SME
Grade 8 Math · Problem type
Clear the fraction
Use this for “3/4 x + 2 = −7”.
Chart
s = (3/4)x + 2
Slope k = 3/4: up 3 for every 4 across
Intercept r = 2: it crosses the y-axis at (0, 2)
s = 3/4 × (−12) + 2 = −7 when x = −12
This is an example. Type your own values to start a new problem.
p
q
x
+
r
=
s
R
Added, times q
worked out (not typed)
S
Right side, times q
worked out (not typed)
x
x
worked out (not typed)
Formulas
R
=
q
×
r
(added,
times
q
=
denominator
×
number
added)
8 = 4 × 2
S
=
q
×
s
(right
side,
times
q
=
denominator
×
right
side)
−28 = 4 × (−7)
x
=
(
S
−
R
)
÷
p
(x
=
(right
side,
times
q
−
added,
times
q)
÷
numerator)
−12 = (−28 − 8) ÷ 3
Assumptions
•
Multiply every term on both sides by the denominator: the whole side, not just the fraction.
•
Then p × x + R = S has whole numbers.
•
Take R from both sides, then divide by p.
Step-by-step
WE KNOW
p = 3 (numerator), q = 4 (denominator), r = 2 (number added), s = −7 (right side)
FIND
added, times q (R), right side, times q (S), x (x)
Step 1 · Find added, times q (R)
Use R = q × r (added, times q = denominator × number added)
Multiply the added number by the denominator too.
R
=
4
×
2
R
=
8
Step 2 · Find right side, times q (S)
Use S = q × s (right side, times q = denominator × right side)
And the right side: every term on both sides.
S
=
4
×
(−7)
Times
4:
3
x
+
8
=
−28
S
=
−28
Step 3 · Find x (x)
Use x = (S − R) ÷ p (x = (right side, times q − added, times q) ÷ numerator)
Now
p
×
x
+
R
=
S
:
take
R
away,
then
divide
by
p
.
x
=
−28 − 8
3
x
=
−
36
3
x
=
−12
Check
Put the numbers back in. Both sides should match.
8 = 4 × 2 ✓
−28 = 4 × (−7) ✓
−12 = (−28 − 8) ÷ 3 ✓
Topic check
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