Finding the Least Common Denominator: 7/9 and 1/4 Explained

To find the least common denominator, we first need to identify the denominators in our fractions.We have two denominators to work with: 9 and 4.Let's break down each denominator into its prime factors. Starting with 9.Nine can be broken down into three times three. Three is a prime number, so we can't break it down any further.Now let's look at four.Four breaks down into two times two. Two is also a prime number.So we can write nine as three times three, and four as two times two.These prime factors are the building blocks we'll use to find the least common denominator.To find our LCD, we need to identify the prime factors of both numbers.Let's visualize how 9 breaks down into three times three.And 4 breaks down into two times two.To find the least common multiple, we take all prime factors using their highest powers from each number.Now we multiply all these factors together.We can visualize this as a grid of our prime factors: two twos from four, and two threes from nine.Multiplying all these factors together gives us thirty-six, our least common denominator.