Sure, let's go step by step through the problem and solution.
### Part 1: Multiplying Fractions and Whole Numbers
#### (a) [tex]\(\frac{2}{7} \times 3\)[/tex]
When multiplying a fraction by a whole number, multiply the numerator by the whole number while keeping the denominator the same.
[tex]\[
\frac{2}{7} \times 3 = \frac{2 \times 3}{7} = \frac{6}{7}
\][/tex]
In decimal form:
[tex]\[
\frac{6}{7} \approx 0.8571
\][/tex]
#### (b) [tex]\(\frac{9}{7} \times 6\)[/tex]
Similarly, multiply the numerator by the whole number and keep the denominator unchanged.
[tex]\[
\frac{9}{7} \times 6 = \frac{9 \times 6}{7} = \frac{54}{7}
\][/tex]
This is an improper fraction. To express it as a mixed fraction:
[tex]\[
54 \div 7 = 7 \text{ R } 5 \implies \frac{54}{7} = 7 \frac{5}{7}
\][/tex]
In decimal form:
[tex]\[
7 \frac{5}{7} \approx 7.7143
\][/tex]
#### (c) [tex]\(3 \times \frac{1}{8}\)[/tex]
Multiply the whole number by the numerator of the fraction.
[tex]\[
3 \times \frac{1}{8} = \frac{3 \times 1}{8} = \frac{3}{8}
\][/tex]
In decimal form:
[tex]\[
\frac{3}{8} = 0.375
\][/tex]
#### (d) [tex]\(\frac{13}{11} \times \frac{1}{2}\)[/tex]
For this multiplication, multiply the numerators together and the denominators together.
[tex]\[
\frac{13}{11} \times \frac{1}{2} = \frac{13 \times 1}{11 \times 2} = \frac{13}{22}
\][/tex]
In decimal form:
[tex]\[
\frac{13}{22} \approx 0.5909
\][/tex]
### Part 2: Represent Pictorially [tex]\(2 \times \frac{2}{5} = \frac{4}{5}\)[/tex]
To represent the multiplication [tex]\(2 \times \frac{2}{5}\)[/tex] pictorially:
1. Start with the fraction [tex]\(\frac{2}{5}\)[/tex].
2. Multiply this fraction by 2:
[tex]\[
2 \times \frac{2}{5} = \frac{2 \times 2}{5} = \frac{4}{5}
\][/tex]
So, [tex]\( \frac{4}{5}\)[/tex].
In this pictorial representation, if you have a shape divided into 5 equal parts, 2 such shapes would have 4 parts shaded out of 5. This shows the fraction [tex]\( \frac{4}{5} \)[/tex].
### Summary:
- [tex]\(\frac{2}{7} \times 3 = \frac{6}{7} \approx 0.8571 \)[/tex]
- [tex]\(\frac{9}{7} \times 6 = \frac{54}{7} \approx 7.7143 \)[/tex]
- [tex]\(3 \times \frac{1}{8} = \frac{3}{8} = 0.375 \)[/tex]
- [tex]\(\frac{13}{11} \times \frac{1}{2} = \frac{13}{22} \approx 0.5909 \)[/tex]
- [tex]\(2 \times \frac{2}{5} = \frac{4}{5} = 0.8 \)[/tex]
Thus, these calculations lead to the final results outlined above.
