consider the expression $-6\\frac{3}{5}-(-7\\frac{4}{15})+2\\frac{1}{5}$. \na. estimate the value of the…

Explanation:

Step1: Estimate the value (for part a)

Round each mixed number to the nearest whole number. (-6\frac{3}{5}\approx - 7), (-(-7\frac{4}{15})\approx7), (2\frac{1}{5}\approx2) Then the expression (-7 + 7+2)

Step2: Calculate the exact value (for part b)

First, convert mixed numbers to improper fractions. (-6\frac{3}{5}=-\frac{6\times5 + 3}{5}=-\frac{33}{5}), (-(-7\frac{4}{15})=\frac{7\times15+4}{15}=\frac{109}{15}), (2\frac{1}{5}=\frac{2\times5 + 1}{5}=\frac{11}{5}) The expression becomes (-\frac{33}{5}+\frac{109}{15}+\frac{11}{5}) Combine the fractions with denominator 5: (\left(-\frac{33}{5}+\frac{11}{5}\right)+\frac{109}{15}=-\frac{22}{5}+\frac{109}{15}) Get a common denominator of 15: (-\frac{22\times3}{5\times3}+\frac{109}{15}=-\frac{66}{15}+\frac{109}{15}) Now, (\frac{-66 + 109}{15}=\frac{43}{15}=2\frac{13}{15})

Step3: Check reasonableness (for part c)

The estimate was (2) and the exact value is (2\frac{13}{15}\approx2.87). Since (2\frac{13}{15}) is close to the estimate of (2) (the difference between (2.87) and (2) is relatively small considering the rounding in the estimate), the exact answer is reasonable.

Answer:

a. Estimate: (2) (by rounding (-6\frac{3}{5}\approx - 7), (-(-7\frac{4}{15})\approx7), (2\frac{1}{5}\approx2) and calculating (-7 + 7+2)) b. Exact value: (\frac{43}{15}=2\frac{13}{15}) c. The exact value (2\frac{13}{15}\approx2.87) is close to the estimate of (2), so it is reasonable.