Collecting like terms

The Maths Habit

Write in algebra.

1These tiles
xxxx
4x
2This tile
x
x
3x + x + x
xxx
3x

Sam tips out a bag of tiles. How would you sort them? How could Sam say what is in the bag quickly?

xxxxxxx

Put the same kind together. Count each kind. An x tile and a cube are not the same kind.

xxxx
Term
One part of an expression. A + or a − sign starts the next term.
xxxxxx
Like terms
Terms with the same letter. Numbers on their own are like terms too.
xxxxxx
Simplify
Collect the like terms, so the expression is shorter.

Simplify 3x + 2 + 2x + 4

xxx2xx4
the tiles
1Sort the terms
3x + 2x2 + 4
x'sxxxxx24numbers
the same kinds together
2Count each kind
5x6
x'sxxxxx24numbers5x6
count each kind
3Write the answer
5x + 6
an x and a number stay apart

Like terms? Yes or no.

13x and 5x
xxxxxxxx
Yes
24x and 4
xxxx4
No
3x and 6x
xxxxxxx
Yes

Simplify 4x + 3 + 2x + 5

xxxx3xx5
xx'snumbers
1Sort the terms
4x + 2x3 + 5
2Count each kind
6x8
3Write the answer
6x + 8

Simplify 3x + 1 + 2x + 6

xxx1xx6
xx'snumbers
1Sort the terms
3x + 2x1 + 6
2Count each kind
5x7
3Write the answer
5x + 7

Simplify 4x + 3 + 2x + 5

xxxx3xx5
xx'snumbers
1Sort the terms
4x + 2x3 + 5
2Count each kind
6x8
3Write the answer
6x + 8

Simplify 2x + 8 + x + 1

xx8x1
xx'snumbers
1Sort the terms
2x + x8 + 1
2Count each kind
3x9
3Write the answer
3x + 9
Remember1Sort the terms2Count each kind3Write the answer

Simplify 4x + 3 + 2x + 5

xxxx3xx5
xx'snumbers
1Sort the terms
4x + 2x3 + 5
2Count each kind
6x8
3Write the answer
6x + 8

Simplify 3 + 4x + 5 + 3x

3xxxx5xxx
xx'snumbers
1Sort the terms
4x + 3x3 + 5
2Count each kind
7x8
3Write the answer
7x + 8
Remember1Sort the terms2Count each kind3Write the answer

Simplify 4x + 3 + 2x + 5

xxxx3xx5
xx'snumbers
1Sort the terms
4x + 2x3 + 5
2Count each kind
6x8
3Write the answer
6x + 8

Simplify 5x + 2 + 2x + 4

xxxxx2xx4
xx'snumbers
1Sort the terms
5x + 2x2 + 4
2Count each kind
7x6
3Write the answer
7x + 6
Remember1Sort the terms2Count each kind3Write the answer

Simplify x + 5 + 2x + 3

x5xx3
xx'snumbers
1Sort the terms
x + 2x5 + 3
2Count each kind
3x8
3Write the answer
3x + 8

Simplify 4x + 1 + 4x + 6

xxxx1xxxx6
xx'snumbers
1Sort the terms
4x + 4x1 + 6
2Count each kind
8x7
3Write the answer
8x + 7

Simplify 6 + 2x + 2 + 5x

6xx2xxxxx
xx'snumbers
1Sort the terms
2x + 5x6 + 2
2Count each kind
7x8
3Write the answer
7x + 8
Remember1Sort the terms2Count each kind3Write the answer

xxxxx−x−x
xxxxx−x−x
each dashed tile cancels a pink tile
  • A dashed tile takes away.
  • The − sign stays with its term.
  • 5x − 2x is five x's, take away two. 3x is left.

What is left? Write it in algebra.

5x − 2xxxxxx−x−x 3x

Simplify 7x + 6 − 3x + 2

xxxxxxx6−x−x−x2
xx'snumbers
1Sort the terms
7x − 3x6 + 2
2Count each kind
4x8
3Write the answer
4x + 8

Simplify 5x + 9 + x − 4

xxxxx9x− 4
xx'snumbers
1Sort the terms
5x + x9 − 4
2Count each kind
6x5
3Write the answer
6x + 5

Simplify 7x + 6 − 3x + 2

xxxxxxx6−x−x−x2
xx'snumbers
1Sort the terms
7x − 3x6 + 2
2Count each kind
4x8
3Write the answer
4x + 8

Simplify 8x + 3 − 2x + 4

xxxxxxxx3−x−x4
xx'snumbers
1Sort the terms
8x − 2x3 + 4
2Count each kind
6x7
3Write the answer
6x + 7
Remember1Sort the terms2Count each kind3Write the answer

Simplify 7x + 6 − 3x + 2

xxxxxxx6−x−x−x2
xx'snumbers
1Sort the terms
7x − 3x6 + 2
2Count each kind
4x8
3Write the answer
4x + 8

Simplify 4x + 9 + 3x − 5

xxxx9xxx− 5
xx'snumbers
1Sort the terms
4x + 3x9 − 5
2Count each kind
7x4
3Write the answer
7x + 4
Remember1Sort the terms2Count each kind3Write the answer

Simplify 7x + 6 − 3x + 2

xxxxxxx6−x−x−x2
xx'snumbers
1Sort the terms
7x − 3x6 + 2
2Count each kind
4x8
3Write the answer
4x + 8

Simplify 6x + 7 − 3x − 2

xxxxxx7−x−x−x− 2
xx'snumbers
1Sort the terms
6x − 3x7 − 2
2Count each kind
3x5
3Write the answer
3x + 5
Remember1Sort the terms2Count each kind3Write the answer

Simplify 5x + 3 − x + 6

xxxxx3−x6
xx'snumbers
1Sort the terms
5x − x3 + 6
2Count each kind
4x9
3Write the answer
4x + 9

Simplify 6x + 8 + 2x − 5

xxxxxx8xx− 5
xx'snumbers
1Sort the terms
6x + 2x8 − 5
2Count each kind
8x3
3Write the answer
8x + 3

Simplify 7x + 5 − 2x − 1

xxxxxxx5−x−x− 1
xx'snumbers
1Sort the terms
7x − 2x5 − 1
2Count each kind
5x4
3Write the answer
5x + 4
Remember1Sort the terms2Count each kind3Write the answer

Collecting like terms worksheet, page 1

Collecting like terms worksheet, page 2

Answer sheet

Is it simplified right? Thumbs up: yes. Thumbs down: no.

  1. 3x + 2x  =  5x

    Yes

  2. 4x + 3  =  7x

    No: it stays 4x + 3

  3. 6x − 2x  =  4x

    Yes

  4. 2x + 4 + 3x  =  9x

    No: 5x + 4

  5. x + 5 + x  =  2x + 5

    Yes

  1. Two bricks add up to make a top brick. The top brick is 7x + 6. One brick is 3x + 2. What is the other brick?

    4x + 4

  2. Write an expression with four terms that simplifies to 5x + 3.

    2x + 1 + 3x + 2

  3. Mo says 7x − 7 simplifies to x. Is Mo right?

    No: 7x and 7 are not like terms

  1. Simplify 3x + 6 + 2x + 1. Step 1 is given.

    5x + 7
    xxx6xx1

  2. Simplify 6x + 4 − 2x + 5

    4x + 9
    xxxxxx4−x−x5

  3. Simplify 2y + 8 + 5y − 3.

    7y + 5
Exit tickets to print