Question

e106b
(7) (\frac{1}{2} - \frac{3}{10} = \frac{square}{10} - \frac{square}{10} = \frac{square}{10} = \frac{square}{5})
(8) (\frac{9}{10} - \frac{1}{2} =)
(9) (\frac{4}{5} - \frac{3}{10} =)
(10) (1\frac{1}{3} - \frac{1}{12} =)
(11) (2\frac{3}{4} - \frac{1}{12} =)
(12) (2\frac{7}{12} - 1\frac{1}{4} =)
(13) (2\frac{7}{12} - 2\frac{5}{12} =)

Explanation:

Step1: Solve (7)

To subtract \(\frac{1}{2}-\frac{3}{10}\), first find a common denominator, which is 10. Convert \(\frac{1}{2}\) to tenths: \(\frac{1}{2}=\frac{5}{10}\). Then subtract: \(\frac{5}{10}-\frac{3}{10}=\frac{2}{10}\), and simplify \(\frac{2}{10}=\frac{1}{5}\). So the boxes are 5, 3, 2, 1.

Step2: Solve (8)

For \(\frac{9}{10}-\frac{1}{2}\), common denominator is 10. Convert \(\frac{1}{2}\) to \(\frac{5}{10}\). Subtract: \(\frac{9}{10}-\frac{5}{10}=\frac{4}{10}=\frac{2}{5}\).

Step3: Solve (9)

For \(\frac{4}{5}-\frac{3}{10}\), common denominator is 10. Convert \(\frac{4}{5}\) to \(\frac{8}{10}\). Subtract: \(\frac{8}{10}-\frac{3}{10}=\frac{5}{10}=\frac{1}{2}\).

Step4: Solve (10)

For \(1\frac{1}{3}-\frac{1}{12}\), convert mixed number to improper fraction: \(1\frac{1}{3}=\frac{4}{3}\). Common denominator is 12. Convert \(\frac{4}{3}\) to \(\frac{16}{12}\). Subtract: \(\frac{16}{12}-\frac{1}{12}=\frac{15}{12}=\frac{5}{4}=1\frac{1}{4}\).

Step5: Solve (11)

For \(2\frac{3}{4}-\frac{1}{12}\), convert mixed number to improper fraction: \(2\frac{3}{4}=\frac{11}{4}\). Common denominator is 12. Convert \(\frac{11}{4}\) to \(\frac{33}{12}\). Subtract: \(\frac{33}{12}-\frac{1}{12}=\frac{32}{12}=\frac{8}{3}=2\frac{2}{3}\).

Step6: Solve (12)

For \(2\frac{7}{12}-1\frac{1}{4}\), convert mixed numbers to improper fractions: \(2\frac{7}{12}=\frac{31}{12}\), \(1\frac{1}{4}=\frac{5}{4}\). Common denominator is 12. Convert \(\frac{5}{4}\) to \(\frac{15}{12}\). Subtract: \(\frac{31}{12}-\frac{15}{12}=\frac{16}{12}=\frac{4}{3}=1\frac{1}{3}\).

Step7: Solve (13)

For \(2\frac{7}{12}-2\frac{5}{12}\), subtract the whole numbers and the fractions separately. Whole numbers: \(2 - 2 = 0\). Fractions: \(\frac{7}{12}-\frac{5}{12}=\frac{2}{12}=\frac{1}{6}\). So the result is \(\frac{1}{6}\).

Answer:

(7) \(\frac{1}{2}-\frac{3}{10}=\frac{5}{10}-\frac{3}{10}=\frac{2}{10}=\frac{1}{5}\) (boxes: 5, 3, 2, 1)
(8) \(\frac{2}{5}\)
(9) \(\frac{1}{2}\)
(10) \(1\frac{1}{4}\)
(11) \(2\frac{2}{3}\)
(12) \(1\frac{1}{3}\)
(13) \(\frac{1}{6}\)