Practice Exercise Questions:

Directions: Write each fraction or ratio in the simplest form.

1. [tex]\( \frac{16}{32} = \frac{1}{2} \)[/tex]

2. [tex]\( \frac{16}{16} = 1 \)[/tex]

3. [tex]\( \frac{32}{16} = 2 \)[/tex]

4. [tex]\( \frac{50}{75} = \frac{2}{3} \)[/tex]

5. [tex]\( \frac{50}{25} = 2 \)[/tex]

6. [tex]\( \frac{75}{25} = 3 \)[/tex]

7. Simplify [tex]\( \frac{32}{70} \)[/tex]

8. Simplify [tex]\( \frac{17}{35} \)[/tex]

Sure! Let's break down how to simplify these fractions and ratios step by step.

1. Simplifying the Ratio 13.16:32

- To simplify the ratio, we look for a common factor to divide both numbers by.
- Here, 13.16 divided by 16 gives 0.82, and 32 divided by 16 gives 2.
- This means the simplified form of the ratio 13.16:32 is 0.82:2.

2. Simplifying the Fraction 14.50/75

- We need to simplify this fraction to its simplest form by finding the greatest common divisor (GCD).
- The GCD of 1450 (14.50 turned into an integer) and 7500 is determined to be 50.
- Dividing both the numerator and the denominator by 50, we get 1450/50 = 29 and 7500/50 = 150.
- Thus, the fraction 14.50/75 simplifies to 29/150.

3. Simplifying the Number 32.70

- The number 32.70 is already in simplest form as it is a decimal number.
- Therefore, it remains 32.7.

4. Simplifying the Fraction 17/35

- We want to check if 17/35 has a common divisor other than 1.
- The numbers 17 and 35 have no common divisors other than 1.
- Therefore, the fraction 17/35 is already in its simplest form.

I hope this detailed explanation helps you understand how to simplify each fraction or ratio! If you have any more questions, feel free to ask.