Simplifying Fractions: 10/11 x 7/9 x 1/2
When dealing with fractions, it's essential to simplify them to their simplest form. In this article, we'll dive into the world of fractions and explore how to simplify the complex expression: 10/11 x 7/9 x 1/2.
Step 1: Multiply the Fractions
To simplify this expression, we need to multiply the fractions. To do this, we'll multiply the numerators (the numbers on top) and multiply the denominators (the numbers on the bottom), like this:
(10/11) × (7/9) × (1/2) = (10 × 7 × 1) / (11 × 9 × 2)
Step 2: Simplify the Numerator
Now, let's simplify the numerator:
10 × 7 × 1 = 70
Step 3: Simplify the Denominator
Next, let's simplify the denominator:
11 × 9 × 2 = 198
Step 4: Write the Simplified Fraction
Now, we can write the simplified fraction:
70/198
Step 5: Find the Greatest Common Divisor (GCD)
To simplify the fraction further, we need to find the GCD of 70 and 198. Using the Euclidean algorithm, we find that the GCD is 2.
Step 6: Divide by the GCD
Now, we can divide both the numerator and denominator by the GCD:
(70 ÷ 2) / (198 ÷ 2) = 35/99
Conclusion
And there you have it! The simplified form of the expression 10/11 x 7/9 x 1/2 is:
35/99
Remember, simplifying fractions is an essential skill in mathematics. By following these steps, you can simplify even the most complex fractions and make them easier to work with.
