What Is Multiplying Binomials With Fractional Coefficients?
Multiplying binomials with fractional coefficients works just like ordinary FOIL: multiply the First, Outer, Inner and Last terms. The only extra step is multiplying fractions, top times top and bottom times bottom.
Then you combine the like terms, which means adding fractions over a common denominator. The calculator does this exactly, so there is no rounding.
Enter each binomial, such as (1/2)x + 3/4, and you get the four partial products and the final expanded result.
How to Use the Multiplying Binomials With Fractional Coefficients Calculator
- Enter each binomial with fractions, such as (1/2)x + 3/4.
- Read the four FOIL products.
- Check the combined result in lowest terms.
Multiplying Binomials With Fractional Coefficients Formula
FOIL
Fraction product
Multiplying Binomials With Fractional Coefficients Variables Explained
| Symbol | Meaning | Notes |
|---|---|---|
| a, b, c, d | Fractional coefficients and constants | |
| First, Outer, Inner, Last | The four partial products of FOIL | |
| Like terms | Terms with the same power of the variable | Added over a common denominator |
| Product | The expanded polynomial |
Multiplying Binomials With Fractional Coefficients Worked Example
With the example values loaded in the calculator above, the steps are:
- First binomial: (1/2)x + 3/4. Second binomial: (2/3)x − 1/5.
- Use FOIL: multiply First, Outer, Inner and Last terms. For fractions, multiply the numerators together and the denominators together.
- First: ((1/2)x)((2/3)x) = (1/3)x²
- Outer: ((1/2)x)(−1/5) = −(1/10)x
- Inner: (3/4)((2/3)x) = (1/2)x
- Last: (3/4)(−1/5) = −3/20
- Combine like terms, adding fractions over a common denominator: (1/3)x² + (2/5)x − 3/20.
Result: Product = (1/3)x² + (2/5)x − 3/20.
Worked example: (1/2 x + 3/4)(2/3 x − 1/5)
First: (1/2 x)(2/3 x) = 1/3 x². Outer: (1/2 x)(−1/5) = −1/10 x. Inner: (3/4)(2/3 x) = 1/2 x. Last: (3/4)(−1/5) = −3/20.
Combine the x terms: −1/10 + 1/2 = −1/10 + 5/10 = 4/10 = 2/5. The product is 1/3 x² + 2/5 x − 3/20.
A way to avoid fractions
Multiply the first binomial by 4 to get 2x + 3, and the second by 15 to get 10x − 3. Multiply those, then divide the result by 4 × 15 = 60. You get the same answer.
Where Multiplying Binomials With Fractional Coefficients Is Used
Algebra homework
Check FOIL with fractions step by step.
Learning fractions in algebra
See how denominators combine.
Checking by substitution
Compare the factors and the product at a chosen value of x.
Common Multiplying Binomials With Fractional Coefficients Mistakes to Avoid
- Reduce each fraction to lowest terms as you go.
- Use a common denominator only when adding like terms.
Multiplying Binomials With Fractional Coefficients Terms and Definitions
- FOIL
- A memory aid for multiplying two binomials.
- Like terms
- Terms with the same variable and exponent.
Multiplying Binomials With Fractional Coefficients FAQs
How do you multiply binomials with fractions?
Use FOIL and multiply the fractions straight across. Then add the like terms over a common denominator.
Do I need a common denominator before multiplying?
No. You only need one to add or combine like terms.
How can I check my answer?
Substitute a value for x in the factors and in the product. Both should give the same number.
Can I clear the fractions first?
Yes. Multiply each binomial by its common denominator, multiply, then divide by the product of those multipliers.