Testinar Grade 7 math

Simplifying Expressions by Combining Like Terms

Students will build Grade 7 mastery of simplifying expressions by combining like terms using models, equations, and test-style reasoning.

CH04-02 Expressions

Directions Solve each problem. Show your reasoning on the page or on separate paper. Check the answer key only after finishing.

Simplify: \(5x+3y-2x+4y\)
1. \(3x+7y\)
2. \(7x+7y\)
3. \(3x-y\)
4. \(10xy\)
Simplify: \(8a+5b-3a-2b\)
1. \(5a+3b\)
2. \(11a+3b\)
3. \(5a+7b\)
4. \(16ab\)
Which terms are like terms?
1. \(4x\) and \(4y\)
2. \(3x^2\) and \(3x\)
3. \(7m\) and \(2m\)
4. \(5xy\) and \(5x\)
Simplify: \(12x-7x+3x\)
1. \(8x\)
2. \(22x\)
3. \(2x\)
4. \(12x\)
Identify which pair are NOT like terms.
1. \(6a^2\) and \(9a^2\)
2. \(5x\) and \(5x^2\)
3. \(-3y\) and \(4y\)
4. \(2mn\) and \(mn\)
Simplify: \(4p+6q+2p-q\)
1. \(6p+5q\)
2. \(6p+7q\)
3. \(4p+6q\)
4. \(12pq\)
Which expression is simplified?
1. \(3x+2x-y\)
2. \(5x+2x-y+y\)
3. \(5x-y\)
4. \(2x+3x+4y\)
What is the coefficient of \(x\) in the simplified form of \(9x-4x+2y\)?
1. \(9\)
2. \(5\)
3. \(4\)
4. \(13\)

Teacher and parent reference

Answer key and explanations

A. \(3x+7y\)
Group like terms by variable: \((5x-2x)+(3y+4y)=(5-2)x+(3+4)y=3x+7y\).
A. \(5a+3b\)
Combine like terms: \((8a-3a)+(5b-2b)=5a+3b\).
C. \(7m\) and \(2m\)
Like terms have the same variable and exponent. Both \(7m\) and \(2m\) contain the variable \(m\) with exponent 1.
A. \(8x\)
Combine coefficients: \((12-7+3)x=8x\).
B. \(5x\) and \(5x^2\)
These have different exponents (\(x^1\) vs. \(x^2\)), so they are not like terms.
A. \(6p+5q\)
Combine like terms: \((4p+2p)+(6q-q)=6p+5q\).
C. \(5x-y\)
A simplified expression has all like terms combined. Option C has no like terms remaining.
B. \(5\)
Simplify: \((9-4)x+2y=5x+2y\). The coefficient of \(x\) is \(5\).