Grade 4 Decomposing Fractions

Visual Model 1

Question: The fraction bar shows \(\frac{5}{6}\) divided into parts. Which equation shows this decomposition?

• A. \(\frac{2}{6}+\frac{3}{6}\)
• B. \(\frac{1}{6}+\frac{4}{6}\)
• C. \(\frac{2}{6}+\frac{2}{6}\)
• D. \(\frac{3}{6}+\frac{1}{6}\)

Why it works: Look at the bar—the light blue section is \(\frac{2}{6}\) and the dark blue is \(\frac{3}{6}\). Add them: \(2+3=5\), so \(\frac{2}{6}+\frac{3}{6}=\frac{5}{6}\) \checkmark.

Answer: \(\frac{2}{6}+\frac{3}{6}\)

Visual Model 2

Question: Here is a number line showing \(\frac{6}{8}\): Which shows one correct way to decompose this into two equal jumps?

• A. Jump \(\frac{3}{8}\), then jump \(\frac{3}{8}\)
• B. Jump \(\frac{2}{8}\), then jump \(\frac{4}{8}\)
• C. Jump \(\frac{4}{8}\), then jump \(\frac{3}{8}\)
• D. Jump \(\frac{1}{8}\), then jump \(\frac{6}{8}\)

Why it works: Two equal jumps of \(\frac{3}{8}\) each: \(3+3=6\), so \(\frac{3}{8}+\frac{3}{8}=\frac{6}{8}\) \checkmark. Both parts are the same!

Answer: Jump \(\frac{3}{8}\), then jump \(\frac{3}{8}\)

Example 1

Question: Look at the two fraction bars: This represents which mixed number?

• A. \(1\frac{2}{3}\)
• B. \(2\frac{2}{3}\)
• C. \(1\frac{1}{3}\)
• D. \(2\frac{1}{3}\)

1. The top bar is a complete whole.
2. The bottom bar shows \(\frac{2}{3}\).
3. Together: one whole plus \(\frac{2}{3}\) equals \(\mathbf{1\frac{2}{3}}\) \checkmark.

Answer: \(1\frac{2}{3}\)

Example 2

Question: Which fraction is shown on the number line?

• A. \(\frac{2}{4}\)
• B. \(\frac{3}{4}\)
• C. \(\frac{5}{8}\)
• D. \(\frac{4}{5}\)

1. The red dot sits at the third mark on the number line, which shows \(\frac{3}{4}\) \checkmark.

Answer: \(\frac{3}{4}\)

Example 3

Question: This fraction bar shows a decomposition. The light part is \(\frac{3}{5}\) and the dark part is \(\frac{2}{5}\). The whole fraction is:

• A. \(\frac{3}{5}\)
• B. \(\frac{2}{5}\)
• C. \(\frac{5}{5}\)
• D. \(\frac{6}{5}\)

1. Light part is \(\frac{3}{5}\), dark part is \(\frac{2}{5}\).
2. Together: \(3+2=5\), so \(\frac{3}{5}+\frac{2}{5}=\frac{5}{5}=1\) whole \checkmark.

Answer: \(\frac{5}{5}\)

Problem 1

Question: A recipe uses \(\frac{9}{4}\) cups of flour. This equals how many whole cups and extra fourths?

• A. \(1\) whole and \(\frac{5}{4}\) extra
• B. \(2\) wholes and \(\frac{1}{4}\) extra
• C. \(2\) wholes and \(\frac{9}{4}\) extra
• D. \(3\) wholes and \(\frac{1}{4}\) extra

Why it works: Break apart \(\frac{9}{4}\): two wholes are \(\frac{4}{4}+\frac{4}{4}\), then add \(\frac{1}{4}\) more. That's \(2\frac{1}{4}\) cups \checkmark.

Answer: \(2\) wholes and \(\frac{1}{4}\) extra

Problem 2

Question: A rectangular garden is divided into 6 equal plots, and the farmer uses 4 of them. Which expression shows \(\frac{4}{6}\) written as a sum of unit fractions?

• A. \(\frac{1}{6}+\frac{1}{6}+\frac{1}{6}+\frac{1}{6}\)
• B. \(\frac{2}{6}+\frac{2}{6}\)
• C. \(\frac{3}{6}+\frac{1}{6}\)
• D. \(\frac{4}{6}+0\)

Why it works: A unit fraction has numerator 1. The farmer uses 4 plots, so we need four \(\frac{1}{6}\) pieces: \(\frac{1}{6}+\frac{1}{6}+\frac{1}{6}+\frac{1}{6}\) \checkmark.

Answer: \(\frac{1}{6}+\frac{1}{6}+\frac{1}{6}+\frac{1}{6}\)