Two-Step Equations with Fractions Worksheets - Free Printable

Let’s solve each of the 8 two-step equations step by step. The goal is to isolate the variable on one side of the equation.

---

1) 5a + 2/3 = -1/6

Step 1: Subtract 2/3 from both sides:

5a = -1/6 - 2/3

To subtract, get a common denominator (LCM of 6 and 3 is 6):

-1/6 - 4/6 = -5/6

So,

5a = -5/6

Step 2: Divide both sides by 5:

a = (-5/6) ÷ 5 = (-5/6) × (1/5) = -1/6

✔ Answer: a = -1/6

---

2) 4/7 = 8(c - 6/7)

Step 1: Divide both sides by 8:

(4/7) ÷ 8 = c - 6/7

→ (4/7) × (1/8) = 4/56 = 1/14

So,

1/14 = c - 6/7

Step 2: Add 6/7 to both sides:

c = 1/14 + 6/7

Convert 6/7 to 12/14:

c = 1/14 + 12/14 = 13/14

✔ Answer: c = 13/14

---

3) (r - 1)/2 = 0

Multiply both sides by 2:

r - 1 = 0

Add 1 to both sides:

r = 1

✔ Answer: r = 1

---

4) -10 - m = -5/9

Step 1: Add 10 to both sides:

-m = -5/9 + 10

Convert 10 to 90/9:

-m = -5/9 + 90/9 = 85/9

Step 2: Multiply both sides by -1:

m = -85/9

✔ Answer: m = -85/9

---

5) 8/5 = (3/5)u + 6/5

Step 1: Subtract 6/5 from both sides:

8/5 - 6/5 = (3/5)u

→ 2/5 = (3/5)u

Step 2: Multiply both sides by 5 to eliminate denominators:

2 = 3u

Then divide by 3:

u = 2/3

✔ Answer: u = 2/3

---

6) (h + 4)/3 = 2/9

Step 1: Multiply both sides by 3:

h + 4 = (2/9) × 3 = 6/9 = 2/3

Step 2: Subtract 4 from both sides:

h = 2/3 - 4

Convert 4 to 12/3:

h = 2/3 - 12/3 = -10/3

✔ Answer: h = -10/3

---

7) (1/6)k - 1 = 5

Step 1: Add 1 to both sides:

(1/6)k = 6

Step 2: Multiply both sides by 6:

k = 6 × 6 = 36

✔ Answer: k = 36

---

8) -1/8 = 7/4 + (3/2)z

Step 1: Subtract 7/4 from both sides:

-1/8 - 7/4 = (3/2)z

Convert 7/4 to 14/8:

-1/8 - 14/8 = -15/8

So,

-15/8 = (3/2)z

Step 2: Multiply both sides by 2/3 to isolate z:

z = (-15/8) × (2/3)

Simplify:

(-15 × 2) / (8 × 3) = (-30)/24 = -5/4 (after dividing numerator and denominator by 6)

✔ Answer: z = -5/4

---

✔ Final Answers:

1) a = -1/6
2) c = 13/14
3) r = 1
4) m = -85/9
5) u = 2/3
6) h = -10/3
7) k = 36
8) z = -5/4

Let me know if you’d like to see any step explained further!