Understanding the Rules of Multiplication

Oct 13, 2025 by recoveryshake.com 134 views

When it comes to multiplication, we often think of multiplying whole numbers together. However, in this case, we have a mix of whole numbers and fractions. The question asks us to multiply 3, 5, and 1/5 together. To solve this problem, we need to understand the rules of multiplying fractions and whole numbers.

Understanding the Rules of Multiplication

When multiplying fractions, we multiply the numerators (the numbers on top) together and the denominators (the numbers on the bottom) together. This is represented by the following formula:

${ \frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d} }$

However, when multiplying a fraction by a whole number, we can simply multiply the numerator by the whole number and keep the denominator the same. This is represented by the following formula:

${ \frac{a}{b} \times c = \frac{a \times c}{b} }$

Applying the Rules to the Problem

Now that we understand the rules of multiplication, let's apply them to the problem at hand. We have 3, 5, and 1/5 that we need to multiply together. We can start by multiplying 3 and 5 together, which gives us:

${ 3 \times 5 = 15 }$

Next, we need to multiply 15 by 1/5. To do this, we can multiply the numerator (15) by 1 and keep the denominator (5) the same. This gives us:

${ 15 \times \frac{1}{5} = \frac{15 \times 1}{5} = \frac{15}{5} }$

Simplifying the Fraction

Now that we have the fraction 15/5, we can simplify it by dividing both the numerator and the denominator by their greatest common divisor (GCD). In this case, the GCD of 15 and 5 is 5. So, we can divide both the numerator and the denominator by 5 to get:

${ \frac{15}{5} = \frac{15 \div 5}{5 \div 5} = \frac{3}{1} }$

Conclusion

In conclusion, when multiplying 3, 5, and 1/5 together, we get 3. This is because multiplying a fraction by a whole number is equivalent to multiplying the numerator by the whole number and keeping the denominator the same.

Final Answer

The final answer is $\boxed{3}$ .

Additional Examples

To further illustrate the concept of multiplying fractions and whole numbers, let's consider a few more examples.

Example 1

${ 2 \times \frac{3}{4} = \frac{2 \times 3}{4} = \frac{6}{4} }$

Example 2

${ 4 \times \frac{2}{3} = \frac{4 \times 2}{3} = \frac{8}{3} }$

Example 3

${ 1 \times \frac{5}{6} = \frac{1 \times 5}{6} = \frac{5}{6} }$

In each of these examples, we multiplied a whole number by a fraction and got a new fraction as a result. This demonstrates the rule that multiplying a fraction by a whole number is equivalent to multiplying the numerator by the whole number and keeping the denominator the same.

Common Mistakes to Avoid

When multiplying fractions and whole numbers, there are a few common mistakes to avoid.

Not simplifying the fraction: Make sure to simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD).
Not following the order of operations: Make sure to follow the order of operations (PEMDAS) when multiplying fractions and whole numbers.
Not using the correct formula: Make sure to use the correct formula for multiplying fractions and whole numbers.

By following these tips and avoiding common mistakes, you can ensure that you are multiplying fractions and whole numbers correctly.