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Quizzes > High School Quizzes > Mathematics

Quiz 3: Fractional Equations Practice Quiz

Sharpen your skills with interactive problems

Difficulty: Moderate
Grade: Grade 8
Study OutcomesCheat Sheet
Colorful paper art promoting a Fraction Equation Frenzy trivia for 6th-grade students.

What is the solution to (1/2)x = 4?
6
4
8
2
Multiplying both sides of the equation by 2 gives x = 8. This method isolates the variable and confirms the correct solution.
What is the value of x in the equation x/3 = 7?
10
3
7
21
Multiplying both sides of the equation by 3 isolates x, resulting in x = 21. This demonstrates basic manipulation of fractional equations.
Solve: (2/3)x = 10. What is x?
12
15
10
20
Multiplying both sides by the reciprocal of 2/3 (which is 3/2) yields x = 15. This straightforward approach reinforces the use of reciprocals in solving equations.
If x/4 = 5/2, what is the value of x?
20
10
12
8
Multiplying both sides by 4 to isolate x gives x = (5/2) Ã - 4 = 10. This simple equation practice solidifies understanding of fraction multiplication.
What is the sum of 1/2 and 1/3?
2/5
7/6
5/6
1/6
Finding a common denominator of 6, we convert 1/2 to 3/6 and 1/3 to 2/6. Adding these fractions gives 5/6, which is the correct result.
Solve: (1/3)x + 2 = 5. What is the value of x?
12
6
3
9
Subtracting 2 from both sides gives (1/3)x = 3, and multiplying by 3 results in x = 9. This reinforces how to isolate the variable in fractional equations.
Find x in the equation: (3/4)x - 1/2 = 2.
8/3
5/3
10/3
4
By adding 1/2 to both sides, the equation becomes (3/4)x = 5/2. Multiplying by 4/3 then gives x = 10/3. This problem applies fractional operations to isolate x.
Solve: x/5 + 1/2 = 1. What is x?
2
3/2
5/2
1/2
Subtracting 1/2 from 1 yields x/5 = 1/2, and multiplying both sides by 5 gives x = 5/2. This exercise emphasizes the importance of reversing operations in an equation.
Determine x if (2/3)x + 1/4 = 11/12.
4
3
1
2
Subtracting 1/4 (equivalent to 3/12) from 11/12 gives (2/3)x = 8/12, which simplifies to 2/3. Multiplying by the reciprocal 3/2 confirms that x = 1.
Solve for x: (3/5)x = 9/10.
3/2
2
9/10
3
Multiplying both sides by the reciprocal of 3/5, which is 5/3, yields x = (9/10) Ã - (5/3) = 3/2. This strengthens the skill of applying reciprocals in fractional equations.
Find x in the equation: (1/2)x - (1/3) = 1/6.
0
1
2
1/2
Adding 1/3 to both sides transforms the equation to (1/2)x = 1/6 + 1/3 = 1/2, and multiplying by 2 results in x = 1. This problem emphasizes combining fractions correctly before isolating the variable.
If (4/7)x + 2 = 6, what is the value of x?
5
6
4
7
Subtracting 2 from both sides gives (4/7)x = 4, then multiplying by 7/4 isolates x, resulting in x = 7. This reinforces how to undo fractional coefficients with their reciprocals.
Solve: (2/5)x - 1/2 = 1/10. What is x?
1
2
3
3/2
First, add 1/2 to both sides to obtain (2/5)x = 1/10 + 5/10 = 3/5. Multiplying by the reciprocal 5/2 then gives x = 3/2. This question highlights systematic fraction addition and multiplication.
Determine x in the equation: (5/6)x + 1/3 = 4/3.
1
7/5
5/6
6/5
Subtract 1/3 (which can be written as 2/6) from 4/3 (or 8/6) to get (5/6)x = 6/6. Multiplying by the reciprocal 6/5 gives x = 6/5. The process underscores the importance of common denominators in equation solving.
Solve: (1/2)x + (1/3)x = 10. What is x?
8
10
12
15
Combine the fractions by finding a common denominator: (1/2 + 1/3)x becomes (3/6 + 2/6)x = (5/6)x. Multiplying both sides by 6/5 yields x = 12.
Find x from the equation: (2/3)x - 1/4 = 5/12.
0
2
1
3
By adding 1/4 (which converts to 3/12) to 5/12, we get (2/3)x = 8/12, which simplifies to 2/3. Multiplying by 3/2 confirms that x = 1.
Solve the equation: (3/7)(x - 2) = 6/7.
2
4
6
0
Multiplying both sides by the reciprocal 7/3 yields x - 2 = 2, so adding 2 to both sides gives x = 4. This question reinforces distributing and isolating variables in fractional equations.
Determine the value of x: x/2 + x/3 = 25.
35
20
25
30
Combining x/2 and x/3 by finding a common denominator results in (3x + 2x)/6 = 5x/6. Multiplying both sides by 6/5 leads to x = 30.
Solve: (x + 1)/3 = (x - 2)/5. What is x?
11/2
-5
5
-11/2
Cross-multiplying gives 5(x + 1) = 3(x - 2), which simplifies to 5x + 5 = 3x - 6. Solving for x yields x = -11/2. This problem emphasizes the use of cross-multiplication in fraction equations.
Solve: (2/3)(x + 4) = 8. What is x?
12
8
6
10
Dividing both sides by 2/3, or equivalently multiplying by 3/2, gives x + 4 = 12. Subtracting 4 from both sides yields x = 8. This question reinforces solving equations by isolating the variable.
0
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Study Outcomes

  1. Apply techniques to solve equations involving fractions.
  2. Analyze and simplify fractional expressions within equations.
  3. Convert complex fraction equations to a common denominator for easier manipulation.
  4. Evaluate solutions for accuracy and check for extraneous results.
  5. Demonstrate understanding of key fractional concepts through quiz problems.

Quiz 3: Fractional Equations Test Cheat Sheet

  1. Understand Fraction Operations - Dive into the world of adding, subtracting, multiplying, and dividing fractions by finding common denominators and simplifying like a pro. Practice until converting fractions feels as easy as pie! Symbolab Fraction Operations Guide
  2. Identify the Least Common Denominator (LCD) - Scouting out the LCD helps you line up those fractions perfectly for smooth calculation - no mismatched denominators allowed! With the LCD in hand, combining fractions becomes a breeze. IntMath on Equations with Fractions
  3. Eliminate Fractions by Multiplying by the LCD - Zap away those pesky fractions by multiplying every term by the LCD, turning complex expressions into friendly whole-number equations. It's like using a secret code to simplify math puzzles! OpenStax Prealgebra Fraction Equations
  4. Apply the Multiplication Property of Equality - When a variable is stuck inside a fraction, multiply both sides by its reciprocal to set it free - variables love reciprocals! This trick keeps equations balanced and your solutions on track. MinuteMath Fraction Equation Solving
  5. Translate Word Problems into Equations - Turn real-life scenarios into math by spotting keywords like "total" or "difference" and mapping them to operations. It's like being a language detective cracking the code of algebra! Symbolab Word-to-Equation Guide
  6. Check Solutions by Substitution - Always plug your answer back into the original equation to make sure it really works - no sneaky mistakes allowed! This final check is your math proof of victory. OpenStax Solution Verification
  7. Practice One-Step Equations with Fractions - Start small by mastering equations with just one operation, like adding or multiplying fractions. Building confidence here means big wins later on! OnlineMathLearning One-Step Equations
  8. Progress to Multi-Step Equations - Combine your newfound skills to tackle equations that need several steps - use the distributive property, combine like terms, and keep your work tidy. Complex problems are just level-ups on your math adventure! OnlineMathLearning Multi-Step Equations
  9. Solve Equations with Variables in the Denominator - Learn how to handle situations where variables hide in the denominator without triggering division-by-zero traps. A careful approach here keeps your solutions valid and your math game strong. IntMath Variables-In-Denominator Tips
  10. Utilize Practice Problems - Keep the momentum by working through tons of practice questions - speed and accuracy will soar with every problem solved. Remember, practice makes perfect (and fractions more fun)! Corbettmaths Fraction Practice
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