Testinar Grade 5 math

Estimating Sums and Differences of Fractions

Students will estimate fraction sums and differences using benchmarks and number sense.

CH04-06 Adding and Subtracting Fractions

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

Estimate: \(\frac{1}{8} + \frac{7}{8}\).
1. \(0\)
2. \(\frac{1}{2}\)
3. \(1\)
4. \(2\)
Estimate: \(\frac{4}{9} + \frac{1}{12}\). Which benchmark is the best estimate?
1. \(0\)
2. \(\frac{1}{2}\)
3. \(1\)
4. \(2\)
Estimate: \(\frac{4}{5} + \frac{1}{6}\).
1. \(0\)
2. \(\frac{1}{2}\)
3. \(1\)
4. \(2\)
Estimate: \(3\frac{2}{7} + 1\frac{1}{8}\).
1. \(3\)
2. \(4\)
3. \(4\frac{1}{2}\)
4. \(5\)
Which benchmark is closest to the sum \(\frac{3}{8}+\frac{2}{7}\)?
1. \(0\)
2. \(2\)
3. \(1\)
4. \(\frac{1}{2}\)
Estimate: \(5\frac{6}{7} - 2\frac{1}{9}\).
1. \(3\)
2. \(6\)
3. \(5\)
4. \(4\)
Estimate each expression. Which result is closest to \(0\)?
1. \(\frac{1}{12}+\frac{1}{15}\)
2. \(\frac{1}{2}+\frac{1}{3}\)
3. \(\frac{7}{8}-\frac{1}{8}\)
4. \(\frac{9}{10}+\frac{8}{9}\)
Which expression has a sum close to \(2\)?
1. \(\frac{1}{10} + \frac{3}{11}\)
2. \(1\frac{1}{12} + \frac{7}{8}\)
3. \(\frac{2}{9} + \frac{1}{7}\)
4. \(\frac{4}{5} + \frac{1}{12}\)

Teacher and parent reference

Answer key and explanations

C. \(1\)
\(\frac{1}{8}\) is close to 0, and \(\frac{7}{8}\) is close to 1. So \(\frac{1}{8} + \frac{7}{8} \approx 0 + 1 = 1\).
B. \(\frac{1}{2}\)
\(\frac{4}{9}\) is close to \(\frac{1}{2}\), and \(\frac{1}{12}\) is small. The sum is just a little more than \(\frac{1}{2}\), so \(\frac{1}{2}\) is the best benchmark estimate.
C. \(1\)
\(\frac{4}{5}\) is close to 1, and \(\frac{1}{6}\) is close to 0. So \(\frac{4}{5} + \frac{1}{6} \approx 1 + 0 = 1\).
B. \(4\)
\(3\frac{2}{7} \approx 3\) and \(1\frac{1}{8} \approx 1\). So \(3\frac{2}{7} + 1\frac{1}{8} \approx 3 + 1 = 4\).
D. \(\frac{1}{2}\)
\(\frac{3}{8}+\frac{2}{7}=\frac{37}{56}\approx0.66\). That is closer to \(\frac{1}{2}\) than to \(1\), so \(\frac{1}{2}\) is the best benchmark choice.
D. \(4\)
\(5\frac{6}{7} \approx 6\) and \(2\frac{1}{9} \approx 2\). So \(5\frac{6}{7} - 2\frac{1}{9} \approx 6 - 2 = 4\).
A. \(\frac{1}{12}+\frac{1}{15}\)
Both fractions in choice A are very small, so their sum is close to 0. The other choices are much closer to \(\frac{3}{4}\), 1, or 2.
B. \(1\frac{1}{12} + \frac{7}{8}\)
\(1\frac{1}{12} \approx 1\) and \(\frac{7}{8} \approx 1\). So \(1\frac{1}{12} + \frac{7}{8} \approx 1 + 1 = 2\). All others sum to less than 1.