Of course! Let's find two equivalent ratios for each of the given ratios.
### Part (i): Finding two equivalent ratios for [tex]\(1:2\)[/tex]
We start with the ratio [tex]\(1:2\)[/tex]. To find equivalent ratios, we can multiply both parts of the ratio by the same number.
1. First Equivalent Ratio:
- Multiply both parts of the ratio by 2:
[tex]\[
1 \times 2 = 2,\quad 2 \times 2 = 4
\][/tex]
- Therefore, the first equivalent ratio is [tex]\(2:4\)[/tex].
2. Second Equivalent Ratio:
- Multiply both parts of the ratio by 3:
[tex]\[
1 \times 3 = 3,\quad 2 \times 3 = 6
\][/tex]
- Therefore, the second equivalent ratio is [tex]\(3:6\)[/tex].
So, the two equivalent ratios for [tex]\(1:2\)[/tex] are [tex]\(2:4\)[/tex] and [tex]\(3:6\)[/tex].
### Part (ii): Finding two equivalent ratios for [tex]\(5:3\)[/tex]
Next, we start with the ratio [tex]\(5:3\)[/tex]. Similarly, we will multiply both parts of the ratio by the same number.
1. First Equivalent Ratio:
- Multiply both parts of the ratio by 2:
[tex]\[
5 \times 2 = 10,\quad 3 \times 2 = 6
\][/tex]
- Therefore, the first equivalent ratio is [tex]\(10:6\)[/tex].
2. Second Equivalent Ratio:
- Multiply both parts of the ratio by 3:
[tex]\[
5 \times 3 = 15,\quad 3 \times 3 = 9
\][/tex]
- Therefore, the second equivalent ratio is [tex]\(15:9\)[/tex].
So, the two equivalent ratios for [tex]\(5:3\)[/tex] are [tex]\(10:6\)[/tex] and [tex]\(15:9\)[/tex].
### Summary
The two equivalent ratios for each given ratio are:
1. For [tex]\(1:2\)[/tex]:
- [tex]\(2:4\)[/tex]
- [tex]\(3:6\)[/tex]
2. For [tex]\(5:3\)[/tex]:
- [tex]\(10:6\)[/tex]
- [tex]\(15:9\)[/tex]
