Problem 26 - Basic College Mathematics

Question

Multiply and simplify. $$ 18 \cdot \frac{5}{6} $$

Step-by-Step Solution

Answer

15

Step 1: Write the given expression

Express the problem as a multiplication: the given problem is written as \(18 \times \frac{5}{6} \)

Step 2: Simplify the expression

Before performing the multiplication, simplify the expression if possible. In this case, you can simplify by canceling out the common factor of 6 in both 18 and 6. Rewrite 18 as \(18 = 3 \times 6 \) and then the expression becomes \( \frac{3 \times 6 \times 5}{6} \), now cancel the common factor of 6 to get \(3 \times 5 \).

Step 3: Perform the multiplication

Now, multiply 3 and 5: \(3 \times 5 = 15\)

Key Concepts

fraction simplification

Simplifying fractions is a key mathematical skill. It involves reducing a fraction to its simplest form, making it easier to work with. In our exercise, we started with the expression \(18 \times \frac{5}{6}\). To simplify, we looked for common factors in the numerator and the denominator.

numerical multiplication

Numerical multiplication is the process of finding the product of two numbers. In this exercise, we needed to multiply two integers. After simplifying the fraction, \( \frac{3 \times 6 \times 5}{6} \), we cancelled out the common factor 6, which led us to \(3 \times 5 = 15\). Multiplying these remaining numbers gave us the final answer.

common factors

Recognizing common factors simplifies complex multiplication. In our problem, we decomposed 18 into \( 3 \times 6 \). Noticing 6 in both the numerator and denominator, cancelling these factors efficiently decreased the numbers involved. This lead to an easier multiplication of 3 and 5, resulting in 15.