Question

bellringer

1. $6\frac{1}{2}+4\frac{2}{5}$
2. $2\frac{3}{4}\times\frac{3}{3}$
3. $7\frac{3}{4}-2\frac{1}{4}=$
4. $\frac{4}{5}\div\frac{2}{5}=$

Explanation:

Step1: Convert to improper fractions

$6\frac{1}{2} = \frac{13}{2}$, $4\frac{2}{5} = \frac{22}{5}$

Step2: Find common denominator

$\frac{13}{2} = \frac{65}{10}$, $\frac{22}{5} = \frac{44}{10}$

Step3: Add the fractions

$\frac{65}{10} + \frac{44}{10} = \frac{109}{10} = 10\frac{9}{10}$

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Step1: Convert to improper fraction

$2\frac{3}{4} = \frac{11}{4}$

Step2: Multiply the fractions

$\frac{11}{4} \times \frac{2}{3} = \frac{11 \times 2}{4 \times 3} = \frac{22}{12}$

Step3: Simplify the result

$\frac{22}{12} = \frac{11}{6} = 1\frac{5}{6}$

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Step1: Subtract whole & fractional parts

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

Step2: Simplify and combine

$\frac{2}{4} = \frac{1}{2}$, $5 + \frac{1}{2} = 5\frac{1}{2}$

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Step1: Rewrite division as multiplication

$\frac{4}{5} \div \frac{2}{5} = \frac{4}{5} \times \frac{5}{2}$

Step2: Cancel and calculate

$\frac{4 \times 5}{5 \times 2} = \frac{4}{2} = 2$

Answer:

1. $10\frac{9}{10}$
2. $1\frac{5}{6}$
3. $5\frac{1}{2}$
4. $2$