Question

ratios equivalent to 3:15

Answer 1

To find ratios equivalent to \(3:15\), we can simplify the ratio first and then generate equivalent ratios by multiplying or dividing both parts by the same non-zero number.

1. **Simplifying the Ratio**:
- The greatest common divisor (GCD) of 3 and 15 is 3.
- Divide both numbers by 3:
\[
\frac{3}{3} : \frac{15}{3} = 1:5
\]
- Therefore, \(3:15\) simplifies to \(1:5\).

2. **Creating Equivalent Ratios**:
- To create equivalent ratios, we can multiply both parts of the simplified ratio \(1:5\) by the same positive integer. Here are a few examples:
- Multiply by 2:
\[
1 \times 2 : 5 \times 2 = 2:10
\]
- Multiply by 3:
\[
1 \times 3 : 5 \times 3 = 3:15 \quad (\text{original ratio})
\]
- Multiply by 4:
\[
1 \times 4 : 5 \times 4 = 4:20
\]
- Multiply by 5:
\[
1 \times 5 : 5 \times 5 = 5:25
\]
- Multiply by 6:
\[
1 \times 6 : 5 \times 6 = 6:30
\]

In summary, some ratios equivalent to \(3:15\) are:
- \(1:5\)
- \(2:10\)
- \(4:20\)
- \(5:25\)
- \(6:30\)
- \(10:50\) (by multiplying by 10, for example)

You can generate infinitely many equivalent ratios by multiplying by any positive integer.