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…
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
