Let's solve each part one by one by finding the compounded ratios.
### a) Compounded ratio of [tex]\(1: 2\)[/tex] and [tex]\(4: 3\)[/tex]
To find the compounded ratio:
1. Multiply the numerators: [tex]\(1 \times 4 = 4\)[/tex].
2. Multiply the denominators: [tex]\(2 \times 3 = 6\)[/tex].
So the compounded ratio is [tex]\( \frac{4}{6} \)[/tex].
### b) Compounded ratio of [tex]\(6: 5\)[/tex] and [tex]\(1: 4\)[/tex]
To find the compounded ratio:
1. Multiply the numerators: [tex]\(6 \times 1 = 6\)[/tex].
2. Multiply the denominators: [tex]\(5 \times 4 = 20\)[/tex].
So the compounded ratio is [tex]\( \frac{6}{20} \)[/tex].
### c) Compounded ratio of [tex]\(7: 9\)[/tex] and [tex]\(6: 5\)[/tex]
To find the compounded ratio:
1. Multiply the numerators: [tex]\(7 \times 6 = 42\)[/tex].
2. Multiply the denominators: [tex]\(9 \times 5 = 45\)[/tex].
So the compounded ratio is [tex]\( \frac{42}{45} \)[/tex].
### d) Compounded ratio of [tex]\(8: 3\)[/tex] and [tex]\(15: 16\)[/tex]
To find the compounded ratio:
1. Multiply the numerators: [tex]\(8 \times 15 = 120\)[/tex].
2. Multiply the denominators: [tex]\(3 \times 16 = 48\)[/tex].
So the compounded ratio is [tex]\( \frac{120}{48} \)[/tex].
Thus, the compounded ratios are:
1. [tex]\( \frac{4}{6} \)[/tex]
2. [tex]\( \frac{6}{20} \)[/tex]
3. [tex]\( \frac{42}{45} \)[/tex]
4. [tex]\( \frac{120}{48} \)[/tex]
