Question

Write each of the fractions below in simplest form.

What do you notice about the fractions? Use your
results to explain why it is helpful to simplify a fraction
before writing it as a decimal.
30/40 12/16 27/36

Answer 1

All the provided fractions simplify to 3/4. Simplifying fractions makes it easier to identify equivalent values and simplifies calculations, including converting fractions to decimals.

Step-by-step explanation:

Let's write each of the given fractions in its simplest form. We need to find the greatest common divisor (GCD) for each fraction's numerator and denominator and then divide both by their GCD to simplify.

• For 30/40, the GCD is 10. So, 30 ÷ 10 = 3 and 40 ÷ 10 = 4. The simplest form is 3/4.
• With 12/16, the GCD is 4. Therefore, 12 ÷ 4 = 3 and 16 ÷ 4 = 4. The simplest form is 3/4.
• For 27/36, the GCD is 9. Thus, 27 ÷ 9 = 3 and 36 ÷ 9 = 4. The simplest form is 3/4.

What we notice about the simplified fractions is that they all equal 3/4. Simplifying fractions is helpful before writing them as decimals because it makes it evident when different fractions represent the same value. This simplification also avoids unnecessary complexity in calculations and helps us recognize equivalent ratios more quickly.