**Equations with rational numbers worksheet :**

Worksheet on equations with rational numbers is much useful to the students who would like to practice solving equations which involve fractions and decimals.

1. Solve : 7n/10 + 3/2 = 3n/5 + 2

2. Solve : k/7 - 6 = 3k/7 + 4

3. Solve : 0.7n + 0.33 = 0.3n + 0.5

**Problem 1 :**

Solve : 7n/10 + 3/2 = 3n/5 + 2

**Solution :**

**Step 1 : **

Find the least common multiple of the denominators (10, 2 and 5).

LCM = 5 x 2 x 1 x 1 x 1

LCM = 10

**Step 2 : **

Multiply both sides of the equation by 10.

10(7n/10 + 3/2) = 10(3n/5 + 2)

Use distributive property.

10(7n/10) + 10(3/2) = 10(3n/5) + 10(2)

Simplify.

7n + 5(3) = 2(3n) + 20

7n + 15 = 6n + 20

**Step 3 :**

Use inverse operations to solve for "n".

Subtract 15 from both sides.

aaaaaaaaaaaaaaaa 7n + 15 = 6n + 20 aaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaa - 15 - 15 aaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaa---------------------- aaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaa 7n = 6n + 5 aaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaa---------------------- aaaaaaaaaaaaaaaa

Subtract 6n from both sides.

aaaaaaaaaaaaaaaa 7n = 6n + 5 aaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaa -6n -6n aaaaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaa -------------------- aaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaa n = 5 aaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaa -------------------- aaaaaaaaaaaaaaaa

**Problem 2 :**

Solve : k/7 - 6 = 3k/7 + 4

**Solution :**

**Step 1 : **

Find the least common multiple of the denominators.

Here, we have the same denominator on both sides. That is 7.

So, LCM = 7.

**Step 2 : **

Multiply both sides of the equation by 7.

7(k/7 - 6) = 7(3k/7 + 4)

Use distributive property.

7(k/7) - 7(6) = 7(3k/7) + 7(4)

Simplify.

k - 42 = 3k + 28

**Step 3 :**

Use inverse operations to solve for "k".

Subtract 28 from both sides.

aaaaaaaaaaaaaaaa k - 42 = 3k + 28 aaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaa - 28 - 28 aaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaa---------------------- aaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaa k - 70 = 3k aaaaaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaa---------------------- aaaaaaaaaaaaaaaaaa

Subtract k from both sides.

aaaaaaaaaaaaaaaaaaaa k - 70 = 3k aaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaa - k - k aaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaa---------------- aaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaa -70 = 2k aaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaa---------------- aaaaaaaaaaaaaaaaaa

Divide both sides by 2.

-70 / 2 = 2k / 2

-35 = k

**Problem 3 : **

Solve : 0.7n + 0.33 = 0.3n + 0.5

**Solution :**

**Step 1 :**

In the second term 0.33 on the left side, we have two digits (more number of digits) after the decimal.

So, multiply both sides of the equation by 10² ( = 100).

100(0.7n + 0.33) = 100(0.3n + 0.5)

100(0.7n) + 100(0.33) = 100(0.3n) + 100(0.5)

70n + 33 = 30n + 50

**Step 2 :**

Subtract 33 from both sides.

aaaaaaaaaaaaaaaa 70n + 33 = 30n + 50 aaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaa - 33 - 33 aaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaa ------------------------ aaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaa 70n = 30n + 17 aaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaa ------------------------ aaaaaaaaaaaaaaaa

Subtract 30n from both sides.

aaaaaaaaaaaaaaaa 70n = 30n + 17 aaaaaaaaaaaaaaaa aaaaaaaaaaaaaa - 30n = -30n aaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaa------------------------- aaaaaaaaaaaaaaaa aaaaaaaaaaaaaaa 40n = 17 aaaaaaaaaaaaaaaa aaaaaaaaaaaaaaa------------------------- aaaaaaaaaaaaaaaa

Divide both sides by 40.

40n/40 = 17/40

n = 0.425

After having gone through the stuff given above, we hope that the students would have understood "Equations with rational numbers worksheet".

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