Certainly! Let's solve each expression step-by-step using the distributive property.
### (i) [tex]\(\left\{\frac{1}{5} \times\left(\frac{-3}{12}\right)\right\}+\left\{\frac{7}{5} \times \frac{5}{12}\right\}\)[/tex]
1. First term:
[tex]\[
\frac{1}{5} \times \left(\frac{-3}{12}\right)
\][/tex]
Multiply the fractions:
[tex]\[
\frac{1 \times (-3)}{5 \times 12} = \frac{-3}{60} = -\frac{1}{20} = -0.05
\][/tex]
So, the first term is [tex]\(-0.05\)[/tex].
2. Second term:
[tex]\[
\frac{7}{5} \times \frac{5}{12}
\][/tex]
Multiply the fractions:
[tex]\[
\frac{7 \times 5}{5 \times 12} = \frac{35}{60} = \frac{7}{12} \approx 0.5833333333333334
\][/tex]
So, the second term is approximately [tex]\(0.5833333333333334\)[/tex].
3. Sum the two terms:
[tex]\[
-0.05 + 0.5833333333333334 \approx 0.5333333333333333
\][/tex]
Therefore, the result of the first expression is [tex]\(0.5333333333333333\)[/tex].
### (ii) [tex]\(\left\{\frac{9}{16} \times \frac{4}{12}\right\}+\left\{\frac{9}{16} \times \frac{-3}{9}\right\}\)[/tex]
1. First term:
[tex]\[
\frac{9}{16} \times \frac{4}{12}
\][/tex]
Multiply the fractions:
[tex]\[
\frac{9 \times 4}{16 \times 12} = \frac{36}{192} = \frac{3}{16} = 0.1875
\][/tex]
So, the first term is [tex]\(0.1875\)[/tex].
2. Second term:
[tex]\[
\frac{9}{16} \times \frac{-3}{9}
\][/tex]
Multiply the fractions:
[tex]\[
\frac{9 \times (-3)}{16 \times 9} = \frac{-27}{144} = \frac{-3}{16} = -0.1875
\][/tex]
So, the second term is [tex]\(-0.1875\)[/tex].
3. Sum the two terms:
[tex]\[
0.1875 + (-0.1875) = 0
\][/tex]
Therefore, the result of the second expression is [tex]\(0.0\)[/tex].
### Summary
- The result of [tex]\(\left\{\frac{1}{5} \times\left(\frac{-3}{12}\right)\right\}+\left\{\frac{7}{5} \times \frac{5}{12}\right\}\)[/tex] is approximately [tex]\(0.5333333333333333\)[/tex].
- The result of [tex]\(\left\{\frac{9}{16} \times \frac{4}{12}\right\}+\left\{\frac{9}{16} \times \frac{-3}{9}\right\}\)[/tex] is [tex]\(0.0\)[/tex].
