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Lesson 1.2.1Lesson 1.2.1

Writing ExpressionsWriting Expressions

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Lesson

1.2.1Writing ExpressionsWriting Expressions

California Standard:Algebra and Functions 1.1Use 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

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Lesson

1.2.1Writing ExpressionsWriting Expressions

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.

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”

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Variable Expressions Describe Word Expressions

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1.2.1Writing ExpressionsWriting Expressions

To write an expression to represent a word sentence you need to figure out what the word sentence actually means.

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Example 1

Solution follows…

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1.2.1Writing ExpressionsWriting Expressions

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.

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Example 2

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1.2.1Writing ExpressionsWriting Expressions

Write a variable expression to describe the sentence “Nine is multiplied by a number, k.”

Solution

The operation phrase being used is “multiplied by.”

So “Nine is multiplied by a number, k” translates as 9 • k or 9k.

The rest of the sentence tells you that it is the number nine and the variable k that are being multiplied together.

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Guided Practice

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1.2.1Writing ExpressionsWriting Expressions

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 11.

4. The product of a number, w, and 10.

5. A number, k, divided into four equal parts.

h + 6

7 – m

w • 10

g

11

k

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You Need to Sort Out the Important Information

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1.2.1Writing ExpressionsWriting Expressions

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.

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Example 3

Solution follows…

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1.2.1Writing ExpressionsWriting Expressions

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…

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Example 3

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1.2.1Writing ExpressionsWriting Expressions

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 + 4 + b buttons.

This expression can be simplified to 2b + 4.

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

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Guided Practice

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1.2.1Writing ExpressionsWriting Expressions

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.

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Guided Practice

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1.2.1Writing ExpressionsWriting Expressions

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.

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Some Expressions Describe More than One Operation

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1.2.1Writing ExpressionsWriting Expressions

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)

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Example 4

Solution follows…

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1.2.1Writing ExpressionsWriting Expressions

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 10. So the phrase in the question translates as 10 – 2y.

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Guided Practice

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1.2.1Writing ExpressionsWriting Expressions

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

7(t – 6)

k(5 + x)

16

m + 7

20 – j

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Independent Practice

Solution follows…

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1.2.1Writing ExpressionsWriting Expressions

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

2w + 9

16 + 3k

p

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Independent Practice

Solution follows…

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1.2.1Writing ExpressionsWriting Expressions

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.

2c – 3

0.5r or r

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Round UpRound Up

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1.2.1Writing ExpressionsWriting Expressions

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.