Converting to Standard Form
The given expression is 2/3x + 5. To convert this to standard form, we need to rewrite it in the form ax + b, where a and b are integers.
Step 1: Multiply the Fraction
To get rid of the fraction, we can multiply both the numerator and denominator by 3.
2/3x = (2 × 3)/(3 × 3)x = 6/9x
Step 2: Simplify the Fraction
Since 6 and 9 have a common factor of 3, we can simplify the fraction.
6/9x = 2/3x
Step 3: Write in Standard Form
Now we can rewrite the expression in standard form.
2/3x + 5 = 2/3x + 15/3
To make the fractions have the same denominator, we can multiply the numerator and denominator of 5 by 3.
2/3x + 5 = 2/3x + 15/3 = (2x + 15)/3
So, the expression 2/3x + 5 in standard form is:
(2x + 15)/3
Let's take a closer look at the concept of standard form and its applications.
What is Standard Form?
Standard form is a way of writing mathematical expressions in a specific format. It is used to make expressions easier to read and work with. In the case of linear expressions, standard form is written in the form ax + b, where a and b are integers.
Why is Standard Form Important?
Standard form is important because it makes it easier to compare and manipulate expressions. It also helps to avoid confusion when working with fractions and decimals.
How is Standard Form Used in Real-Life Applications?
Standard form is used in a variety of real-life applications, including:
- Science: Standard form is used in scientific notation to express very large or very small numbers.
- Engineering: Standard form is used in engineering to express quantities such as length, mass, and time.
- Finance: Standard form is used in finance to express quantities such as interest rates and investment returns.
In conclusion, converting an expression to standard form is an important skill in mathematics. It helps to make expressions easier to read and work with, and it has a wide range of applications in science, engineering, and finance.
Key Takeaways
- Standard form is a way of writing mathematical expressions in a specific format.
- It is used to make expressions easier to read and work with.
- Standard form is important in a variety of real-life applications, including science, engineering, and finance.
Next Steps
Now that we have learned how to convert an expression to standard form, let's practice with some more examples.