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Quizzes > High School Quizzes > Mathematics

Ace Dividing Fractions Practice Quiz

Sharpen math skills: Compare, divide and multiply fractions.

Difficulty: Moderate
Grade: Grade 4
Study OutcomesCheat Sheet
Colorful paper art promoting a Divide Compare Fractions quiz for middle school students.

Compute 1/2 ÷ 1/4.
2
4
1/8
1/2
Dividing by a fraction is the same as multiplying by its reciprocal. Here, multiplying 1/2 by 4 gives 2. The other options are common mistakes when working with reciprocals.
What is 3/4 ÷ 1/2?
1/2
3/2
3/4
1
Dividing by 1/2 means multiplying by its reciprocal, 2. Thus, 3/4 multiplied by 2 equals 6/4, which simplifies to 3/2. The other choices do not apply the reciprocal rule correctly.
Which fraction is larger: 2/3 or 3/5?
3/5
2/3
Cannot determine
They are equal
By converting to decimals or cross-multiplying (2Ã - 5 vs. 3Ã - 3), 2/3 proves larger than 3/5. The other alternatives ignore proper comparison methods.
How do you express the division 4/9 ÷ 2/3 as a multiplication?
4/9 ÷ 3/2
4/9 Ã - 2/3
3/4 Ã - 2/9
4/9 Ã - 3/2
Dividing by a fraction is equivalent to multiplying by its reciprocal. Replacing 2/3 with its reciprocal, 3/2, gives 4/9 Ã - 3/2. The other options misrepresent the correct procedure.
Simplify the expression (2/5) ÷ (10/3).
1/5
6/50
3/25
5/2
Changing the division to multiplication by the reciprocal gives (2/5) Ã - (3/10), resulting in 6/50, which simplifies to 3/25. The other options reflect common missteps in simplification.
What is 5/8 ÷ 1/4?
1/2
5/2
5/32
10/8
Multiplying 5/8 by the reciprocal of 1/4 (which is 4) gives 20/8 that simplifies to 5/2. The other options do not correctly apply the reciprocal multiplication.
Divide 7/10 by 2/5. What is the result?
7/10
2/7
17/20
7/4
Dividing 7/10 by 2/5 is the same as multiplying 7/10 by 5/2, which results in 35/20 that simplifies to 7/4. The alternatives show common miscalculations.
If 3/4 ÷ x = 9/8, what is x?
4/9
8/9
3/2
2/3
Rearranging the equation gives x = (3/4) ÷ (9/8), which simplifies to 2/3. The other options result from misinterpreting the division process.
Which is greater: 5/6 or 7/9?
5/6
They are equal
7/9
Cannot be determined
Using cross multiplication, 5 Ã - 9 = 45 and 7 Ã - 6 = 42, so 5/6 is greater than 7/9. The other choices ignore proper fraction comparison methods.
Solve the expression: (1/3 ÷ 2/7) ÷ (5/6).
7/5
35/36
5/7
7/6
First, 1/3 ÷ 2/7 equals 1/3 à - 7/2, which is 7/6. Then, dividing 7/6 by 5/6 yields 7/5. The answer choices represent common pitfalls in sequential operations.
Find (3/5) ÷ (1/5).
3
1/3
15
5/3
When dividing fractions with the same denominator, simply divide the numerators. Thus (3/5) ÷ (1/5) equals 3. The other options reflect misuse of the division rule.
A recipe requires 2/3 cup of milk per serving. How many servings can be made from 4 cups of milk?
5
7
6
8
Dividing the total amount of milk (4 cups) by the amount needed per serving (2/3 cup) gives 4 ÷ (2/3), which is equivalent to 4 à - (3/2) = 6 servings. The other answers result from miscalculating the division.
What is the simplified form of the expression (8/15) ÷ (16/45)?
2/3
3/2
5/4
1/2
Converting the division to multiplication by the reciprocal yields (8/15) Ã - (45/16). This simplifies to 360/240, which is 3/2 after reducing. The other options are results of miscalculation.
If (x/y) ÷ (2/3) = 9/8, find the value of x/y.
9/16
4/3
3/4
16/9
Multiplying both sides of the equation by 2/3 gives x/y = (9/8) Ã - (2/3), which simplifies to 3/4. The other alternatives stem from common errors in handling the operations.
Evaluate the expression: [(5/12) ÷ (5/9)] ÷ (1/4).
3
1/3
4
1
First, dividing 5/12 by 5/9 gives (5/12) Ã - (9/5) = 3/4. Then dividing 3/4 by 1/4 results in 3. The other options arise from incorrect application of division procedures.
Solve: (3/4 ÷ 2/5) ÷ (6/7 ÷ 3/14).
15/32
15/8
5/16
8/15
First, 3/4 ÷ 2/5 equals 15/8 and 6/7 ÷ 3/14 equals 4. Dividing 15/8 by 4 gives 15/32. The incorrect choices result from misordering the operations or miscalculating the reciprocals.
A student mistakenly solved (7/10 ÷ 1/2) by multiplying by 1/2 instead of its reciprocal, obtaining 7/20. What is the correct answer and where did the error occur?
7/20; error was due to inverting the dividend
7/5; error was due to using 1/2 instead of its reciprocal
5/7; error was due to misreading the division sign
1/5; error was due to multiplying both fractions
The correct process is to multiply 7/10 by the reciprocal of 1/2 (which is 2), resulting in 7/5. The student's error stemmed from using 1/2 directly instead of 2. The other options misidentify the mistake and result.
Determine the value of a expressed by the equation (a/3) ÷ (4/7) = (2a/9), assuming a ≠0.
a can be any number
a = 12/7
a = 0
No solution
Simplifying the left side gives (a/3) à - (7/4) = 7a/12. Setting 7a/12 equal to 2a/9 and canceling a (since a ≠0) leads to an impossible equality. Thus, there is no nonzero solution for a.
Compare the expressions (5/8 ÷ 2/3) and (15/16 ÷ 3/4). Which one is larger?
(5/8 ÷ 2/3) is larger
Cannot determine
(15/16 ÷ 3/4) is larger
Both are equal
Evaluating the expressions: (5/8 ÷ 2/3) equals 15/16, while (15/16 ÷ 3/4) equals 5/4. Since 5/4 is greater than 15/16, the second expression is larger. The alternatives do not reflect correct calculations.
A tank is filled using a hose that fills 3/7 of the tank in 2/5 hours. How many hours will it take to fill the entire tank at the same rate?
14/15 hours
2/5 hours
7/3 hours
15/14 hours
The filling rate is 3/7 of the tank in 2/5 hours. Dividing 1 by the rate (which is equivalent to multiplying 2/5 by 7/3) results in 14/15 hours to fill the tank. The other options come from inverting the fraction incorrectly.
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Study Outcomes

  1. Understand the process of dividing fractions by identifying numerators and denominators.
  2. Apply fraction division techniques to solve problems accurately.
  3. Compare fractions by analyzing their decimal or common denominator equivalents.
  4. Analyze problem steps to identify and correct common mistakes in fraction operations.
  5. Evaluate feedback to enhance overall confidence in fraction division and comparison.

Dividing & Multiplying Fractions Cheat Sheet

  1. Flip it and multiply! - When you divide by a fraction, tip the second one upside down (take the reciprocal) and switch the ÷ to ×. It's like a secret handshake that always leads you to the right answer! For example, 2/3 ÷ 4/5 becomes 2/3 × 5/4, giving 10/12 or simplified to 5/6. Symbolab Dividing Fractions
    2. www.symbolab.com
  2. Divide by whole numbers with ease - Treat a whole number as a fraction with denominator 1, then flip it to multiply. So 3/4 ÷ 2 becomes 3/4 × 1/2, which equals 3/8. This trick works every time and keeps your brain happy! Symbolab Whole‑Number Divisions
    3. www.symbolab.com
  3. Same bottom, bigger top wins - When two fractions share a denominator, simply compare numerators. The larger number on top means a larger piece of the same-sized pie. For instance, 5/8 is greater than 3/8 because 5 slices are more than 3. HomeschoolMath Comparing Fractions
    4. www.homeschoolmath.net
  4. Same top, smaller bottom wins - If fractions have the same numerator, the one with the smaller denominator has bigger slices. So 3/4 beats 3/5, since dividing into 4 parts gives you larger pieces than dividing into 5. Easy-peasy visual proof! HomeschoolMath Comparing Fractions
    5. www.homeschoolmath.net
  5. Get common to compare different fractions - Turn 2/3 and 3/4 into equivalent fractions with the same bottom: 8/12 vs. 9/12. Now it's obvious that 9/12 (3/4) is the winner! Finding common denominators clears up any confusion. MrsLaug's Fraction Guide
    6. mrslaug.weebly.com
  6. Visualize with models - Draw number lines or fraction bars to see how pieces stack up. This hands‑on approach turns abstract numbers into colorful, intuitive comparisons. You'll never forget which fraction is bigger when you actually see it! Media4Math Lesson
    7. www.media4math.com
  7. Use benchmarks like 1/2 - If one fraction dips below 1/2 and another soars above, the latter wins the race. For example, 3/8 is less than 1/2, while 5/8 is greater - so 5/8 is obviously larger. Benchmarks make quick work of comparisons. HomeschoolMath Benchmarks
    8. www.homeschoolmath.net
  8. Cross‑multiply for a fast check - Multiply tops by opposite bottoms: for 4/5 vs. 3/4, compute 4×4=16 and 5×3=15. Since 16 is bigger, 4/5 wins. No need for common denominators - just a quick calculation! GreeneMath Comparison
    9. www.greenemath.com
  9. Keep, Change, Flip - Stuck on division? Remember "Keep, Change, Flip": keep the first fraction, change ÷ to ×, flip the second. This catchy phrase locks in the method so you never forget the steps. Symbolab Mnemonics
    10. www.symbolab.com
  10. Simplify every answer - After you divide or compare, always reduce your fraction to its simplest form. It looks cleaner, is easier to use in future problems, and shows you've got mastery over the material. Symbolab Simplifying Guide
    11. www.symbolab.com
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