Question

3-3 write algebraic expressions
period: 3-8
define a variable. then write each phrase as an algebraic expression.

1. nine less than a number
2. five times the number of books in the library
3. three more pancakes than his brother ate
4. two more than seven times lynn’s age
5. 9 minutes less than frances’ time
6. the quotient of 7 and m
7. the quotient of 9 and 4, less than m
8. 9 times a number, decreased by 10
9. 12 less than the amount of pete’s pencils
10. 3 less than willow’s awards

Explanation:

Problem 4: two more than seven times Lynn’s age

Step 1: Define the variable

Let \( a \) represent Lynn's age.

Step 2: Translate "seven times Lynn’s age"

Seven times Lynn’s age is \( 7 \times a = 7a \).

Step 3: Translate "two more than seven times Lynn’s age"

Two more than \( 7a \) means we add 2 to \( 7a \), so the expression is \( 7a + 2 \).

Step 1: Find the quotient of 9 and 4

The quotient of 9 and 4 is \( \frac{9}{4} \).

Step 2: Translate "the quotient of 9 and 4, less than m"

"Less than" here means we subtract the quotient from \( m \), so the expression is \( m - \frac{9}{4} \).

Step 1: Define the variable

Let \( w \) represent the number of Willow’s awards.

Step 2: Translate "3 less than Willow’s awards"

3 less than \( w \) means we subtract 3 from \( w \), so the expression is \( w - 3 \).

Answer:

\( 7a + 2 \) (where \( a \) is Lynn's age)

Problem 7: the quotient of 9 and 4, less than m