Solving Fractional Equations: 17/9 x = 5 4/9 and 5/8
In this article, we will explore how to solve two fractional equations: 17/9 x = 5 4/9 and 5/8. Fractions can be intimidating, but with the right approach, solving these equations can be a breeze.
Equation 1: 17/9 x = 5 4/9
To solve this equation, we need to start by converting the mixed number 5 4/9 to an improper fraction.
Converting Mixed Numbers to Improper Fractions
A mixed number consists of a whole number part and a fractional part. To convert a mixed number to an improper fraction, we multiply the whole number part by the denominator and then add the numerator.
5 4/9 = (5 x 9) + 4 / 9 = 49/9
Now that we have converted the mixed number to an improper fraction, we can rewrite the equation as:
17/9 x = 49/9
Solving the Equation
To solve for x, we can cross-multiply:
(17/9) x = 49/9
Multiply both sides by 9 to eliminate the denominator:
17x = 49
Divide both sides by 17 to solve for x:
x = 49/17
x = 2 15/17
Equation 2: 5/8**
This equation is a simple fraction, and we can solve it directly.
Solving the Equation
Let's multiply both sides by 8 to eliminate the denominator:
5x = 8
Divide both sides by 5 to solve for x:
x = 8/5
x = 1 3/5
And that's it! We have solved both fractional equations. Remember to always convert mixed numbers to improper fractions before solving, and don't be afraid to cross-multiply to solve for the variable.
