Year 8 Equations with Fractions Dr J Frost Last modified: 23 rd March 2014.

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Presentation transcript:

Year 8 Equations with Fractions Dr J Frost Last modified: 23 rd March 2014

RECAP: Solving Linear Equations GARY Help Gary find the crumpet by solving the following linear equations. 5a + 7 = 42 a = 7 5x + 3 = 3x – 5 x = -4 1 – 2x = 8 x = -7/2 2(3 + 4x) = 6 – 4x x = 0 x + 1 = x + 2 No solution ? ? ? ? ? Nom

Exercise 1 Solve the following equations: (leave your answers as fractions where appropriate) 5x – 1 = 49x = 10 2x + 5 = 1x = -2 1 – x = 10x = -9 9x – 3 = -15x = -4/3 9 – 6x = 7x = 1/3 Solve the following equations: 2x – 1 = x + 1x = 2 9x – 1 = 6x + 4x = 5/3 7y + 1 = 9y + 6y = -5/2 1 – 8z = 2 – 5zz = -1/3 4 – 5z = 3 – 2zz = 1/3 4x + 5 = 2 – 3x x = -3/ ? ? ? ? ? ? ? ? ? Solve the following equations (or else): 2(x + 1) = 4x = 1 5(x – 3) = 15x + 5x = (2x + 4) = 9x + 4x = 3 5(3 – 4y) = 1 + 2(y + 1)y = 6/11 1 – 2(x – 4) = 3xx = 9/5 x + 2x(3 + x) = 2x 2 - 3x = -3/7 ? ? ? ? ? ? ? ?

Equations with Fractions We previously saw that we can do the ‘opposite’ of an operation to ‘cancel it out’, e.g. If 2x = 6, we divided by 2 to cancel out the “times 2” on the x. × 3 ? ?

Example (First times both sides by 3, then solve as normal) ?

Examples (First add 2 to both sides, then times both sides by 3) ? Add 5 to both sides. Then times both sides by 4 to get x = 4x (But we could have done these two steps the other way around) Then solve as normal. ?

Test Your Understanding ? ? ? 11 3 Bro Tip: In general, when solving an equation, we should multiply by the denominator of any fraction, so that we no longer have any fractions lurking about.

(Vote with your diaries) Solve for x.

6/55/610/610/7 (Vote with your diaries) Solve for x.

45/940/955/950/9 (Vote with your diaries) Solve for x.

Exercises Solve the following equations for x  ? ? ? ? ? ? ? ? ? ? ? ? ?