Sure! Let's go step-by-step to find two equivalent ratios for each given ratio.
### a) \(3:1\)
To find equivalent ratios, we multiply both terms of the ratio by the same number.
1. Multiply both terms by 2:
- \(3 \times 2 = 6\)
- \(1 \times 2 = 2\)
So, one equivalent ratio is \(6:2\).
2. Multiply both terms by 3:
- \(3 \times 3 = 9\)
- \(1 \times 3 = 3\)
Thus, another equivalent ratio is \(9:3\).
Therefore, the two equivalent ratios for \(3:1\) are \(6:2\) and \(9:3\).
### b) \(4:2\)
1. Multiply both terms by 2:
- \(4 \times 2 = 8\)
- \(2 \times 2 = 4\)
One equivalent ratio is \(8:4\).
2. Multiply both terms by 3:
- \(4 \times 3 = 12\)
- \(2 \times 3 = 6\)
Another equivalent ratio is \(12:6\).
Therefore, the two equivalent ratios for \(4:2\) are \(8:4\) and \(12:6\).
### c) \(1:2\)
1. Multiply both terms by 2:
- \(1 \times 2 = 2\)
- \(2 \times 2 = 4\)
One equivalent ratio is \(2:4\).
2. Multiply both terms by 3:
- \(1 \times 3 = 3\)
- \(2 \times 3 = 6\)
Another equivalent ratio is \(3:6\).
Therefore, the two equivalent ratios for \(1:2\) are \(2:4\) and \(3:6\).
### f) \(4:9\)
1. Multiply both terms by 2:
- \(4 \times 2 = 8\)
- \(9 \times 2 = 18\)
One equivalent ratio is \(8:18\).
2. Multiply both terms by 3:
- \(4 \times 3 = 12\)
- \(9 \times 3 = 27\)
Another equivalent ratio is \(12:27\).
Therefore, the two equivalent ratios for \(4:9\) are \(8:18\) and \(12:27\).
### g) \(7:8\)
1. Multiply both terms by 2:
- \(7 \times 2 = 14\)
- \(8 \times 2 = 16\)
One equivalent ratio is \(14:16\).
2. Multiply both terms by 3:
- \(7 \times 3 = 21\)
- \(8 \times 3 = 24\)
Another equivalent ratio is \(21:24\).
Therefore, the two equivalent ratios for \(7:8\) are \(14:16\) and \(21:24\).
### h) \(8:3\)
1. Multiply both terms by 2:
- \(8 \times 2 = 16\)
- \(3 \times 2 = 6\)
One equivalent ratio is \(16:6\).
2. Multiply both terms by 3:
- \(8 \times 3 = 24\)
- \(3 \times 3 = 9\)
Another equivalent ratio is \(24:9\).
Therefore, the two equivalent ratios for [tex]\(8:3\)[/tex] are [tex]\(16:6\)[/tex] and [tex]\(24:9\)[/tex].
