Combine Like Terms and Recognize Their Units
Group only terms with identical variable parts.
About 25 minutes, plus any extended practice
Supplied materials
- Paper and a pencil; drawing and spoken explanations are welcome. An adult may read directions and options aloud.
- Supplied worked-case record: Rewrite 3x+5+4x as 7x+5 because three copies of x and four copies total seven.
- All quantities and shape descriptions are supplied in the worked example and questions; no purchase or personal information is needed.
Learn the idea
Like terms contain the same variable part. Their coefficients can be combined just as equal units can be counted together. Constants are different from variable terms and must remain separate. Terms with different exponents are also not like terms. This preserves the expression’s meaning for every variable value.
Group only terms with identical variable parts. Add their coefficients and keep constants separate. Explain the grouping as counts of one common variable-sized quantity and check the rewritten expression with a supplied input.
Match the entire variable part before combining terms. Constants and variable terms are not like units. Underline like variable terms with one style and box constants separately.
- Underline like variable terms with one style and box constants separately.
- Work through the supplied example and label what each number or attribute represents.
- Group only terms with identical variable parts.
- Answer the check, then try the three changed-input practice questions and explain one correction.
See the method in action
Rewrite 3x+5+4x as 7x+5 because three copies of x and four copies total seven. The five is a fixed amount, not five copies of x. Also, x²+x cannot become 2x² because their variable parts are different. Match the entire variable part before combining terms. Constants and variable terms are not like units. Underline like variable terms with one style and box constants separately.
Check your reasoning
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Helpful tips
- Match the entire variable part before combining terms.
- Constants and variable terms are not like units.
See the answer and explanation
5x+5
Combine coefficients of x and leave the constant five unchanged.
Take it further
Simplify 6a+2+4a+7. Expected: 10a+9.
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More practice: try new cases
Choose an answer for each problem. Explain your method on paper, then use the feedback to decide what to revisit.
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Check the subject sources
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