Compare two fractions with different numerators and different denominators using concrete models, benchmarks
(0, ½, 1), common denominators, and/or common numerators, recording the comparisons with symbols >, =, or <,
and justifying the conclusions.

Explain that comparison of two fractions is valid only when the two fractions refer to the same whole.

Arkansas Academic Standards:
4.NF.A.2

Compare two fractions with different numerators and different denominators (e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2)

Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols (>, =, <), and justify the conclusions (e.g., by using a visual fraction model)

Arizona - K-12 Academic Standards:
4.NF.A.2

Compare two fractions with different numerators and different denominators (e.g., by creating common denominators or numerators and by comparing to a benchmark fraction).

Understand that comparisons are valid only when the two fractions refer to the same size whole.

Record the results of comparisons with symbols >, =, or <, and justify the conclusions.

Common Core State Standards:
Math.4.NF.2 or 4.NF.A.2

Compare two fractions with different numerators and different
denominators, e.g., by creating common denominators or numerators,
or by comparing to a benchmark fraction such as 1/2. Recognize that
comparisons are valid only when the two fractions refer to the same
whole. Record the results of comparisons with symbols >, =, or <, and
justify the conclusions, e.g., by using a visual fraction model.

Georgia Standards of Excellence (GSE):
MGSE4.NF.2

Compare two fractions with different numerators and different denominators, e.g., by
using visual fraction models, by creating common denominators or numerators, or by comparing to a
benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer
to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the
conclusions.

North Carolina - Standard Course of Study:
4.NF.2

Compare two fractions with different numerators and different denominators, using the denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions by:

Reasoning about their size and using area and length models.

Using benchmark fractions 0, 1/2, and a whole.

Comparing common numerator or common denominators.

New York State Next Generation Learning Standards:
4.NF.2

Compare two fractions with different numerators and different denominators. e.g., by creating common denominators or numerators, or by comparing to a
benchmark fraction such as 1/2 Recognize that comparisons are valid only when the two fractions refer to the same whole. Note: Without specifying the whole, the shaded area could represent the
fraction 3/2 (if one square is the whole) or 3/4 (if the entire rectangle is the whole). Record the results of comparisons with symbols >, =, or <, and justify the conclusions. e.g., using a visual fraction model

Tennessee Academic Standards:
4.NF.A.2

Compare two fractions with different numerators and different
denominators by creating common denominators or common numerators or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Use the symbols >, =, or < to show the relationship and justify the conclusions.

Wisconsin Academic Standards:
4.NF.A.2

Compare fractions with different numerators and different denominators while recognizing that
comparisons are valid only when the fractions refer to the same whole. Justify the conclusions by
using visual fraction models (e.g., tape diagrams and number lines) and by reasoning about the size
of the fractions, using benchmark fractions (including whole numbers), or creating common
denominators or numerators. Describe the result of the comparison using words and symbols ( >, =,
and < ).

Pennsylvania Core Standards:
CC.2.1.4.C.1

Extend the understanding of fractions to show equivalence and ordering.

Pennsylvania Core Standards:
M04.A-F.1.1.2

Compare two fractions with different numerators and different denominators (denominators limited to 2, 3, 4, 5, 6, 8, 10, 12, and 100) using the symbols >, =, or < and justify the conclusions.)

Florida - Benchmarks for Excellent Student Thinking:
MA.4.FR.1.4

Plot, order and compare fractions, including mixed numbers and fractions greater than one, with different numerators and different denominators.

4th Grade Math - Compare Fractions Lesson

To compare fractions using models, it helps to divide the models into the same number of equal pieces.

Example:

The first model is divided into two equal parts, and one part is shaded. So, the first model shows $\frac{1}{2}$.

The second model is divided into three equal parts, and two parts are shaded. So, the second model shows $\frac{2}{3}$.

To compare the fractions, it helps to divide the models into the same number of equal pieces. This is called finding a common denominator.

The least common denominator is the least common multiple of 2 and 3, which is 6. Divide both models into six parts.

?

The model with more parts shaded represents the greater fraction. So, $\frac{1}{2}<\frac{2}{3}$.

If two fractions have a common denominator, the fraction with the larger numerator is larger.

The least common denominator of fractions is the least common multiple of the denominators.

Example:

One way to compare fractions is to find a common denominator. The least common denominator is the least common multiple of 6 and 4, which is 12. Multiply both fractions by a fraction equivalent to 1 so that both fractions have 12 as their denominator.

First, since 6 × 2 = 12, multiply $\frac{1}{6}$ by $\frac{2}{2}$ to find a fraction equivalent to $\frac{1}{6}$ with a denominator of 12.

$\frac{1}{6}\times \frac{2}{2}=\frac{2}{12}$

Next, since 4 × 3 = 12, multiply $\frac{3}{4}$ by $\frac{3}{3}$ to find a fraction equivalent to $\frac{3}{4}$ with a denominator of 12.

$\frac{3}{4}\times \frac{3}{3}=\frac{9}{12}$

Then, compare the numerators. 9 > 2, so $\frac{9}{12}>\frac{2}{12}$.

Since $\frac{3}{4}$ is equivalent to $\frac{9}{12}$, and $\frac{1}{6}$ is equivalent to $\frac{2}{12}$, $\frac{3}{4}>\frac{1}{6}$.

If two fractions have a common numerator, the fraction with the smaller denominator is larger.

The least common numerator of fractions is the least common multiple of the numerators.

Example:

One way to compare fractions is to find a common numerator.

In this case, the least common numerator is the least common multiple of 1 and 2, which is 2. Multiply $\frac{1}{5}$ by a fraction equivalent to 1 so that both fractions have 2 as their numerator.

Since 1 × 2 = 2, multiply $\frac{1}{5}$ by $\frac{2}{2}$ to find a fraction equivalent to $\frac{1}{5}$ with a numerator of 2.

$\frac{1}{5}\times \frac{2}{2}=\frac{2}{10}$

Then, compare the denominators. 10 < 12, so $\frac{2}{10}>\frac{2}{12}$.

Since $\frac{1}{5}$ is equivalent to $\frac{2}{10}$, $\frac{1}{5}>\frac{2}{12}$.