Question

1. what is the lcm of 15 and 25? *

your answer

1. what is the gcf of 16 and 54? *

your answer

1. find the unknown value in the pair of equivalent fractions. *

\\(\frac{1}{8}=\frac{?}{4}\\)
your answer

Explanation:

Question 12:

Step1: Prime factorize 15 and 25

Prime factorization of \( 15 = 3 \times 5 \)
Prime factorization of \( 25 = 5 \times 5 \)

Step2: Find LCM by taking highest powers

For LCM, we take the highest power of each prime factor present.
For prime factor 3: highest power is \( 3^1 \)
For prime factor 5: highest power is \( 5^2 \)
So, \( LCM = 3^1 \times 5^2 = 3 \times 25 = 75 \)

Step1: Prime factorize 16 and 54

Prime factorization of \( 16 = 2 \times 2 \times 2 \times 2 = 2^4 \)
Prime factorization of \( 54 = 2 \times 3 \times 3 \times 3 = 2^1 \times 3^3 \)

Step2: Find GCF by taking lowest powers

For GCF, we take the lowest power of common prime factors.
The common prime factor is 2, and its lowest power is \( 2^1 \)
So, \( GCF = 2 \)

Step1: Let the unknown be \( x \)

We have the equation \( \frac{1}{8}=\frac{x}{4} \)

Step2: Cross - multiply to solve for \( x \)

Cross - multiplying gives \( 8x = 1\times4 \)
Then, \( x=\frac{4}{8}=\frac{1}{2}=0.5 \) (or we can think of it as dividing the denominator 8 by 2 to get 4, so we also divide the numerator 1 by 2 to get \( \frac{1}{2} \))

Answer:

75

Question 13: