Writing Expressions from Verbal Phrases
To write expressions from verbal phrases that group quantities, use parentheses around any sum or difference that is then operated on by another operation, ensuring the grouping is performed first. Phrases like the sum of a and b, times c translate to (a + b) times c. This Grade 5 math skill from Eureka Math Chapter 8 covers writing algebraic expressions.
Key Concepts
To translate verbal phrases that group quantities, use parentheses $()$. Phrases like "the sum of..." or "the difference between..." that are then multiplied or divided require parentheses to ensure the addition or subtraction is performed first. For example, "the sum of $a$ and $b$, times $c$" is written as $(a + b) \times c$.
Common Questions
How do you write an expression for the sum of 7 and 2, multiplied by 8?
Parentheses group the sum first: (7 + 2) times 8. Without parentheses, the expression 7 + 2 times 8 would mean add 7 to the product of 2 and 8, giving a different answer.
When do you need parentheses in an expression?
Use parentheses when a verbal phrase says a grouped operation (like a sum or difference) is then combined with another operation, ensuring the grouping is calculated before the outer operation.
What is an example of writing a verbal phrase as an expression?
Four times the sum of 1.5 and 6.2 is written as 4 times (1.5 + 6.2), because the parentheses tell you to add 1.5 and 6.2 first, then multiply the result by 4.
Why do parentheses change the value of an expression?
Parentheses override the default order of operations by signaling which calculation must happen first, so the same numbers with and without parentheses can produce completely different results.