Question

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

0.2 = ____ 0.28 = ____

1. what is the lcm of 4 and 6?

______

Explanation:

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

For \( 0.2 \):

Step 1: Write as fraction over 10

\( 0.2 = \frac{2}{10} \)

Step 2: Simplify by dividing numerator and denominator by GCD(2,10)=2

\( \frac{2\div2}{10\div2} = \frac{1}{5} \)

For \( 0.28 \):

Step 1: Write as fraction over 100

\( 0.28 = \frac{28}{100} \)

Step 2: Simplify by dividing numerator and denominator by GCD(28,100)=4

\( \frac{28\div4}{100\div4} = \frac{7}{25} \)

Step 1: Prime factorize 4 and 6

\( 4 = 2^2 \), \( 6 = 2 \times 3 \)

Step 2: Take highest power of each prime

For prime 2: \( 2^2 \); For prime 3: \( 3^1 \)

Step 3: Multiply these together

\( 2^2 \times 3 = 4 \times 3 = 12 \)

Answer:

(for Q5):
\( 0.2 = \boldsymbol{\frac{1}{5}} \), \( 0.28 = \boldsymbol{\frac{7}{25}} \)

Question 6: What is the LCM of 4 and 6?