Common Core: 4th Grade Math : Number & Operations: €”Fractions

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

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Example Questions

Example Question #21 : Explain Equivalent Fractions With Fraction Models: Ccss.Math.Content.4.Nf.A.1

Select the fraction that is equivalent to \(\displaystyle \frac{1}{6}\)


1 6

Possible Answers:

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

2 12

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

4 8

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

2 3

Correct answer:

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

2 12

Explanation:

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

Notice that when we line up our fraction models, which are the exact same size, the same portion of the rectangle is filled in. 

1 6

2 12

Also, notice that \(\displaystyle \frac{1}{6}\) was doubled to get  \(\displaystyle \frac{2}{12}\)

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

Example Question #142 : Fractions

Select the fraction that is equivalent to \(\displaystyle \frac{2}{3}\)

2 3

Possible Answers:

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

1 2

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

1 5

\(\displaystyle \frac{4}{6}\)

4 6

Correct answer:

\(\displaystyle \frac{4}{6}\)

4 6

Explanation:

\(\displaystyle \frac{2}{3}=\frac{4}{6}\) 

Notice that when we line up our fraction models, which are the exact same size, the same portion of the rectangle is filled in. 

2 3

4 6

Also, notice that \(\displaystyle \frac{2}{3}\) was doubled to get  \(\displaystyle \frac{4}{6}\)

\(\displaystyle \frac{2}{3}\times\frac{2}{2}=\frac{4}{6}\)

Example Question #21 : Number & Operations: €”Fractions

Select the fraction that is equivalent to \(\displaystyle \frac{2}{3}\)

2 3

Possible Answers:

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

8 12

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

1 2

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

2 12

Correct answer:

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

8 12

Explanation:

\(\displaystyle \frac{2}{3}=\frac{8}{12}\) 

Notice that when we line up our fraction models, which are the exact same size, the same portion of the rectangle is filled in. 

2 3

8 12

Also, notice that \(\displaystyle \frac{2}{3}\) was multiplied by \(\displaystyle \frac{4}{4}\) to get  \(\displaystyle \frac{8}{12}\)

\(\displaystyle \frac{2}{3}\times\frac{4}{4}=\frac{8}{12}\)

Example Question #22 : Explain Equivalent Fractions With Fraction Models: Ccss.Math.Content.4.Nf.A.1

Select the fraction that is equivalent to \(\displaystyle \frac{1}{3}\)

1 3

 

Possible Answers:

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

1 2

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

4 12

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

2 4

Correct answer:

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

4 12

Explanation:

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

Notice that when we line up our fraction models, which are the exact same size, the same portion of the rectangle is filled in. 

1 3

 

4 12

Also, notice that \(\displaystyle \frac{1}{3}\) was multiplied by \(\displaystyle \frac{4}{4}\) to get  \(\displaystyle \frac{4}{12}\)

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

Example Question #12 : How To Order Fractions From Least To Greatest Or From Greatest To Least

Select the symbol to correctly fill in the blank below. 

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

Possible Answers:

\(\displaystyle =\)

\(\displaystyle >\)

\(\displaystyle < \)

Correct answer:

\(\displaystyle >\)

Explanation:

To compare fractions, we need to first make common denominators. 

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

Now that we have common denominators, we can compare numerators. The fraction with the bigger numerator has the greater value. 

\(\displaystyle \frac{4}{8}>\frac{1}{8}\)

Example Question #21 : Number & Operations: €”Fractions

Select the symbol to correctly fill in the blank below. 

\(\displaystyle \frac{3}{4}\) __________\(\displaystyle \frac{7}{8}\)

Possible Answers:

\(\displaystyle >\)

\(\displaystyle < \)

\(\displaystyle =\)

Correct answer:

\(\displaystyle < \)

Explanation:

To compare fractions, we need to first make common denominators. 

\(\displaystyle \frac{3}{4}\times\frac{2}{2}=\frac{6}{8}\)

Now that we have common denominators, we can compare numerators. The fraction with the bigger numerator has the greater value. 

\(\displaystyle \frac{6}{8}< \frac{7}{8}\)

Example Question #23 : Number & Operations: €”Fractions

Select the symbol to correctly fill in the blank below. 

\(\displaystyle \frac{1}{2}\) __________\(\displaystyle \frac{6}{12}\)

Possible Answers:

\(\displaystyle =\)

\(\displaystyle < \)

\(\displaystyle >\)

Correct answer:

\(\displaystyle =\)

Explanation:

To compare fractions, we need to first make common denominators. 

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

Now that we have common denominators, we can compare numerators. The fraction with the bigger numerator has the greater value. 

\(\displaystyle \frac{6}{12}=\frac{6}{12}\)

Example Question #1 : How To Compare Fractions

Select the symbol to correctly fill in the blank below. 

\(\displaystyle \frac{5}{7}\) __________\(\displaystyle \frac{1}{3}\)

Possible Answers:

\(\displaystyle =\)

\(\displaystyle >\)

\(\displaystyle < \)

Correct answer:

\(\displaystyle >\)

Explanation:

To compare fractions, we need to first make common denominators. 

\(\displaystyle \frac{5}{7}\times\frac{3}{3}=\frac{15}{21}\)

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

Now that we have common denominators, we can compare numerators. The fraction with the bigger numerator has the greater value. 

\(\displaystyle \frac{15}{21}>\frac{7}{21}\)

Example Question #21 : Extend Understanding Of Fraction Equivalence And Ordering

Select the symbol to correctly fill in the blank below. 

\(\displaystyle \frac{2}{3}\)__________\(\displaystyle \frac{4}{5}\)

Possible Answers:

\(\displaystyle < \)

\(\displaystyle >\)

\(\displaystyle =\)

Correct answer:

\(\displaystyle < \)

Explanation:

To compare fractions, we need to first make common denominators. 

\(\displaystyle \frac{2}{3}\times\frac{5}{5}=\frac{10}{15}\)

\(\displaystyle \frac{4}{5}\times\frac{3}{3}=\frac{12}{15}\)

Now that we have common denominators, we can compare numerators. The fraction with the bigger numerator has the greater value. 

\(\displaystyle \frac{10}{15}< \frac{12}{15}\)

Example Question #22 : Extend Understanding Of Fraction Equivalence And Ordering

Select the symbol to correctly fill in the blank below. 

\(\displaystyle \frac{5}{10}\) __________\(\displaystyle \frac{1}{2}\)

Possible Answers:

\(\displaystyle < \)

\(\displaystyle =\)

\(\displaystyle >\)

Correct answer:

\(\displaystyle =\)

Explanation:

To compare fractions, we need to first make common denominators. 

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

Now that we have common denominators, we can compare numerators. The fraction with the bigger numerator has the greater value. 

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

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