Write the ratio as a fraction in simplest form, with whole numbers in the numerator and denominator.16 yd : 56 yd

1. Break Down the Problem

To express the ratio 16 yd : 56 yd as a fraction in simplest form, we need to divide both numbers by their greatest common divisor (GCD).

2. Relevant Concepts

The ratio can be written as a fraction: $\frac{16}{56}$ To simplify this fraction, we will find the GCD of 16 and 56.

3. Analysis and Detail

To find the GCD of 16 and 56:

• The factors of 16 are: 1, 2, 4, 8, 16
• The factors of 56 are: 1, 2, 4, 7, 8, 14, 28, 56

The GCD is the largest factor that both numbers share, which is 8.

Simplifying the fraction:

Now we divide both the numerator and the denominator by the GCD (8): $\frac{16 \div 8}{56 \div 8} = \frac{2}{7}$

4. Verify and Summarize

To verify, we can convert back from the simplified fraction to original values: $2 \times 56 = 112 \quad \text{and} \quad 7 \times 16 = 112$ Both calculations yield the same product, confirming that our simplification is correct.

Final Answer

The ratio 16 yd : 56 yd as a fraction in simplest form is $\frac{2}{7}$.