When you have to deal with equations that include both fractions and decimals, it can seem a bit tricky. But don’t worry! Here’s a simple guide to help you work through them confidently.
1. Get Rid of Fractions:
First, let's eliminate the fractions because they make things harder. You can do this by finding the least common multiple (LCM) of the bottom numbers (denominators) in your fractions.
For example, if you have an equation like ( \frac{2}{3}x + 0.5 = 4 ), the LCM of the denominators (which is 3) can help us. Multiply every part of the equation by 3 to get rid of the fraction:
[
3 \left( \frac{2}{3}x \right) + 3(0.5) = 3(4)
]
This changes the equation to:
[
2x + 1.5 = 12
]
2. Change Decimals to Whole Numbers:
If there are still decimals in your equation, try to turn them into fractions or whole numbers. You can do this by multiplying everything by 10, 100, or another nice round number.
In our example, let's multiply everything by 10:
[
20x + 15 = 120
]
3. Solve the Equation:
Now, you can solve the equation just like you normally would! Rearrange it to get the variable (the letter) by itself.
For our example, it looks like this:
[
20x = 120 - 15
]
[
20x = 105
]
Then, divide to find ( x ):
[
x = \frac{105}{20}
]
This simplifies to:
[
x = 5.25
]
4. Check Your Work:
Finally, always plug your answer back into the original equation to see if everything fits together.
By following these easy steps, you’ll be able to handle equations with fractions and decimals without any trouble!
When you have to deal with equations that include both fractions and decimals, it can seem a bit tricky. But don’t worry! Here’s a simple guide to help you work through them confidently.
1. Get Rid of Fractions:
First, let's eliminate the fractions because they make things harder. You can do this by finding the least common multiple (LCM) of the bottom numbers (denominators) in your fractions.
For example, if you have an equation like ( \frac{2}{3}x + 0.5 = 4 ), the LCM of the denominators (which is 3) can help us. Multiply every part of the equation by 3 to get rid of the fraction:
[
3 \left( \frac{2}{3}x \right) + 3(0.5) = 3(4)
]
This changes the equation to:
[
2x + 1.5 = 12
]
2. Change Decimals to Whole Numbers:
If there are still decimals in your equation, try to turn them into fractions or whole numbers. You can do this by multiplying everything by 10, 100, or another nice round number.
In our example, let's multiply everything by 10:
[
20x + 15 = 120
]
3. Solve the Equation:
Now, you can solve the equation just like you normally would! Rearrange it to get the variable (the letter) by itself.
For our example, it looks like this:
[
20x = 120 - 15
]
[
20x = 105
]
Then, divide to find ( x ):
[
x = \frac{105}{20}
]
This simplifies to:
[
x = 5.25
]
4. Check Your Work:
Finally, always plug your answer back into the original equation to see if everything fits together.
By following these easy steps, you’ll be able to handle equations with fractions and decimals without any trouble!