Problem 44
Question
Simplify each expression. \(5 m+2 m\)
Step-by-Step Solution
Verified Answer
7m
1Step 1: Identify Like Terms
The terms in the expression are 5m and 2m. These terms are 'like terms' because they both contain the variable m.
2Step 2: Combine Like Terms
Add the coefficients of the like terms together. The coefficients are 5 and 2. So, add these coefficients: 5 + 2 = 7.
3Step 3: Rewrite the Expression
After combining the coefficients, multiply the sum by the variable m. This gives the simplified expression 7m.
Key Concepts
simplifying algebraic expressionscoefficientslike terms
simplifying algebraic expressions
Simplifying algebraic expressions means making them as simple as possible. This involves combining like terms, which share the same variable and exponent. For example, in the expression \(5m + 2m\), both terms share the variable \(m\).
By simplifying, we combine these terms into one, which makes the expression easier to work with.
Simplification is vital in algebra, as it helps solve equations and understand mathematical relationships more clearly.
By simplifying, we combine these terms into one, which makes the expression easier to work with.
Simplification is vital in algebra, as it helps solve equations and understand mathematical relationships more clearly.
coefficients
Coefficients are the numerical parts of terms that include variables. In the expression \(5m + 2m\), the coefficients are 5 and 2.
These numbers tell us how many of the variable we are dealing with. For example, \(5m\) means five times \(m\), and \(2m\) means two times \(m\).
When combining like terms, you add the coefficients while keeping the variable part the same. This step is crucial in making the expression simpler.
These numbers tell us how many of the variable we are dealing with. For example, \(5m\) means five times \(m\), and \(2m\) means two times \(m\).
When combining like terms, you add the coefficients while keeping the variable part the same. This step is crucial in making the expression simpler.
like terms
Like terms are terms that contain the same variable raised to the same power. They can be combined by adding or subtracting their coefficients.
In the example \(5m + 2m\), both terms are like terms because they have the variable \(m\).
To combine them, we add their coefficients: 5 + 2, which equals 7. So, \(5m + 2m\) simplifies to \(7m\).
Understanding and identifying like terms are fundamental skills for simplifying algebraic expressions.
In the example \(5m + 2m\), both terms are like terms because they have the variable \(m\).
To combine them, we add their coefficients: 5 + 2, which equals 7. So, \(5m + 2m\) simplifies to \(7m\).
Understanding and identifying like terms are fundamental skills for simplifying algebraic expressions.