add the numerators. 

\(\displaystyle 7\frac{2}{8}+7\frac{1}{8}+7\frac{4}{8}=21\frac{7}{8}\)

Example Question #112 : Number & Operations: €”Fractions

\(\displaystyle 14\frac{6}{10}\) is equal to which of the options below? 

Possible Answers:

\(\displaystyle 3\frac{2}{10}+6\frac{2}{10}+6\frac{2}{10}\)

\(\displaystyle 3\frac{1}{10}+6\frac{2}{10}+5\frac{2}{10}\)

\(\displaystyle 3\frac{1}{10}+6\frac{2}{10}+6\frac{2}{10}\)

\(\displaystyle 3\frac{2}{10}+6\frac{2}{10}+5\frac{2}{10}\)

\(\displaystyle 3\frac{2}{10}+6\frac{3}{10}+5\frac{2}{10}\)

Correct answer:

\(\displaystyle 3\frac{2}{10}+6\frac{2}{10}+5\frac{2}{10}\)

Explanation:

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

Don't forget, when we add fractions, we have to have common denominators and we only add the numerators. 

\(\displaystyle 3\frac{2}{10}+6\frac{2}{10}+5\frac{2}{10}=14\frac{6}{10}\)

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