Equations with fractions

Solve (x + 5)/2 = (x + 12)/3

The aim is to get x on its own. Whatever we do to one side, we do to the other, so the equation stays balanced. This one takes 4 steps.

1. (x + 5)/2 = (x + 12)/3The question.

2. Step 1: Multiply by 6 on both sides ×6

   There are fractions. Multiply both sides by 6 to clear them: 6 is the smallest number that all the bottoms go into.

   3(x + 5) = 2(x + 12)

   Multiplying every term by the same number keeps the balance.

3. Step 2: Expand the brackets on both sides expand

   Expand the brackets first, so you can see all the x terms.

   3x + 15 = 2x + 24

   Multiply the number outside by everything inside.

4. Step 3: Subtract 2x on both sides −2x

   There’s x on both sides. Take away 2x on both sides so x is only on one side. Choosing the smaller x keeps the numbers positive.

   x + 15 = 24

   On the right, the 2x cancels out. Now there’s no x on the right.

   You can add or take away x terms, just like numbers.

5. Step 4: Subtract 15 on both sides −15

   On the left, the x part has + 15 with it. Take 15 away from both sides to get rid of it.

   x = 9

   On the left, the 15 cancels out. x is on its own. x = 9.

   + 15 is undone by − 15.

Answer: x = 9

Check it

Put x = 9 back into the question. If both sides come to the same number, the answer is right.

Left side: (x + 5)/2 → 7

Right side: (x + 12)/3 → 7

✓ Both sides are 7, so x = 9 is right.

Now try it yourself

Solve this one in Algebra Balance. You choose each step, and it explains what happened, with hints if you get stuck.

Practise this in Algebra Balance

More like this

• (x + 1)/2 = (x + 4)/5
• (x + 3)/3 = (x + 7)/4
• (x + 6)/3 = (x + 19)/6
• (x + 6)/2 = (x + 15)/3
• (x + 2)/3 = (x + 12)/6
• (x + 2)/2 = (x + 15)/4
• (x + 1)/2 = (x + 10)/5
• (x + 3)/3 = (x + 8)/4