• MathsFirst Home
• Online Maths Help
  • Notation
  • Arithmetic
    • Decimals
    • Fractions
    • HCF and LCM
    • Order of Operations
    • Signed Numbers
  • Algebra
    • Exponents
      • Integer Exponents
      • Fractional Exponents
      • Exponents Worksheet
    • Combining Like Terms
    • Simple Expansions
    • Factorisation
    • Mathematical Formulae
      • Constructing Formulae
      • Rearranging Formulae
        • Order of Operations for Algebraic Expressions
        • Inverse Operations and Functions
        • Rearranging Equations I (Simple Equations)
        • Rearranging Equations II (Quadratic Equations)
        • Rearranging Equations III (Harder Examples)
      • Area, Surface Area and Volume Formulae
    • Coordinate Systems and Graphs
    • Linear Equations & Graphs
    • Simultaneous Linear Equations
    • Polynomials
    • Quadratic Polynomials
    • Rational Functions
    • Logarithms
  • Calculus
    • Differentiation
      • Tangents, Derivatives and Differentiation
      • The Basic Rules
      • Products and Quotients
      • Chain Rule
      • Logarithmic Differentiation
      • Mixed Differentiation Problems
      • Sign of the Derivative
      • Sign of the Second Derivative
    • Integration
      • Basic Integrals
      • Multiple, Sum and Difference Rules
      • Linear Substitution
      • Simpler Integration by Substitution
      • Harder Integration by Substitution
      • Trig Substitution 1
      • Trig Substitution 2
      • Integration by Parts
  • Trigonometry
    • Pythagoras Theorem
    • Trig Functions and Related Topics
• First Year Maths Pathways
• Readiness Quizzes
• Study Maths
  at Massey
  • Undergraduate
  • Postgraduate
• Other Math Links
• About MathsFirst
• Contact Us

Fractions

Multiplication

Imagine for a moment that you have some leftover pie. This bit is 5/12 of the original pie. Now we want just 2/5 of the leftovers for a yummy snack. To work out how much pie we get we need to find out what 2/5 of 5/12 is, we need to multiply the fractions.

     =

2/5 × 5/12 = (2×5)/(5×12) = 10/60 = 2/12 = 1/6

To multiply two fractions we simply multiply their numerators and multiply their denominators, reducing the answer if possible:

           =

The answer is called the product of the two fractions.

Example

Click on the question marks to see an example of multiplication of fractions shown step-by-step.

More Examples

Now study a few more examples of multiplying two fractions.

Exercise

Now practise solving a few exercises on your own. Remember to reduce the answer if possible.

Imagine that you have several pies with the same amount leftover from each. We can calculate the amount of pie left by multiplying the amount remaining by the number of pies.

3 × = =

3 × 5/12 = 3/1 × 5/12 = 15/12 = 5/4

To multiply an integer by a fraction, first write the integer as a fraction and then multiply as usual.

Example

Click on the question marks below to see the example worked out step-by-step.

or simply

More Examples

Exercise

Practice with some of these exercises:

Multiplication of signed fractions

Just as for all operations, the same basic methods apply to signed fractions. The only extra complication is that we must remember to deal with the sign. Decide the sign first before you multiply so you don't forget.

Signs of numbers after multiplication

Examples

Exercise

Now try some exercises. Remember to reduce the fractions if possible.

<< Equivalent Fractions | Fractions Index | Reciprocals >>