Add and Subtract Fractions: Stretch (Year 6) | CGP Plus - Free Printable

To solve the given problems, we need to add and subtract fractions. The key steps involve finding a common denominator, performing the operations, simplifying the result, and converting improper fractions to mixed numbers if necessary. Let's solve each problem step by step.

---

Problem 1:

\[
\frac{5}{7} + \frac{3}{4}
\]

1. Find the least common denominator (LCD):
- The denominators are 7 and 4.
- The LCD of 7 and 4 is \(7 \times 4 = 28\).

2. Rewrite each fraction with the LCD as the denominator:
\[
\frac{5}{7} = \frac{5 \times 4}{7 \times 4} = \frac{20}{28}
\]
\[
\frac{3}{4} = \frac{3 \times 7}{4 \times 7} = \frac{21}{28}
\]

3. Add the fractions:
\[
\frac{20}{28} + \frac{21}{28} = \frac{20 + 21}{28} = \frac{41}{28}
\]

4. Simplify and convert to a mixed number:
- \(\frac{41}{28}\) is an improper fraction.
- Convert to a mixed number: \(41 \div 28 = 1\) remainder \(13\).
- So, \(\frac{41}{28} = 1 \frac{13}{28}\).

Answer:
\[
\boxed{1 \frac{13}{28}}
\]

---

Problem 2:

\[
\frac{2}{3} - \frac{4}{11}
\]

1. Find the least common denominator (LCD):
- The denominators are 3 and 11.
- The LCD of 3 and 11 is \(3 \times 11 = 33\).

2. Rewrite each fraction with the LCD as the denominator:
\[
\frac{2}{3} = \frac{2 \times 11}{3 \times 11} = \frac{22}{33}
\]
\[
\frac{4}{11} = \frac{4 \times 3}{11 \times 3} = \frac{12}{33}
\]

3. Subtract the fractions:
\[
\frac{22}{33} - \frac{12}{33} = \frac{22 - 12}{33} = \frac{10}{33}
\]

4. Simplify:
- \(\frac{10}{33}\) is already in simplest form.

Answer:
\[
\boxed{\frac{10}{33}}
\]

---

Problem 3:

\[
\frac{5}{8} + \frac{6}{7}
\]

1. Find the least common denominator (LCD):
- The denominators are 8 and 7.
- The LCD of 8 and 7 is \(8 \times 7 = 56\).

2. Rewrite each fraction with the LCD as the denominator:
\[
\frac{5}{8} = \frac{5 \times 7}{8 \times 7} = \frac{35}{56}
\]
\[
\frac{6}{7} = \frac{6 \times 8}{7 \times 8} = \frac{48}{56}
\]

3. Add the fractions:
\[
\frac{35}{56} + \frac{48}{56} = \frac{35 + 48}{56} = \frac{83}{56}
\]

4. Convert to a mixed number:
- \(\frac{83}{56}\) is an improper fraction.
- Convert to a mixed number: \(83 \div 56 = 1\) remainder \(27\).
- So, \(\frac{83}{56} = 1 \frac{27}{56}\).

Answer:
\[
\boxed{1 \frac{27}{56}}
\]

---

Problem 4:

\[
\frac{13}{15} - \frac{3}{4}
\]

1. Find the least common denominator (LCD):
- The denominators are 15 and 4.
- The LCD of 15 and 4 is \(15 \times 4 = 60\).

2. Rewrite each fraction with the LCD as the denominator:
\[
\frac{13}{15} = \frac{13 \times 4}{15 \times 4} = \frac{52}{60}
\]
\[
\frac{3}{4} = \frac{3 \times 15}{4 \times 15} = \frac{45}{60}
\]

3. Subtract the fractions:
\[
\frac{52}{60} - \frac{45}{60} = \frac{52 - 45}{60} = \frac{7}{60}
\]

4. Simplify:
- \(\frac{7}{60}\) is already in simplest form.

Answer:
\[
\boxed{\frac{7}{60}}
\]

---

Problem 5:

\[
\frac{5}{12} + \frac{9}{18}
\]

1. Simplify \(\frac{9}{18}\):
- \(\frac{9}{18} = \frac{1}{2}\).

2. Find the least common denominator (LCD):
- The denominators are 12 and 2.
- The LCD of 12 and 2 is 12.

3. Rewrite each fraction with the LCD as the denominator:
\[
\frac{5}{12} = \frac{5}{12}
\]
\[
\frac{1}{2} = \frac{1 \times 6}{2 \times 6} = \frac{6}{12}
\]

4. Add the fractions:
\[
\frac{5}{12} + \frac{6}{12} = \frac{5 + 6}{12} = \frac{11}{12}
\]

5. Simplify:
- \(\frac{11}{12}\) is already in simplest form.

Answer:
\[
\boxed{\frac{11}{12}}
\]

---

Problem 6:

\[
\frac{9}{12} - \frac{3}{16}
\]

1. Simplify \(\frac{9}{12}\):
- \(\frac{9}{12} = \frac{3}{4}\).

2. Find the least common denominator (LCD):
- The denominators are 4 and 16.
- The LCD of 4 and 16 is 16.

3. Rewrite each fraction with the LCD as the denominator:
\[
\frac{3}{4} = \frac{3 \times 4}{4 \times 4} = \frac{12}{16}
\]
\[
\frac{3}{16} = \frac{3}{16}
\]

4. Subtract the fractions:
\[
\frac{12}{16} - \frac{3}{16} = \frac{12 - 3}{16} = \frac{9}{16}
\]

5. Simplify:
- \(\frac{9}{16}\) is already in simplest form.

Answer:
\[
\boxed{\frac{9}{16}}
\]

---

Problem 7:

\[
\frac{1}{4} + \frac{3}{5} + \frac{3}{10}
\]

1. Find the least common denominator (LCD):
- The denominators are 4, 5, and 10.
- The LCD of 4, 5, and 10 is 20.

2. Rewrite each fraction with the LCD as the denominator:
\[
\frac{1}{4} = \frac{1 \times 5}{4 \times 5} = \frac{5}{20}
\]
\[
\frac{3}{5} = \frac{3 \times 4}{5 \times 4} = \frac{12}{20}
\]
\[
\frac{3}{10} = \frac{3 \times 2}{10 \times 2} = \frac{6}{20}
\]

3. Add the fractions:
\[
\frac{5}{20} + \frac{12}{20} + \frac{6}{20} = \frac{5 + 12 + 6}{20} = \frac{23}{20}
\]

4. Convert to a mixed number:
- \(\frac{23}{20}\) is an improper fraction.
- Convert to a mixed number: \(23 \div 20 = 1\) remainder \(3\).
- So, \(\frac{23}{20} = 1 \frac{3}{20}\).

Answer:
\[
\boxed{1 \frac{3}{20}}
\]

---

Problem 8:

\[
\frac{13}{18} - \frac{25}{45}
\]

1. Simplify \(\frac{25}{45}\):
- \(\frac{25}{45} = \frac{5}{9}\).

2. Find the least common denominator (LCD):
- The denominators are 18 and 9.
- The LCD of 18 and 9 is 18.

3. Rewrite each fraction with the LCD as the denominator:
\[
\frac{13}{18} = \frac{13}{18}
\]
\[
\frac{5}{9} = \frac{5 \times 2}{9 \times 2} = \frac{10}{18}
\]

4. Subtract the fractions:
\[
\frac{13}{18} - \frac{10}{18} = \frac{13 - 10}{18} = \frac{3}{18}
\]

5. Simplify:
- \(\frac{3}{18} = \frac{1}{6}\).

Answer:
\[
\boxed{\frac{1}{6}}
\]

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Final Answers:

\[
\boxed{1 \frac{13}{28}, \frac{10}{33}, 1 \frac{27}{56}, \frac{7}{60}, \frac{11}{12}, \frac{9}{16}, 1 \frac{3}{20}, \frac{1}{6}}
\]