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 #41 : Build Fractions From Unit Fractions

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

Possible Answers:

\(\displaystyle 5\)

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

\(\displaystyle \frac{1}{50}\)

\(\displaystyle \frac{3}{15}\)

\(\displaystyle 2\)

Correct answer:

\(\displaystyle 2\)

Explanation:

When we multiply a fraction by a whole number we need to make the whole number into a fraction by putting our whole number over \(\displaystyle 1\).

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

\(\displaystyle \frac{10}{5}=2\) because \(\displaystyle 5\) can go into \(\displaystyle 10\) two times.

Example Question #42 : Build Fractions From Unit Fractions

\(\displaystyle 11\times\frac{1}{3}=\)

Possible Answers:

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

\(\displaystyle 6\)

\(\displaystyle 7\)

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

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

Correct answer:

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

Explanation:

When we multiply a fraction by a whole number we need to make the whole number into a fraction by putting our whole number over \(\displaystyle 1\).

\(\displaystyle \frac{11}{1}\times\frac{1}{3}=\frac{11}{3}\)

\(\displaystyle \frac{11}{3}=3\frac{2}{3}\) because \(\displaystyle 3\) can go into \(\displaystyle 11\) three times, and \(\displaystyle \frac{2}{3}\) is left over. 

Example Question #74 : How To Multiply Fractions

\(\displaystyle 12\times\frac{3}{4}=\)

Possible Answers:

\(\displaystyle 4\)

\(\displaystyle 9\)

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

\(\displaystyle \frac{9}{12}\)

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

Correct answer:

\(\displaystyle 9\)

Explanation:

When we multiply a fraction by a whole number we need to make the whole number into a fraction by putting our whole number over \(\displaystyle 1\).

\(\displaystyle \frac{12}{1}\times\frac{3}{4}=\frac{36}{4}\)

\(\displaystyle \frac{36}{4}=9\) because \(\displaystyle 4\) can go into \(\displaystyle 36\) nine times.

Example Question #75 : How To Multiply Fractions

\(\displaystyle 8\times\frac{1}{3}=\)

Possible Answers:

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

\(\displaystyle 6\)

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

\(\displaystyle 3\)

\(\displaystyle \frac{8}{24}\)

Correct answer:

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

Explanation:

When we multiply a fraction by a whole number we need to make the whole number into a fraction by putting our whole number over \(\displaystyle 1\).

\(\displaystyle \frac{8}{1}\times\frac{1}{3}=\frac{8}{3}\)

\(\displaystyle \frac{8}{3}=2\frac{2}{3}\) because \(\displaystyle 3\) can go into \(\displaystyle 8\) two times, and \(\displaystyle \frac{2}{3}\) is left over. 

Example Question #43 : Build Fractions From Unit Fractions

\(\displaystyle 7\times\frac{3}{8}=\)

Possible Answers:

\(\displaystyle 7\frac{3}{8}\)

\(\displaystyle 5\)

\(\displaystyle \frac{21}{56}\)

\(\displaystyle 4\)

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

Correct answer:

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

Explanation:

When we multiply a fraction by a whole number we need to make the whole number into a fraction by putting our whole number over \(\displaystyle 1\).

\(\displaystyle \frac{7}{1}\times\frac{3}{8}=\frac{21}{8}\)

\(\displaystyle \frac{21}{8}=2\frac{5}{8}\) because \(\displaystyle 8\) can go into \(\displaystyle 21\) two times, and \(\displaystyle \frac{5}{8}\) is left over. 

Example Question #44 : Build Fractions From Unit Fractions

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

Possible Answers:

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

\(\displaystyle 3\)

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

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

\(\displaystyle 4\)

Correct answer:

\(\displaystyle 4\)

Explanation:

When we multiply a fraction by a whole number we need to make the whole number into a fraction by putting our whole number over \(\displaystyle 1\).

\(\displaystyle \frac{6}{1}\times\frac{2}{3}=\frac{12}{3}\)

\(\displaystyle \frac{12}{3}=4\) because \(\displaystyle 3\) can go into \(\displaystyle 12\) four times.

Example Question #45 : Build Fractions From Unit Fractions

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

Possible Answers:

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

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

\(\displaystyle 5\)

\(\displaystyle \frac{1}{25}\)

\(\displaystyle 1\)

Correct answer:

\(\displaystyle 1\)

Explanation:

When we multiply a fraction by a whole number we need to make the whole number into a fraction by putting our whole number over \(\displaystyle 1\).

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

\(\displaystyle \frac{5}{5}=1\) because \(\displaystyle 5\) can go into \(\displaystyle 5\) one time.

Example Question #11 : Multiply A Fraction By A Whole Number: Ccss.Math.Content.4.Nf.B.4

\(\displaystyle 4\times\frac{1}{7}=\)

Possible Answers:

\(\displaystyle 7\)

\(\displaystyle \frac{4}{28}\)

\(\displaystyle \frac{1}{28}\)

\(\displaystyle 4\frac{1}{7}\)

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

Correct answer:

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

Explanation:

When we multiply a fraction by a whole number we need to make the whole number into a fraction by putting our whole number over \(\displaystyle 1\).

\(\displaystyle \frac{4}{1}\times\frac{1}{7}=\frac{4}{7}\)

 

Example Question #81 : How To Multiply Fractions

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

Possible Answers:

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

\(\displaystyle 3\)

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

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

\(\displaystyle 1\)

Correct answer:

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

Explanation:

When we multiply a fraction by a whole number we need to make the whole number into a fraction by putting our whole number over \(\displaystyle 1\).

\(\displaystyle \frac{3}{1}\times\frac{2}{5}=\frac{6}{5}\)

\(\displaystyle \frac{6}{5}=1\frac{1}{5}\) because \(\displaystyle 5\) can go into \(\displaystyle 6\) one time, and \(\displaystyle \frac{1}{5}\) is left over. 

Example Question #1 : Understand A Fraction A/B As A Multiple Of 1/B: Ccss.Math.Content.4.Nf.B.4a

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

Possible Answers:

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

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

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

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

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

Correct answer:

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

Explanation:

\(\displaystyle 3\times\frac{1}{3}\) means the same thing as adding \(\displaystyle \frac{1}{3}\) three times.

On our number line, we can make \(\displaystyle 3\) jumps of \(\displaystyle \frac{1}{3}\)

3 3 number line

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