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Quizzes > High School Quizzes > Mathematics

Functions Math Quiz Practice Test

Boost math skills with division and fraction quizzes

Difficulty: Moderate
Grade: Grade 3
Study OutcomesCheat Sheet
Colorful paper art promoting Fraction Division Frenzy, a dynamic math quiz for middle school students.

What is 1/2 ÷ 1/4?
1/2
2
1/8
4
Dividing by a fraction means multiplying by its reciprocal. In this case, 1/2 multiplied by 4 yields 2.
What is 3/4 ÷ 1/2?
1/2
3/8
3/2
2/3
Multiplying 3/4 by the reciprocal of 1/2 (which is 2) results in 6/4. This simplifies to 3/2, which is the correct answer.
Evaluate 1/3 ÷ 1/9.
3
9
1/27
1/12
By multiplying 1/3 by the reciprocal of 1/9 (which is 9), you obtain 9/3. This simplifies to 3, making it the correct answer.
Find the result of 5/6 ÷ 1/3.
5/2
2/5
3/2
1/2
Dividing by a fraction is equivalent to multiplying by its reciprocal. Thus, 5/6 multiplied by 3 gives 15/6, which simplifies to 5/2.
Solve: 2/5 ÷ 2/3.
6/5
1/5
3/5
5/6
Multiplying 2/5 by the reciprocal of 2/3 (which is 3/2) results in 6/10. Simplifying this fraction gives 3/5.
What is 7/8 ÷ 1/2?
1/4
7/16
7/4
14/16
Multiplying 7/8 by the reciprocal of 1/2, which is 2, gives 14/8. This simplifies to 7/4, the correct answer.
What is (2/3) ÷ (4/9)?
2/3
4/3
9/8
3/2
Multiplying 2/3 by the reciprocal of 4/9 (which is 9/4) gives 18/12. Simplifying that fraction results in 3/2.
Compute (5/7) ÷ (10/21).
2/3
3/2
7/5
5/3
Multiplying 5/7 by the reciprocal of 10/21 (which is 21/10) produces 105/70. After simplification by dividing numerator and denominator by 35, the result is 3/2.
How many 1/8 cups are needed to measure 3/4 cup of milk?
12
4
6
8
Dividing 3/4 by 1/8 is equivalent to multiplying 3/4 by 8, which results in 6. Therefore, six 1/8 cups are needed.
If a car travels 3/5 mile using 1/6 gallon of gas, what is its fuel efficiency in miles per gallon?
18/5
3/2
9/5
3/10
Dividing 3/5 by 1/6 (or multiplying 3/5 by 6) results in 18/5 miles per gallon. This is the car's fuel efficiency.
Solve for x: x = (4/5) ÷ (8/15).
15/40
3/2
8/15
4/3
Multiplying 4/5 by the reciprocal of 8/15 (which is 15/8) gives 60/40. Simplifying this fraction results in 3/2, which is the value of x.
Divide 1/4 by 2/3 and simplify.
4/3
2/3
8/3
3/8
To divide 1/4 by 2/3, multiply 1/4 by the reciprocal of 2/3, which is 3/2. This calculation results in 3/8 after simplification.
Which expression is equivalent to (3/10) ÷ (1/2)?
5/3
2/3
1/5
3/5
Dividing by 1/2 is the same as multiplying by 2. Thus, 3/10 Ã - 2 equals 6/10, which simplifies to 3/5.
A container holds 2/3 liter of juice. If each serving is 1/9 liter, how many servings does the container provide?
7
6
5
4
Dividing 2/3 by 1/9 is accomplished by multiplying 2/3 by 9, resulting in 18/3, which simplifies to 6 servings. This is the number of servings available.
Calculate (7/9) ÷ (14/27).
27/9
2/3
7/14
3/2
Multiply 7/9 by the reciprocal of 14/27, which is 27/14, to obtain 189/126. Simplifying this fraction gives 3/2.
Solve for y in the equation: (y/2) ÷ (3/4) = 4. Find y.
6
12
8
4
Rewriting the division as multiplication, (y/2) Ã - (4/3) equals 4. Solving the resulting equation yields y = 6.
If (3/5)x ÷ (2/7) = 7, what is the value of x?
21/10
7/3
10/3
3/10
Multiply (3/5)x by the reciprocal of (2/7) to get (21x/10) = 7. Solving for x gives x = 10/3.
A tank is 2/3 full of water. If 1/4 of the empty space is filled with water, what fraction of the tank is full now?
1/2
8/9
3/4
2/3
The empty portion of the tank is 1/3, and filling 1/4 of it adds 1/12 to the 2/3 already filled. Adding these gives 2/3 + 1/12 = 9/12, which simplifies to 3/4.
Simplify the expression: (5/12) ÷ [(15/8) ÷ (10/3)].
16/27
20/21
5/9
20/27
First, evaluate the inner division: (15/8) ÷ (10/3) equals 15/8 à - 3/10, which simplifies to 9/16. Then, (5/12) ÷ (9/16) is the same as 5/12 à - 16/9, resulting in 20/27.
Express the operation ((1/2 ÷ 3/4) ÷ (5/6 ÷ 2/3)) as a single simplified fraction.
5/4
8/15
15/8
2/3
First, compute 1/2 ÷ 3/4 = 2/3 and 5/6 ÷ 2/3 = 5/4. Then, (2/3) ÷ (5/4) equals 2/3 à - 4/5, which simplifies to 8/15.
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Study Outcomes

  1. Understand the process of dividing fractions using reciprocal multiplication.
  2. Apply the reciprocal method to simplify division problems involving fractions.
  3. Simplify and reduce resulting fractions accurately after division.
  4. Analyze and solve word problems that incorporate fraction division scenarios.

Division, Fraction & Functions Cheat Sheet

  1. Keep, Change, Flip Method - Kick off your dividing‑fractions adventure by keeping the first fraction, swapping the ÷ for a ×, and flipping the second fraction into its reciprocal. This nifty trick turns a scary division into a friendly multiplication problem - like turning a dragon into a puppy! Give \(3/4 ÷ 2/5\) a spin and see it smoothly become \(3/4 × 5/2\). Math is Fun: Dividing Fractions
  2. Convert Mixed Numbers - Before you divide, transform any mixed numbers into improper fractions by multiplying the whole number by the denominator and adding the numerator. It's like leveling up in a game - 1 2/3 effortlessly turns into 5/3, so you can keep cruising through fraction problems. A clear start makes for a smoother finish! SplashLearn: Dividing Fractions
  3. Division Is Inverse Multiplication - Remember that dividing by a fraction is just multiplying by its reciprocal because division and multiplication are best buddies working in reverse. Think of it as walking backward through a maze - you retrace the multiplication path to get right back where you started. Understanding this relationship makes fraction division feel like child's play! The Math Doctors: How & Why
  4. Simplify Before You Multiply - Slash those fractions down to size by simplifying before you multiply - cancel common factors straight across the numerators and denominators. For instance, \(2/4 × 3/6\) quickly becomes \(1/2 × 1/2\), giving you \(1/4\) in just two easy steps. Fewer numbers, fewer headaches, more wins! Math is Fun: Simplifying Fractions
  5. Beware Division by Zero - Division by zero is a no-go zone; it's undefined and will crash your math game. Whenever you see something like \(3/4 ÷ 0\), pump the brakes - there's no valid answer. Keeping an eye out for zeros keeps your solutions valid and your math mojo intact. SplashLearn: Fraction Dangers
  6. Divide by a Whole Number - Converting a whole number into a fraction is as simple as popping a "/1" on the end. So \(3/4 ÷ 2\) becomes \(3/4 ÷ 2/1\), letting you apply your trusty keep‑change‑flip move. This tiny tweak means whole numbers can join the fraction‑division party, too! Math is Fun: Fractions & Whole Numbers
  7. Apply Real‑World Scenarios - Take your skills into the real world by dividing ingredients in recipes or splitting a pizza slice by slice. Turning fraction problems into everyday puzzles makes learning memorable and downright delicious. Practice on real tasks, and you'll be ready for any fraction emergency! SplashLearn: Real‑World Fractions
  8. Use Visual Models - Draw pie charts, number lines, or domino‑style bars to see how fractions divide in action. Visuals transform abstract numbers into colorful, bite‑sized pieces that your brain can easily digest. When you can picture the problem, the solution almost draws itself! SplashLearn: Visual Fraction Models
  9. Check by Multiplying Back - Verify your answer by multiplying the quotient by the divisor to see if you get the original dividend. If \(3/4 ÷ 2/5 = 15/8\), then \(15/8 × 2/5\) should snap back to \(3/4\). It's your secret proof‑checking handshake that keeps mistakes at bay. Math is Fun: Fraction Check
  10. Practice Makes Perfect - Level up your fraction‑division skills with worksheets, quizzes, and timed drills. The more you practice, the more confident and lightning‑fast you'll become. Turn practice into a challenge with friends, and watch your fraction powers soar! Math Salamanders: Worksheets
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