Question

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

0.4 = ____ 0.16 = ____

1. what is the lcm of 8 and 12?

Explanation:

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

For \(0.4\):

Step 1: Write as fraction over 10

\(0.4=\frac{4}{10}\)

Step 2: Simplify the fraction

Divide numerator and denominator by their GCD (2). \(\frac{4\div2}{10\div2}=\frac{2}{5}\)

Step 1: Write as fraction over 100

\(0.16 = \frac{16}{100}\)

Step 2: Simplify the fraction

Divide numerator and denominator by their GCD (4). \(\frac{16\div4}{100\div4}=\frac{4}{25}\)

Step 1: Prime factorize 8 and 12

Prime factors of \(8 = 2\times2\times2=2^{3}\)
Prime factors of \(12=2\times2\times3 = 2^{2}\times3\)

Step 2: Find LCM using prime factors

LCM is the product of the highest powers of all prime factors. So, for prime 2, highest power is \(2^{3}\), for prime 3, highest power is \(3^{1}\). Then \(LCM=2^{3}\times3=8\times3 = 24\)

Answer:

\(\frac{2}{5}\)

For \(0.16\):