Arithmetic and terms

Fractions

Fractions are in almost every Studienkolleg maths entrance test, usually without a calculator. You need to add, subtract, multiply and divide them quickly and simplify the result.

München Named for the T, M and W maths tests at Studienkolleg München. Source

The rules

• Add or subtract: bring both fractions to a common denominator, then add the numerators: a/b + c/d = (ad + bc)/bd.
• Multiply: numerator times numerator, denominator times denominator: a/b · c/d = ac/bd.
• Divide: multiply by the reciprocal: a/b ÷ c/d = a/b · d/c.
• Simplify by dividing numerator and denominator by their greatest common factor, ideally before you multiply.

Practice questions with solutions

Generated by the same engine as the Kollego course and solvable without a calculator. Pick an answer in your head, then open the solution.

1. 1. What is 5% of 250?

   • a262.5
   • b25.0
   • c237.5
   • d12.5
   Show solution

   Answer: 12.5

   'p percent of x' = (p / 100) · x.

   5/100 · 250 = 12.5.

2. 2. Compute: 2/12 + 46/12

   • a3
   • b5
   • c4
   • d48
   Show solution

   Answer: 4

   Same denominator: add the numerators, then simplify.

   (2 + 46) / 12 = 48/12 = 4.

3. 3. What is 5% of 800?

   • a760
   • b40
   • c80
   • d840
   Show solution

   Answer: 40

   'p percent of x' = (p / 100) · x.

   5/100 · 800 = 40.

4. 4. Compute: 2/6 + 10/6

   • a1
   • b3
   • c12
   • d2
   Show solution

   Answer: 2

   Same denominator: add the numerators, then simplify.

   (2 + 10) / 6 = 12/6 = 2.

5. 5. Compute without a calculator: (1/3 + 1/6) : (1/3 − 1/6)

   • a4
   • b9
   • c3
   • d1/3
   Show solution

   Answer: 3

   Bringen Sie each bracket to the common denominator p·q; dividing by a fraction is multiplying by its reciprocal.

   (9/18) : (3/18) = 9/3 = 3.

6. 6. Compute: 3/6 + 3/6

   • a0
   • b2
   • c6
   • d1
   Show solution

   Answer: 1

   Same denominator: add the numerators, then simplify.

   (3 + 3) / 6 = 6/6 = 1.

Common mistakes

• Adding denominators: 1/2 + 1/3 is 5/6, not 2/5.
• Forgetting to flip the second fraction when dividing.
• Leaving a result unsimplified when the options are simplified.

Related topics

All maths topics · T-Kurs · M-Kurs · W-Kurs