Question

15,247 Learners found this answer helpful

calculate.

(1) \\(2\frac{1}{2} - \frac{2}{3} - \frac{1}{6}\\)
\\(= 2\frac{\box}{6} - \frac{4}{6} - \frac{1}{6}\\)
\\(= 1\frac{\box}{6} - \frac{4}{6} - \frac{1}{6}\\)
\\(=\\)

(2) \\(2\frac{1}{9} - \frac{1}{2} - \frac{1}{3}\\)
\\(=\\)

(3) \\(3\frac{2}{3} - \frac{5}{6} - \frac{1}{2}\\)
\\(=\\)

(4) \\(2\frac{7}{9} - \frac{1}{2} - \frac{2}{3}\\)
\\(=\\)

Explanation:

Find common denominators

To subtract fractions, find the least common multiple of the denominators for each problem.

• For (1): Denominators are 2, 3, 6. The least common multiple is 6.
• For (2): Denominators are 9, 2, 3. The least common multiple is 18.
• For (3): Denominators are 3, 6, 2. The least common multiple is 6.
• For (4): Denominators are 9, 2, 3. The least common multiple is 18.

Solve Question (1)

Convert fractions to have denominator 6 and fill in the blanks:

$$ 2\frac{1}{2} - \frac{2}{3} - \frac{1}{6} = 2\frac{3}{6} - \frac{4}{6} - \frac{1}{6} $$

The first blank box contains \(3\).
Since \(\frac{3}{6} < \frac{4}{6}\), borrow 1 from the whole number 2:

$$ 2\frac{3}{6} = 1\frac{9}{6} $$

The second blank box contains \(9\).
Subtract the fractions:

$$ 1\frac{9}{6} - \frac{4}{6} - \frac{1}{6} = 1\frac{4}{6} = 1\frac{2}{3} $$

Solve Question (2)

Convert to a common denominator of 18:

$$ 2\frac{1}{9} - \frac{1}{2} - \frac{1}{3} = 2\frac{2}{18} - \frac{9}{18} - \frac{6}{18} $$

Borrow 1 from the whole number 2:

$$ 1\frac{20}{18} - \frac{9}{18} - \frac{6}{18} = 1\frac{5}{18} $$

Solve Question (3)

Convert to a common denominator of 6:

$$ 3\frac{2}{3} - \frac{5}{6} - \frac{1}{2} = 3\frac{4}{6} - \frac{5}{6} - \frac{3}{6} $$

Borrow 1 from the whole number 3:

$$ 2\frac{10}{6} - \frac{5}{6} - \frac{3}{6} = 2\frac{2}{6} = 2\frac{1}{3} $$

Solve Question (4)

Convert to a common denominator of 18:

$$ 2\frac{7}{9} - \frac{1}{2} - \frac{2}{3} = 2\frac{14}{18} - \frac{9}{18} - \frac{12}{18} $$

Subtract step-by-step:

$$ 2\frac{14}{18} - \frac{9}{18} = 2\frac{5}{18} $$

Borrow 1 from the whole number 2:

$$ 1\frac{23}{18} - \frac{12}{18} = 1\frac{11}{18} $$

Answer:

No.	Answer
(2)	\(1\frac{5}{18}\)
(3)	\(2\frac{1}{3}\)
(4)	\(1\frac{11}{18}\)