Question

estimate 10/9 - 7/6 =

Answer 1

To estimate \( \frac{10}{9} - \frac{7}{6} \), we can first convert the fractions to a more manageable form.

1. The decimal approximation of \( \frac{10}{9} \) is approximately \( 1.11 \).
2. The decimal approximation of \( \frac{7}{6} \) is approximately \( 1.17 \).

Now, we can subtract the two estimated values:

\[
1.11 - 1.17 \approx -0.06
\]

For more accuracy, we can calculate the fractions with a common denominator:

The least common multiple (LCM) of 9 and 6 is 18.

Rewriting the fractions with a denominator of 18:

\[
\frac{10}{9} = \frac{10 \times 2}{9 \times 2} = \frac{20}{18}
\]

\[
\frac{7}{6} = \frac{7 \times 3}{6 \times 3} = \frac{21}{18}
\]

Now we can subtract:

\[
\frac{20}{18} - \frac{21}{18} = \frac{20 - 21}{18} = \frac{-1}{18}
\]

So, \( \frac{10}{9} - \frac{7}{6} = -\frac{1}{18} \), which is approximately \( -0.056 \).

Thus, the estimated value is approximately \( -0.06 \).