Problem 33 - Basic College Mathematics

Question

Multiply. $$ \frac{2}{11} \cdot 4 $$

Step-by-Step Solution

Answer

\frac{8}{11}

Step 1: Identify the given values

Given a fraction \( \frac{2}{11} \) and a whole number 4, notice that the multiplication between them is required.

Step 2: Rewrite the whole number as a fraction

To make it easier to multiply, rewrite the whole number 4 as a fraction \(\frac{4}{1}\).

Step 3: Multiply the numerators together

Multiply the numerators of the two fractions: \(\frac{2}{11} \cdot \frac{4}{1} \Rightarrow 2 \cdot 4 = 8\).

Step 4: Multiply the denominators together

Multiply the denominators of the two fractions: \(\frac{2}{11} \cdot \frac{4}{1} \Rightarrow 11 \cdot 1 = 11\).

Step 5: Write the final fraction

Combine the products of the numerators and denominators: \(\frac{8}{11}\). This is already in its simplest form.

Key Concepts

fractions

Fractions are a way to represent numbers that are not whole. They consist of two parts: a numerator and a denominator.
Imagine you have a pizza cut into 11 slices. If you eat 2 slices, you can describe the eaten part as a fraction: \(\frac{2}{11}\).
This fraction means 2 out of 11 parts.
Fractions are essential in everyday life, from cooking to dividing objects among people.
They help you understand portions and ratios.

numerator

The numerator is the top number of a fraction. It tells you how many parts of the whole you have.
In the fraction \(\frac{2}{11}\), the numerator is 2.
Think of the numerator as the number of pieces of a pie you have.
When multiplying fractions, you simply multiply the numerators together.
For example, \(2 \cdot 4 = 8\), which gives you the new numerator in the resulting fraction.

denominator

The denominator is the bottom number of a fraction. It denotes the total number of equal parts the whole is divided into.
In the fraction \(\frac{2}{11}\), the denominator is 11.
The denominator helps you understand the proportion of the parts you are working with.
When multiplying fractions, you also multiply the denominators together.
For instance, in our example, \(11 \cdot 1 = 11\), which remains the denominator in the final fraction.

whole numbers

Whole numbers are numbers without fractions or decimals. They include 0, 1, 2, 3, and so on.
When you multiply a whole number by a fraction, you can convert the whole number into a fraction for easier calculation.
For example, the whole number 4 can be written as \(\frac{4}{1}\).
This step ensures both numbers are in the same format, simplifying the multiplication process.
Understanding whole numbers and their interaction with fractions is crucial for accurate calculations in various scenarios.