Question

fraction operations adding & subtracting fractions 1. $8\frac{1}{2}-4\frac{2}{5}$ 2. $4\frac{3}{7}+(-2\frac{1}{5})$ 3. $-1\frac{1}{2}-2\frac{3}{4}$ 4. $5\frac{4}{5}-2\frac{5}{6}$ 5. $4\frac{5}{8}-1\frac{2}{5}$ 6. $\frac{5}{6}+4\frac{7}{8}$

Explanation:

Step1: Convert to improper fractions

$3\frac{1}{2} = \frac{7}{2}$, $4\frac{2}{5} = \frac{22}{5}$

Step2: Find common denominator (10)

$\frac{7}{2} = \frac{35}{10}$, $\frac{22}{5} = \frac{44}{10}$

Step3: Subtract the fractions

$\frac{35}{10} - \frac{44}{10} = -\frac{9}{10}$

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Step1: Convert to improper fractions

$4\frac{1}{7} = \frac{29}{7}$, $-2\frac{1}{3} = -\frac{7}{3}$

Step2: Find common denominator (21)

$\frac{29}{7} = \frac{87}{21}$, $-\frac{7}{3} = -\frac{49}{21}$

Step3: Add the fractions

$\frac{87}{21} + (-\frac{49}{21}) = \frac{38}{21} = 1\frac{17}{21}$

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Step1: Convert to improper fractions

$-1\frac{1}{2} = -\frac{3}{2}$, $2\frac{4}{7} = \frac{18}{7}$

Step2: Find common denominator (14)

$-\frac{3}{2} = -\frac{21}{14}$, $\frac{18}{7} = \frac{36}{14}$

Step3: Subtract the fractions

$-\frac{21}{14} - \frac{36}{14} = -\frac{57}{14} = -4\frac{1}{14}$

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Step1: Convert to improper fractions

$3\frac{4}{5} = \frac{19}{5}$, $2\frac{5}{6} = \frac{17}{6}$

Step2: Find common denominator (30)

$\frac{19}{5} = \frac{114}{30}$, $\frac{17}{6} = \frac{85}{30}$

Step3: Subtract the fractions

$\frac{114}{30} - \frac{85}{30} = \frac{29}{30}$

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Step1: Convert to improper fractions

$4\frac{5}{8} = \frac{37}{8}$, $1\frac{2}{5} = \frac{7}{5}$

Step2: Find common denominator (40)

$\frac{37}{8} = \frac{185}{40}$, $\frac{7}{5} = \frac{56}{40}$

Step3: Subtract the fractions

$\frac{185}{40} - \frac{56}{40} = \frac{129}{40} = 3\frac{9}{40}$

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Step1: Convert to improper fractions

$\frac{5}{6} = \frac{5}{6}$, $4\frac{7}{8} = \frac{39}{8}$

Step2: Find common denominator (24)

$\frac{5}{6} = \frac{20}{24}$, $\frac{39}{8} = \frac{117}{24}$

Step3: Add the fractions

$\frac{20}{24} + \frac{117}{24} = \frac{137}{24} = 5\frac{17}{24}$

Answer:

1. $-\frac{9}{10}$
2. $1\frac{17}{21}$
3. $-4\frac{1}{14}$
4. $\frac{29}{30}$
5. $3\frac{9}{40}$
6. $5\frac{17}{24}$