Transcript Writing Expressions Lesson 1.2.1 Lesson 1.2.1 Writing Expressions California Standard: What it means for you: Algebra and Functions 1.1 You’ll learn how to change word descriptions into math expressions. Use variables.

Writing Expressions
Lesson 1.2.1
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Lesson
1.2.1
Writing Expressions
California Standard:
What it means for you:
Algebra and Functions 1.1
You’ll learn how to change
word descriptions into math
expressions.
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).
Key Words:
•
•
•
•
addition
subtraction
product
quotient
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Lesson
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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.
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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.
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Lesson
1.2.1
Example
Writing Expressions
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.
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Solution follows…
Lesson
1.2.1
Example
Writing Expressions
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.
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Solution follows…
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.
h+6
2. Seven is decreased by a number, m. 7 – m
3. A number, g, divided by 11.
g
11
4. The product of a number, w, and 10. w • 10
5. A number, k, divided into four equal parts.
k
4
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Solution follows…
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.
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Lesson
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Example
Writing Expressions
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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.
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Solution
Solutioncontinues…
follows…
Lesson
1.2.1
Example
Writing Expressions
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 + 4 + b buttons.
This expression can be simplified to 2b + 4.
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Lesson
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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?
2x, where x is the width of the rectangle.
7. Jenny has five fewer apples than Jamal.
How many apples does Jenny have in total?
x – 5, where x is the number of apples Jamal has.
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Solution follows…
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?
$0.75x, where x is the number of glasses sold.
9. A gym charges $10 per month membership plus
$3 per visit. What is the cost of using the gym for a month?
$(10 + 3x), where x is the number of visits.
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Solution follows…
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)
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Lesson
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Example
Writing Expressions
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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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Solution follows…
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.
2q + 5
11. Sixteen divided by the sum of a number, m, and 7.
16
m+7
j
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12. Twenty decreased by a quarter of a number, j.
20 –
13. The product of 7 and six less than a number, t.
7(t – 6)
14. The product of a number, k, and the sum of 5
and a number, x. k(5 + x)
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Solution follows…
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. 6h
2. A number, y, decreased by eleven.
3. A fifteenth of a number, p.
y – 11
p
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4. Nine more than twice a number, w.
2w + 9
5. Sixteen increased by the product of a number, k, and three.
16 + 3k
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Solution follows…
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. 0.5r or r
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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
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Solution follows…
Lesson
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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.
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