Step by step
The question
Question: simplify x/2 + x/3.
Simplify means: write it shorter, with the same value.
x2 + x3
1 Group like terms
Terms are the parts between the + and − signs.
Like terms are the same kind: same letters, same powers.
All the x terms go together.
Each colour is one kind.
like terms = same letters,
same powers
To add fractions, the bottoms must be the same.
We count up in 2s and in 3s.
6 is the first number in both lists.
x/2 is 3x/6: top and bottom times 3.
x/3 is 2x/6: top and bottom times 2.
Now the bottoms are the same, so we add the tops.
x/2 + x/3 is 5x/6.
In 2s: 2, 4, 6
In 3s: 3, 6
x2 + x3 = 3x6 + 2x6 = 5x6
So the expression is 5x/6.
= 5x6
2 Check
Let's check.
We pick a number for each letter: x = 2.
We put it into the start.
Start: 12 × 2 + 13 × 2 = 1 + 23 = 53
Now into our answer.
Answer: 56 × 2 = 53
Both give 5/3.
Same value, so 5x/6 is right!
Both give 53
Let's look back.
First: group like terms.
Last: check.
Answer
= 5x6