Select all ratios equivalent to 6:4.

Steps to Solve

1. Identify the Simplified Ratio

The given ratio is (6:4). To simplify it, divide both numbers by their greatest common divisor (GCD), which is (2):

[ \frac{6 \div 2}{4 \div 2} = \frac{3}{2}
]

So the simplified form is (3:2).

2. Simplify Each Ratio

Now, simplify each of the provided ratios to check if any of them equal (3:2).

• Ratio 1: (60:2)
  Divide both parts by (2):
  [ \frac{60 \div 2}{2 \div 2} = \frac{30}{1} \quad \text{(not equivalent)} ]

• Ratio 2: (35:6)
  This ratio cannot be simplified to (3:2). It is already in its simplest form: (35:6) (not equivalent).

• Ratio 3: (4:14)
  Divide both parts by (2):
  [ \frac{4 \div 2}{14 \div 2} = \frac{2}{7} \quad \text{(not equivalent)} ]

• Ratio 4: (42:28)
  Divide both parts by (14):
  [ \frac{42 \div 14}{28 \div 14} = \frac{3}{2} \quad \text{(equivalent)} ]

3. Conclusion
   The only ratio equivalent to (6:4) (or (3:2)) is (42:28).