G S Rehill's Interactive Maths Software Series - "Building a Strong Foundation in Mathematics" from mathsteacher.com.au.

 

Year 10 Interactive Maths - Second Edition


Equations Containing Fractions

Clear the fractions by multiplying both sides of the equation by the lowest common multiple of the denominators. Then solve the equation by applying the same operation(s) to both sides of it.

Example 9

Solve (2x + 1) / 3 = (x + 4) / 2 for x.
Solution:

Multiply both sides by 6 which is the Lowest Common Multiple of 3 and 2. Then use the Distributive Law to remove the brackets, subtract 2 from both sides and finally subtract 3x from both sides.
Check:

If you substitute x = 10 into the LHS and the RHS of the equation, we find the LHS = RHS. So, our solution, x = 10, is correct.


Example 10

Solve m / 4 - (2 - m) / 3 = 1/ 4 for m.
Solution:

Multiply both sides of the equation by 12 which is the Lowest Common Multiple of 4 and 3.

Use the Distributive Law to remove the brackets, then collect like terms, add 8 to both sides and finally divide both sides by 7 to find m = 1 4 / 7.

 

Study Another Topic in Chapter 2: Linear Equations and Inequalities

[ Solving Equations ] [ Equations Involving Two or More Operations ] [ Equations Containing Brackets ] [ Equations Containing Fractions ] [ Problem Solving ] [ Consecutive Numbers ] [ Solving Inequalities ] [ Adding a Number to Each Side of an Inequality ] [ Multiplying Each Side of an Inequality by a Positive Number ] [ Dividing Each Side of an Inequality by a Positive Number ] [ Multiplying Each Side of an Inequality by a Negative Number ] [ Dividing Each Side of an Inequality by a Negative Number ] [ Inequalities Involving Two Operations ] [ Inequalities Containing Brackets ] [ Inequalities Containing Fractions ] [ Transposition of Formulas ] [ Transpositions Involving Subtraction ] [ Transpositions Involving Division ] [ Transpositions Involving Multiplication ] [ Transpositions Involving Squares ] [ Transpositions Involving Square Roots ] [ Transpositions Involving Brackets ] [ Transpositions Involving Fractions ] [ Transpositions Involving Two or More Operations ] [ Subject Occurring Twice ] [ Substitution ] [ Problem Solving ] [ Problem Solving Unit ] [ Symbols ] [ Index ]

 
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