Equivalent Expressions Reveal Meaning
Aligned to 7.EE.A.2 — Common Core State Standards for Mathematics.
What this lesson teaches
Rewriting an expression in a different but equivalent form can make a relationship easier to see. Combining like terms or factoring shows structure without changing the value.
Worked examples
Example 1
A price plus 5% tax is p + 0.05p. Factoring gives 1.05p, which shows the total is 105% of the original price. For p = 80: 1.05 × 80 = $84.
Example 2
A 15% discount is p − 0.15p, which factors to 0.85p — you pay 85% of the price. One multiplication instead of two steps.
Example 3
Two forms can both be correct and say different things. 5(x + 2) emphasizes five equal groups; 5x + 10 emphasizes a flat $10 added on.
Practice questions
- Rewrite x + x + x + x as a product, and explain what it shows.
- Show that c − 0.10c equals 0.90c, and explain what 0.90c means.
- A field's length is w + 3 and its width is w. Write the perimeter in simplest form.
Watch the lesson
Every lesson comes with a video taught in English and Spanish — the same video the QR code in the printed workbook opens.
▶ Watch this lessonEn español
Expresiones Equivalentes Revelan el Significado
Reescribir una expresión en otra forma equivalente puede hacer más visible una relación. Combinar términos semejantes o factorizar muestra la estructura sin cambiar el valor.
Ejemplo 1: Un precio más 5% de impuesto es p + 0.05p. Al factorizar queda 1.05p, lo que muestra que el total es 105% del precio original. Para p = 80: 1.05 × 80 = $84.
Ejemplo 2: Un descuento de 15% es p − 0.15p, que se factoriza como 0.85p — pagas el 85% del precio. Una multiplicación en vez de dos pasos.
Ejemplo 3: Dos formas pueden ser correctas y decir cosas distintas. 5(x + 2) destaca cinco grupos iguales; 5x + 10 destaca $10 fijos agregados.
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