Testinar Grade 4 math

Fraction as Sum of Unit Fractions

Students will decompose a fraction into a sum of unit fractions and represent the decomposition with equations and models.

CH04-01 Fraction Addition and Subtraction

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Score: ____ / 8

Directions Solve each problem. Show your reasoning on the page or on separate paper. Check the answer key only after finishing.

Which expression shows \(\frac{3}{5}\) as a sum of unit fractions?
1. \(\frac{1}{5}+\frac{1}{5}\)
2. \(\frac{1}{5}+\frac{1}{5}+\frac{1}{5}\)
3. \(\frac{3}{5}+\frac{3}{5}+\frac{3}{5}\)
4. \(\frac{3}{5}\)
Which fraction bar shows \(\frac{4}{6}\) as a sum of unit fractions?
1. 4 parts shaded, 6 total
2. 3 parts shaded, 3 total
3. 3 parts shaded, 4 total
4. 2 parts shaded, 3 total
What is \(\frac{2}{3}\) as a sum of unit fractions?
1. \(\frac{1}{2}+\frac{1}{2}\)
2. \(\frac{1}{3}+\frac{1}{3}\)
3. \(\frac{2}{3}+\frac{1}{3}\)
4. \(\frac{3}{3}\)
Sam has a strip of paper divided into 8 equal parts. He colors 5 parts. Which expression shows the fraction colored as a sum of unit fractions?
1. \(\frac{1}{8}+\frac{1}{8}+\frac{1}{8}+\frac{1}{8}+\frac{1}{8}\)
2. \(\frac{5}{8}+\frac{5}{8}\)
3. \(\frac{1}{5}+\frac{1}{5}+\frac{1}{5}+\frac{1}{5}+\frac{1}{5}\)
4. \(\frac{5}{8}\)
Which number sentence is correct?
1. \(\frac{1}{4}+\frac{1}{4}+\frac{1}{4}=\frac{3}{12}\)
2. \(\frac{1}{4}+\frac{1}{4}+\frac{1}{4}=\frac{3}{4}\)
3. \(\frac{1}{3}+\frac{1}{3}+\frac{1}{3}=\frac{3}{9}\)
4. \(\frac{1}{6}+\frac{1}{6}=\frac{2}{12}\)
Ming shares a pizza cut into 12 equal slices. He eats 3 slices. Show how many slices he ate as a sum of unit fractions.
1. \(\frac{3}{12}\)
2. \(\frac{1}{12}+\frac{1}{12}+\frac{1}{12}\)
3. \(\frac{1}{3}+\frac{1}{3}\)
4. \(\frac{3}{3}\)
A number line shows equal hops from 0 to \(\frac{6}{10}\). How many hops of \(\frac{1}{10}\) are needed?
1. 3 hops
2. 4 hops
3. 6 hops
4. 10 hops
How many unit fractions of \(\frac{1}{7}\) make \(\frac{5}{7}\)?
1. 2
2. 5
3. 7
4. 12

Teacher and parent reference

Answer key and explanations

B. \(\frac{1}{5}+\frac{1}{5}+\frac{1}{5}\)
A unit fraction always has a numerator of \(1\). So \(\frac{3}{5}\) breaks down into three copies of \(\frac{1}{5}\): \(\mathbf{\frac{3}{5}=\frac{1}{5}+\frac{1}{5}+\frac{1}{5}}\).
A. 4 parts shaded, 6 total
In the fraction bar, we have 4 shaded parts out of 6 equal parts. Each piece is a unit fraction \(\frac{1}{6}\). So we have \(\mathbf{\frac{4}{6}=\underbrace{\frac{1}{6}+\frac{1}{6}+\frac{1}{6}+\frac{1}{6}}_{4 \text{ copies}}}\).
B. \(\frac{1}{3}+\frac{1}{3}\)
\(\frac{2}{3}\) means two pieces, each of size \(\frac{1}{3}\). So \(\mathbf{\frac{2}{3}=\frac{1}{3}+\frac{1}{3}}\)—two unit fractions added together.
A. \(\frac{1}{8}+\frac{1}{8}+\frac{1}{8}+\frac{1}{8}+\frac{1}{8}\)
Sam colored 5 pieces out of 8 equal parts, so the fraction is \(\frac{5}{8}\). This is the sum of five unit fractions: \(\mathbf{\frac{5}{8}=\underbrace{\frac{1}{8}+\frac{1}{8}+\frac{1}{8}+\frac{1}{8}+\frac{1}{8}}_{5 \text{ copies}}}\).
B. \(\frac{1}{4}+\frac{1}{4}+\frac{1}{4}=\frac{3}{4}\)
When we add unit fractions with the same denominator, we keep the denominator and add the numerators. \(\frac{1}{4}+\frac{1}{4}+\frac{1}{4}\) has three 1's in the numerator, so it equals \(\mathbf{\frac{3}{4}}\). The other choices incorrectly change the denominator.
B. \(\frac{1}{12}+\frac{1}{12}+\frac{1}{12}\)
Ming ate 3 slices out of 12 equal slices, so the fraction is \(\frac{3}{12}\). Breaking this into unit fractions: \(\mathbf{\frac{3}{12}=\frac{1}{12}+\frac{1}{12}+\frac{1}{12}}\)—three slices, each representing \(\frac{1}{12}\) of the pizza.
C. 6 hops
To reach \(\frac{6}{10}\) with hops of \(\frac{1}{10}\), we count: each hop is one unit fraction, and we need 6 copies to equal \(\frac{6}{10}\). So \(\mathbf{6 \text{ hops}}\) gets us there!
B. 5
\(\frac{5}{7}\) means we have 5 equal pieces, and each piece is \(\frac{1}{7}\). So \(\mathbf{5}\) unit fractions of \(\frac{1}{7}\) make up \(\frac{5}{7}\).