4.3.A 4.3.B MA.4.FR.2.1

Decompose Fractions 4th Grade

Florida - Benchmarks for Excellent Student Thinking: MA.4.FR.2.1
Decompose a fraction, including mixed numbers and fractions greater than one, into a sum of fractions with the same denominator in multiple ways. Demonstrate each decomposition with objects, drawings and equations

A fraction with a numerator greater than one can be written as the
sum of unit fractions with the same denominator as the fraction.

A unit fraction is a fraction that has 1 as its numerator.
A unit fraction is one part of a whole divided into equal parts.

The fraction

\frac{5}{8}

is five parts of a whole divided into eight equal parts.

Since the numerator is five, five-eighths can be separated into five equal parts that are each

\frac{1}{8}

of the whole.

+

+

+

+

So,

\frac{5}{8}

is equal to the sum of five

\frac{1}{8}

's, or

\frac{1}{8}

\frac{1}{8}

\frac{1}{8}

\frac{1}{8}

\frac{1}{8}

The fraction

\frac{7}{5}

is seven parts of wholes divided into five equal parts.

Since the numerator is seven, seven-fifths can be separated into seven equal parts that are each

\frac{1}{5}

of the whole.

So,

\frac{7}{5}

is equal to the sum of seven

\frac{1}{5}

's, or

\frac{1}{5}

\frac{1}{5}

\frac{1}{5}

\frac{1}{5}

\frac{1}{5}

\frac{1}{5}

\frac{1}{5}

A fraction with a numerator greater than one can be written as
the sum of other fractions with smaller numerators.

The fraction strip is divided into six equal parts, so each part represents

\frac{1}{6}

The shaded parts of the model can be separated into one fraction strip with one part shaded and two fraction strips with two parts shaded.

$\frac{1}{6}$
$\frac{2}{6}$
$\frac{2}{6}$

So,

\frac{1}{6} + \frac{2}{6} + \frac{2}{6}

is equal to the fraction modeled in the question.

Find which two fractions have a sum that equals

\frac{11}{12}

.
The two fractions that have a sum that equals

\frac{11}{12}

have numerators whose sum equals 11 and denominators that are 12.

In the expression

\frac{5}{12} + \frac{6}{12}

, the sum of the numerators is 5 + 6 = 11, and the denominators are 12.

So,

\frac{11}{12}

is equal to

\frac{5}{12} + \frac{6}{12}

Decompose Fractions

Florida - Benchmarks for Excellent Student Thinking: MA.4.FR.2.1

Decompose a fraction, including mixed numbers and fractions greater than one, into a sum of fractions with the same denominator in multiple ways. Demonstrate each decomposition with objects, drawings and equations

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