Question

1. convert each decimal to a fraction in simplest form.

0.9 =
0.45 =

1. what is the lcm of 3 and 5?

Explanation:

Question 5: Convert each decimal to a fraction in simplest form.

For \( 0.9 \):

Step1: Write as fraction over 10

Since \( 0.9 \) is one decimal place, we can write it as \( \frac{9}{10} \).

Step2: Check if reducible

The greatest common divisor (GCD) of 9 and 10 is 1, so it's already in simplest form.

Step1: Write as fraction over 100

Since \( 0.45 \) is two decimal places, we write it as \( \frac{45}{100} \).

Step2: Simplify the fraction

Find the GCD of 45 and 100. The GCD of 45 and 100 is 5. Divide numerator and denominator by 5: \( \frac{45\div5}{100\div5}=\frac{9}{20} \).

Step1: Recall LCM of coprime numbers

3 and 5 are coprime (their GCD is 1). For coprime numbers, the LCM is the product of the numbers.

Step2: Calculate the product

Multiply 3 and 5: \( 3\times5 = 15 \).

Answer:

\( \frac{9}{10} \)

For \( 0.45 \):