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Evaluate: $\frac{3}{4} + \frac{6}{7} \div \frac{4}{5} - \frac{4}{7}$ . Express the answer as a mixed number in lowest

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Find trigonometric ratios using a Pythagorean or reciprocal identity

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Q. Evaluate:

\frac{3}{4} + \frac{6}{7} \div \frac{4}{5} - \frac{4}{7}

. Express the answer as a mixed number in lowest

Follow Order of Operations: First, we need to follow the order of operations, which means we do the division first. $\frac{3}{4} + \left(\frac{6}{7} \div \frac{4}{5}\right) - \frac{4}{7}$
Division of Fractions: Now, let's do the division. To divide fractions, we multiply by the reciprocal of the second fraction. $\frac{6}{7} \div \frac{4}{5} = \frac{6}{7} \times \frac{5}{4}$
Simplify Result: Multiplying the fractions gives us: $\newline$ $(6 \times 5) / (7 \times 4) = \frac{30}{28}$ $\newline$ But this can be simplified to: $\newline$ $\frac{30}{28} = \frac{15}{14}$
Substitute Result: Now we substitute the result back into the original expression: $\frac{3}{4} + \frac{15}{14} - \frac{4}{7}$
Find Common Denominator: We need a common denominator to add and subtract the fractions. The least common denominator (LCD) for $4$ , $14$ , and $7$ is $28$ . So we convert each fraction: $\frac{3}{4} = \frac{21}{28}$ , $\frac{15}{14} = \frac{30}{28}$ , and $\frac{4}{7} = \frac{16}{28}$
Add and Subtract Fractions: Now we add and subtract the fractions with the common denominator: $\frac{21}{28} + \frac{30}{28} - \frac{16}{28}$
Add and Subtract Fractions: Now we add and subtract the fractions with the common denominator: $\newline$ $\frac{21}{28} + \frac{30}{28} - \frac{16}{28}$ Adding and subtracting the numerators gives us: $\newline$ $(21 + 30 - 16) / 28 = \frac{35}{28}$

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