1. Writing Expressions
Lesson 1.2.1

2. Writing Expressions 1.2.1 California Standard: What it means for you:
Lesson
1.2.1
Writing Expressions
California Standard:
Algebra and Functions 1.1
Use variables and appropriate operations to write an expression, an equation, an inequality, or a system of equations or inequalities that represents a verbal description (e.g., three less than a number, half as large as area A).
What it means for you:
You’ll learn how to change word descriptions into math expressions.
Key Words:
addition
subtraction
product
quotient

3. “two more than x” is the same as “x + 2”
Lesson
1.2.1
Writing Expressions
You can use both a word expression and a math expression to describe the same situation.
“two more than x” is the same as “x + 2”
In Section 1.1 you practiced changing numeric and variable expressions into word expressions.
This Lesson is all about doing the reverse — changing word expressions into math expressions.

4. Lesson
1.2.1
Writing Expressions
Variable Expressions Describe Word Expressions
To write an expression to represent a word sentence you need to figure out what the word sentence actually means.

5. Lesson
1.2.1
Writing Expressions
Example 1
Write a variable expression to describe the sentence “A number, x, is increased by five.”
Solution
The phrase “a number, x” is telling you that x is the variable being used.
The words “increased by” are telling you that something is being added on to the variable x. In this case it is the number five.
So the sentence “A number, x, is increased by five” translates as x + 5.
Solution follows…

6. Lesson
1.2.1
Writing Expressions
Example 2
Write a variable expression to describe the sentence “Nine is multiplied by a number, k.”
Solution
The operation phrase being used is “multiplied by.”
The rest of the sentence tells you that it is the number nine and the variable k that are being multiplied together.
So “Nine is multiplied by a number, k” translates as 9 • k or 9k.
Solution follows…

7. Writing Expressions 1.2.1 Guided Practice
Lesson
1.2.1
Writing Expressions
Guided Practice
Write variable expressions to describe the phrases in Exercises 1–5.
1. Six more than a number, h. 2. Seven is decreased by a number, m. 3. A number, g, divided by The product of a number, w, and A number, k, divided into four equal parts.
h + 6
7 – m g 11
w • 10 k 4
Solution follows…

8. Lesson
1.2.1
Writing Expressions
You Need to Sort Out the Important Information
You’ll often need to write a math expression as the first step toward solving a word problem.
That might include choosing variables as well as working out what operations the words are describing.

9. Lesson
1.2.1
Writing Expressions
Example 3
Carla and Bob have been making buttons to sell at a fund-raiser. Carla made four more than Bob. Write an expression to describe how many buttons they made between them.
Solution
First you need to work out what the expression you have to write must describe. In this case the expression must describe the total number of buttons made by Carla and Bob.
See if there is an unknown number in the question: you don’t know how many buttons Bob made. You don’t know how many Carla made either, but you can say how many she made compared with Bob, so you only need one variable.
Solution continues…
Solution follows…

10. Lesson
1.2.1
Writing Expressions
Example 3
Carla and Bob have been making buttons to sell at a fund-raiser. Carla made four more than Bob. Write an expression to describe how many buttons they made between them.
Solution
Assign a letter or symbol to the unknown number: let b = the number of buttons Bob made.
Then you need to identify any operation phrases: “more than” is an addition phrase.
Carla made 4 more buttons than Bob, so she made b + 4 buttons. Which means that together they made b b buttons.
This expression can be simplified to 2b + 4.

11. Writing Expressions 1.2.1 Guided Practice
Lesson
1.2.1
Writing Expressions
Guided Practice
Write variable expressions to describe the sentences in Exercises 6–7. Use x as the variable in each case, and say what it represents.
6. A rectangle has a length of 2 inches. What is its area?
7. Jenny has five fewer apples than Jamal. How many apples does Jenny have in total?
2x, where x is the width of the rectangle.
x – 5, where x is the number of apples Jamal has.
Solution follows…

12. Writing Expressions 1.2.1 Guided Practice
Lesson
1.2.1
Writing Expressions
Guided Practice
Write variable expressions to describe the sentences in Exercises 8–9. Use x as the variable in each case, and say what it represents.
8. The student council is selling fruit juice at the prom for $0.75 a glass. How much money will they take?
9. A gym charges $10 per month membership plus $3 per visit. What is the cost of using the gym for a month?
$0.75x, where x is the number of glasses sold.
$(10 + 3x), where x is the number of visits.
Solution follows…

13. Twelve divided by four less than x.
Lesson
1.2.1
Writing Expressions
Some Expressions Describe More than One Operation
You can also translate sentences with multiple operations in the same way. You just need to spot all the separate operations and work out what order to write them in.
Twelve divided by four less than x.
12 ÷ (x – 4)

14. Lesson
1.2.1
Writing Expressions
Example 4
Write a variable expression to describe the phrase “ten decreased by the product of a number, y, and two.”
Solution
In this question the phrase contains two different operations, so you need to work out which operation is carried out first.
The two operations here are “decreased by,” which is a subtraction phrase, and “product,” which means multiplication.
You’re told to subtract the product from 10. So you need to work out the product first — this is the product of y and 2, which is 2y.
Now you have to subtract this product, 2y, from So the phrase in the question translates as 10 – 2y.
Solution follows…

15. Writing Expressions 1.2.1 Guided Practice
Lesson
1.2.1
Writing Expressions
Guided Practice
Write variable expressions to describe the phrases in Exercises 10–14.
10. Five more than twice a number, q.
11. Sixteen divided by the sum of a number, m, and 7.
12. Twenty decreased by a quarter of a number, j.
13. The product of 7 and six less than a number, t.
14. The product of a number, k, and the sum of 5 and a number, x.
2q + 5 16
m + 7
20 – j 4
7(t – 6)
k(5 + x)
Solution follows…

16. Writing Expressions 1.2.1 Independent Practice
Lesson
1.2.1
Writing Expressions
Independent Practice
Write variable expressions to describe the phrases in Exercises 1–5.
1. The product of six and a number, h.
2. A number, y, decreased by eleven.
3. A fifteenth of a number, p.
4. Nine more than twice a number, w.
5. Sixteen increased by the product of a number, k, and three. 6h
y – 11 p 15
2w + 9
16 + 3k
Solution follows…

17. Writing Expressions 1.2.1 Independent Practice
Lesson
1.2.1
Writing Expressions
Independent Practice
6. A pen costs half as much as a ruler. Write an expression to describe how much the pen costs, using r as the cost of the ruler.
7. Peter has three fewer cards than Neva. Write an expression to describe how many cards they have together, using c as the number of cards Neva has.
0.5r or r 2
2c – 3
Solution follows…

18. Writing Expressions 1.2.1 Round Up
Lesson
1.2.1
Writing Expressions
Round Up
Changing word expressions into algebra expressions is all about spotting the operation phrases and working out what order the operations need to be written in.
Writing expressions is the first step toward writing equations — a skill that you’ll use when solving problems later in this Section.