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

Order a 12-month Year 7 Interactive Maths software Homework Licence for only $19.95. Order a 12-month Year 8 Interactive Maths software Homework Licence for only $19.95. Order a 12-month Year 9 Interactive Maths software Homework Licence for only $19.95. Order a 12-month Year 10 Interactive Maths software Homework Licence for only $19.95.

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.

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