12) Equations Including Fractions.ppt
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This document discusses solving equations that include fractions. It provides examples of making fractions equivalent before combining like terms, such as when there are multiple fractions on one side of the equation. The examples show setting fractions equal to each other, isolating the variable, and solving for the variable value. Key steps involve making denominators the same and then adding or subtracting fractions with the same denominator.
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12) Equations Including Fractions.ppt
- 2. Starter • Making equivalent fractions 2 3 15 = 3 7 27 = 4x 9 36 = 10 16x 63
- 3. Equations Including Fractions • We have reviewed solving equations with ‘x’ on one side and ‘x’ on both sides • Today we will extend this to equations with fractions in • The method is essentially the same, get all the x’s on one side, and all the numbers on the other…
- 4. Equations Including Fractions x 3 = 6 = x 18 x 3 x 3
- 5. Equations Including Fractions x 5 = 1 = x 5 5 + 4 + 4 - 4 x 5 x 5 = x 25
- 6. Equations Including Fractions x + 8 4 = 3 = x + 8 12 x 4 x 4 = x 4 - 8 - 8
- 7. Equations Including Fractions x 4 = 3 4 = 3x + 4 9 x 12 x 12 When there are multiple fractions, make them equivalent first! 1 3 + 3x 12 = 9 12 4 12 + = 3x 5 - 4 - 4 ÷ 3 ÷ 3 = x 1 2/3
- 8. Equations Including Fractions 3x 2 = 1 6 = 45x - 18 5 x 30 x 30 When there are multiple fractions, make them equivalent first! 3 5 - 45x 30 = 5 30 18 30 - = 45x 23 + 18 + 18 ÷ 45 ÷ 45 = x 23/45
- 9. Equations Including Fractions 5x 3 = 2 5 = 25x 6 x 15 x 15 When there are multiple fractions, make them equivalent first! 3 - 25x 15 = 6 15 3 - = 25x 51 + 45 + 45 ÷ 25 ÷ 25 = x 2 1/25 - 45
- 10. Equations Including Fractions 2x 5 = 10 x 15 x 15 When there are multiple fractions, make them equivalent first! x + 1 3 + = 11x + 5 150 Group x’s - 5 - 5 = 145 6x 15 = 10 5x + 5 15 + 6x = 150 5x + 5 + 11x = 13 2/11 x ÷ 11 ÷ 11
- 11. Equations Including Fractions 7 a = 5 8 = 56 5a x 8a x 8a When there are multiple fractions, make them equivalent first! 4 + 56 8a = 5a 8a 4 + = 56 -27a - 32a - 32a ÷ -27 ÷ -27 = -2 2/27 a + 32a
- 12. Plenary 3(x – 4) 2 = 8 = 3(x – 4) 16 x 2 x 2 = 3x 28 Expand the bracket = 3x – 12 16 + 12 + 12 ÷ 3 ÷ 3 = x 9 1/3
- 13. Plenary 3(x – 4) 2 = 8 = 3(x – 4) 16 x 2 x 2 = x 9 1/3 = x - 4 5 1/3 + 4 + 4 ÷ 3 ÷ 3 Alternatively…
- 14. Plenary (x + 6) 4 = 2x + 5 = x + 6 8x + 20 x 4 x 4 = -14 7x -x = 6 7x + 20 - 20 - 20 ÷ 7 ÷ 7 = -2 x - x
- 15. Summary • We have extended our knowledge of solving equations • We have looked at ways of ‘cancelling’ a fraction • We have done this with x on one side or both sides of the equation