Problem 65 - Prealgebra

Question

Find \(\frac{3}{8}\) of 64.

Step-by-Step Solution

Answer

\( \frac{3}{8} \) of 64 is 24.

Step 1: Understand the Problem

We need to find the fraction \( \frac{3}{8} \) of the number 64. To do this, we need to multiply the fraction by the number.

Step 2: Set Up the Multiplication

Write the problem as a multiplication expression: \( \frac{3}{8} \times 64 \). This means we will multiply the numerator of the fraction by 64 and then divide by the denominator.

Step 3: Perform the Multiplication

First, perform the multiplication of the numerator by the whole number: \( 3 \times 64 = 192 \).

Step 4: Divide by the Denominator

Now, take the result from the multiplication and divide by the denominator: \( \frac{192}{8} \).

Step 5: Compute the Final Result

Divide 192 by 8: \( 192 \div 8 = 24 \). So, \( \frac{3}{8} \) of 64 is 24.

Key Concepts

Numerator and Denominator

Fractions are a crucial part of mathematics, and understanding their components helps solve many problems. A fraction consists of two parts: the numerator and the denominator.

• The numerator is the top number in a fraction, which indicates how many parts of the whole are being considered.
• The denominator is the bottom number, showing how many parts the whole is divided into.

In the fraction \( \frac{3}{8} \), 3 is the numerator and 8 is the denominator. This means we are considering 3 parts out of a total of 8 equal parts.
Understanding these components not only helps in identifying what part of the whole we're working with but also lays the groundwork for operations like multiplication and division with fractions.

Division in Fractions

Division is an integral operation in the realm of fractions. To truly grasp fraction division, it's important to understand what it entails.

• Dividing a fraction by a number involves splitting the parts represented by the numerator into more parts—that's where the denominator plays a crucial role.
• After multiplying the numerator by the whole number, division helps in scaling down the product to reflect the proper portion outlined by the denominator.

For instance, when we multiply 3 by 64 resulting in 192, we divide 192 by the denominator, which is 8 in our original fraction \( \frac{3}{8} \). This division calculates how many full sets of 8 can be made from 192, ultimately providing the answer of 24.

Whole Numbers Multiplication

Multiplying whole numbers with fractions might seem daunting, but by breaking it into steps, it becomes simpler.

• Start by multiplying the whole number with the numerator of the fraction.
• Ignore the denominator initially when performing this multiplication.

In our exercise, multiplying the whole number 64 by the numerator 3 gives us 192. This step translates the fractional division into a form that's ready to be simplified by the denominator.
Mastering whole numbers multiplication in the context of fractions opens doors to solving more complex fraction calculations with ease, providing a strong foundation for understanding even larger mathematical concepts.