Question

Select all ratios equivalent to 7:4.
77:44
22:7
13:1
25:6

Answer 1

To find ratios equivalent to \( 7:4 \), we can simplify or compare each of the given ratios to see if they reduce to the same fraction.

1. **\( 77:44 \)**
To simplify \( 77:44 \), we can divide both numbers by their greatest common divisor, which is 11:
\[
77 \div 11 = 7 \quad \text{and} \quad 44 \div 11 = 4
\]
Thus, \( 77:44 \) simplifies to \( 7:4 \), which is equivalent.

2. **\( 22:7 \)**
To see if \( 22:7 \) is equivalent to \( 7:4 \), we can compare \( \frac{22}{7} \) and \( \frac{7}{4} \):
Cross-multiplying gives \( 22 \times 4 \) and \( 7 \times 7 \):
\[
88 \neq 49
\]
Therefore, \( 22:7 \) is not equivalent.

3. **\( 13:1 \)**
Compare \( \frac{13}{1} \) and \( \frac{7}{4} \):
Cross-multiplying gives \( 13 \times 4 \) and \( 7 \times 1 \):
\[
52 \neq 7
\]
Thus, \( 13:1 \) is not equivalent.

4. **\( 25:6 \)**
Compare \( \frac{25}{6} \) and \( \frac{7}{4} \):
Cross-multiplying gives \( 25 \times 4 \) and \( 7 \times 6 \):
\[
100 \neq 42
\]
Therefore, \( 25:6 \) is not equivalent.

In conclusion, the only ratio equivalent to \( 7:4 \) is:

- **\( 77:44 \)**