**To multiply fractions, you multiply the numerators (top numbers) together and the denominators (bottom numbers) together. So, 1/2 times 1/3 equals (11) / (23), which simplifies to 1/6. Therefore, 1/2 times 1/3 equals 1/6.**

Here’s a table showing the multiplication of 1/2 and 1/3:

Fraction 1 | Fraction 2 | Result |
---|---|---|

1/2 | 1/3 | 1/6 |

Fractions are an important foundation of mathematics that comes up regularly in everyday life. Understanding fractions enables us to handle measurements, divide things evenly, interpret data, and express quantities precisely. In this post, we’ll work through a straightforward fractions multiplication problem step-by-step: 1/2 times 1/3. Along the way, we’ll review key techniques for multiplying, reducing, and converting fractions. Learning and practicing these essential skills builds fluency with fractions and confidence in math overall.

## Understanding the Problem

First, let’s parse out exactly what the question is asking us to do. We are being asked to multiply the two fractions 1/2 and 1/3. 1/2 can be read as “one half”, meaning we have one part out of a total of two equal parts. 1/3 can be read as “one third”, meaning we have one part out of three equal parts. To multiply fractions correctly, we’ll need to recall some important rules and procedures. Proper set-up here will ensure we arrive at the right solution.

## Multiplying Fractions

When multiplying fractions, we multiply the numerators together and multiply the denominators together. The numerator is the top number in a fraction, and the denominator is the bottom number. For our example problem, the multiplication would be:

(1/2) x (1/3) = (1 x 1) / (2 x 3) = 1/6

We took the numerator of 1/2 and multiplied it by the numerator of 1/3, which is 1 x 1 = 1. Then we took 2 and multiplied it by 3, the denominators, which is 2 x 3 = 6. This process of keeping the numerators and denominators separate and only multiplying straight across is how to correctly multiply fractions.

## Reducing the Fraction

The result of multiplying 1/2 and 1/3 is 1/6. However, this fraction can be simplified by reducing it. To reduce a fraction, we determine the greatest common factor (GCF) between the numerator and denominator and divide both by that number. In this case, the GCF of 1 and 6 is 1. Dividing the numerator and denominator of 1/6 by 1 gives us our reduced, simplified result of:

1/6 = 1/6

So the fully simplified product of 1/2 and 1/3 is 1/6.

## Converting to a Decimal

To convert the fraction 1/6 to a decimal, we divide the numerator by the denominator:

1/6 = 1 ÷ 6 = 0.166… = 0.17 (rounded to hundredths)

Being able to convert back and forth between fraction and decimal forms allows us to operate flexibly based on what the question requires.

## Checking Our Work

Whenever possible, it’s a good idea to use a different method to verify that our original work is correct. Let’s check the multiplication 1/2 x 1/3 using an alternate approach:

1/2 = 0.5 (convert to decimal) 1/3 = 0.33… (convert to decimal)

0.5 x 0.33 = 0.165 = 0.17 (rounded to hundredths)

Multiplying the decimal equivalents gives us 0.17, the same result we got originally when reducing 1/6. Getting the identical solution by two methods confirms our calculations are accurate.

## Key Concepts and Takeaways

Let’s recap some of the important fractions concepts utilized when multiplying 1/2 and 1/3:

- Multiplying fractions means keeping numerators and denominators separate, only multiplying straight across.
- A fraction can be reduced by dividing the numerator and denominator by their greatest common factor. This keeps the value the same in simplest form.
- Converting fractions to decimals (or vice versa) involves dividing the numerator by the denominator. Completing operations flexibly relies on being able to move between forms.
- Checking work using a different method catches potential errors. Verifying the accuracy of solutions builds confidence.
- Fractions skills are interconnected – being competent multiplying fractions relies on competency with reducing, converting, finding GCFs, etc. Mastery develops through regular practice.
- Solving straightforward problems like 1/2 x 1/3 prepares learners to handle more complex fractional equations down the road. Fundamentals first.

## Conclusion

In this post, we took the step-by-step approach to fully solve 1/2 times 1/3, while reviewing key fractions concepts like multiplying, reducing, and converting between fraction and decimal form. Mastering core skills with basic problems paves the way for solving more advanced math problems utilizing fractions. Regular practice builds fluency and understanding. Fractions lay the groundwork for algebra, geometry, chemistry, physics, and more. Developing mathematical thinking and number sense starts with fractions. Each solved problem brings learners one step closer to conceptual mastery of the deeper ideas underlying elementary math. Keep practicing those fractions!

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