What is 15 Over 100 Simplified?

What is 15 Over 100 Simplified?

To simplify 15 over 100, you can reduce the fraction by dividing both the numerator and denominator by their greatest common divisor, which is 5.

15 ÷ 5 = 3 100 ÷ 5 = 20

So, 15 over 100 simplifies to 3/20.

Simplifying Fractions

Fractions express a part-to-whole relationship between numbers. Simplifying a fraction involves rewriting it in lowest terms to express the ratio in its simplest form. For example, the fraction 15/100 can be simplified by reducing it to a lower numerator and denominator.

Let’s look at the step-by-step process:

Factor the Numerator and Denominator

15 = 3 x 5 100 = 2 x 2 x 5 x 5

The greatest common factor (GCF) between 15 and 100 is 5.

Divide By the GCF

To simplify, divide both the numerator and denominator by the GCF:

15/100 Divide numerator and denominator by 5: 15/5 / 100/5 The GCF divides out: 3/20

So 15/100 simplified is 3/20.

Understanding Simplifying

Simplifying fractions makes them easier to add, subtract, multiply and divide. Simpler fractions also help reveal the underlying numerical relationship.

For example:

15/100 = 0.15 = 15%

All express a part-to-whole relationship, but the simplified form makes the ratio clearer.

Checking the Work

We can double check that 3/20 is the simplified form of 15/100 by multiplying the simplified fraction back to the original:

3/20 * (20/5) = 15/100

Since the product equals the original fraction, this confirms that 3/20 is the correctly simplified form.

Being comfortable simplifying fractions by reducing terms develops fluency with fractions as the most fundamental rational numbers. Simplest form aids deeper understanding.

In summary, to simplify a fraction, factor the numerator and denominator completely, identify the GCF, and divide both numerator and denominator by that GCF. This provides the fraction in lowest terms.