Solving One-Step Addition & Subtraction Equations with Fractions
Solving one-step addition and subtraction equations with fractions means using inverse operations to isolate the variable. For x + 1/3 = 5/6, subtract 1/3 from both sides: x = 5/6 - 1/3 = 5/6 - 2/6 = 3/6 = 1/2. For y - 2/5 = 3/10, add 2/5 to both sides: y = 3/10 + 2/5 = 3/10 + 4/10 = 7/10. This 6th grade algebra skill from enVision Mathematics Grade 6 extends equation solving to rational numbers and requires fluency with fraction addition and subtraction.
Key Concepts
Property To solve for a variable, use inverse operations. Addition Property of Equality: If $a = b$, then $a + c = b + c$. Subtraction Property of Equality: If $a = b$, then $a c = b c$.
Examples Solve for $x$: $x + \frac{1}{5} = 2 \tfrac{4}{5}$ $$x + \frac{1}{5} \frac{1}{5} = 2 \tfrac{4}{5} \frac{1}{5}$$ $$x = 2 \tfrac{3}{5}$$.
Solve for $y$: $y \frac{1}{3} = 1 \tfrac{1}{2}$ $$y \frac{1}{3} + \frac{1}{3} = 1 \tfrac{1}{2} + \frac{1}{3}$$ $$y = 1 \tfrac{5}{6}$$.
Common Questions
How do you solve a one-step equation with fractions using addition or subtraction?
Apply the inverse operation to both sides. For x + 1/3 = 5/6: subtract 1/3 from both sides. Convert 1/3 = 2/6, so x = 5/6 - 2/6 = 3/6 = 1/2.
What inverse operation cancels addition in an equation?
Subtraction cancels addition. If x + 1/3 = 5/6, subtract 1/3 from both sides to isolate x.
How do you subtract fractions with unlike denominators when solving equations?
Find the least common denominator, convert both fractions, then subtract numerators. For 5/6 - 1/3: LCD = 6, so 5/6 - 2/6 = 3/6 = 1/2.
What grade solves one-step fraction equations?
One-step addition and subtraction equations with fractions are a 6th grade algebra topic in enVision Mathematics Grade 6, connecting equation-solving skills to fraction fluency.
How do you check your answer in a fraction equation?
Substitute your answer back into the original equation and verify both sides are equal. For x = 1/2 in x + 1/3 = 5/6: 1/2 + 1/3 = 3/6 + 2/6 = 5/6. Correct.
Why is the inverse operation important in equation solving?
The inverse operation undoes whatever is being done to the variable, leaving it isolated on one side. Without this principle, you would have to guess the answer through trial and error.