Question

Find each quantity. $$\frac{3}{4} \text { of } 120$$

Short answer

90

Step-by-step solution

Understand the Problem

The problem is asking to find what is \(\frac{3}{4}\) of 120. This means we need to calculate \[ \frac{3}{4} \times 120 \]

Multiply the Numbers

To solve \(\frac{3}{4} \times 120\), first multiply the numerator 3 by 120: \(\frac{3 \times 120}{4}\)

Perform the Division

Next, divide the result by the denominator 4: \(\frac{360}{4}\). This gives 90.

Key concepts

numerator

In any fraction, the top number is known as the numerator. It represents the number of parts we are interested in. For example, in the fraction \(\frac{3}{4}\), the numerator is 3. This shows that we are considering 3 parts out of a total of 4 parts. When we multiply fractions, we start by multiplying the numerators together. In our example, we multiplied the numerator 3 by 120 to get 360. Never forget: the numerator is crucial in determining how many portions you have from a whole.

denominator

The bottom number of a fraction is called the denominator. It indicates the total number of equal parts the whole is divided into. In our example, \(\frac{3}{4}\), the denominator is 4. This tells us that the whole is divided into 4 equal parts. Once we multiply the numerator by the given number, we need to consider the denominator. After finding 360 in our previous step, we divide by the denominator 4 to find the final answer. The denominator helps us to properly scale our fraction to fit the given quantity.

division

Division is an essential operation in math. It helps us to distribute or share parts of a whole. In the problem \(\frac{3}{4} \text { of } 120\), after multiplying the numerator by 120, we use division in the final step. We divide 360 by the denominator 4. By doing this, we find how many equal parts each of these segments represents. This yields the final result, which is 90. Division breaks down complex multiplications into manageable pieces.

multiplication

Multiplication tells us how many times to add a number to itself. In fraction multiplication, we multiply across the numerators and across the denominators. For the problem \(\frac{3}{4} \text{ of} 120\), we started by multiplying the numerator 3 by 120. This gives us 360. When it comes to fractions, multiplication is straightforward: just multiply the top numbers together and the bottom numbers together. Multiplication can simplify complex problems when used with fractions, providing a clear method for problem-solving.