Chapter 3 Numeric And Algebraic Expressions
Section 3.4: Write Algebraic Expressions
Page 139 Exercise 1 Answer
The difference between the number of games the Hornets won and the number of games the Lynx won is two. The Lynx always win two more games than the Hornets. Thus, if the Lynx won g games, the Hornets must win two less.
A mathematical expression describing how many games the Hornets won is g − 2.
In this expression the greater number (the number of games the Lynx win) is given as the variable and the lesser number (the number of games the Hornets win) is then expressed in relation to that variable.
In the other expression, given as
n + 2,
where n marks the number of games the Hornets won, and n + 2 the number of games the Lynx won. Here the lesser number is given as the variable and the greater number is then expressed in relation to that variable.
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Result
g − 2
For g − 2, the number of games the Lynx won is the variable and the number of games the Hornets won is expressed in relation to that variable. For n + 2, the number of games the Hornets won is the variable and the number of games the Lynx won is expressed in relation to that variable.
Page 139 Exercise 1a Answer
The pairs of numbers are: 3 and 5, 6 and 8, 9 and 11. What those pairs have in common is that when subtracted they all give two as a result.
The pattern seen in the data is then the number of games won by the Lynx is 2 more than the number of games won by the Hornets.
Result
Each pair of number has a difference of 2. The pattern seen in the data is the number of games won by the Lynx is 2 more than the number of games won by the Hornets.
Page 139 Exercise 1b Answer
When the Hornets won 3 games, the Lynx won 5, which can be written as 3 + 2 = 5.
When the Hornets won 6 games, the Lynx won 8, which can be written as 6 + 2 = 8.
When the Hornets won 9 games, the Lynx won 11, which can be written as 9 + 2 = 11.
Result
Page 139 Exercise 1c Answer
In the table we can see that when the Hornets won 3 games, the Lynx won 5, the difference being two. The Hornets 6, the Lynx 8, the difference again is two. The Hornets 9, the Lynx 11, the difference again is two.
Thus, the pattern is: if the Hornets win n games, the Lynx win n + 2 games, since the difference is than (n + 2) – n which than equals two.
Result
If the Hornets win n games, the Lynx win n+2 games.
Page 140 Exercise 1 Answer
The algebraic expressions which represent the total cost of the mystery books Rachel bought are
m × 6.50,m ⋅ 6.50 and m(6.50).
The expressions above are algebraic expressions because each of them contains a variable – a letter which represents an unknown quantity, in this case the letter m which represents the number of mystery book Rachel bought. The expressions also contain an operation – multiplication.
Result
m × 6.50, m ⋅ 6.50, and m(6.50)
The expressions are algebraic expressions because each of them contains a variable and an operation.
Page 141 Exercise 2 Answer
The algebraic expression which represents “8 minus the quantity b divided by 6” is
8 − b ÷ 6.
Result
8 − b ÷ 6
Page 141 Exercise 3 Answer
A term is each part of an expression separated by a plus sign or a minus sign.
The expression r ÷ 9 + 5.5 has two terms. The first term is the quotient r ÷ 9 and the second term is 5.5.
Result
The expression has two terms.
Page 142 Exercise 1 Answer
To write an algebraic expression we can use a variable, which is written as a letter and it represents a quantity that can change, and at least one of the following operations: addition, subtraction, multiplication, and division.
For example, we can use the variable x and the operation addition to write the following algebraic expression:
x + 3,
or we can use the variable y and the operation multiplication to write:
7 × y.
Result
To write an algebraic expression we can use a variable, which is written as a letter and it represents a quantity that can change, and at least one of the following operations: addition, subtraction, multiplication, and division.
Page 142 Exercise 2 Answer
The variable in the given algebraic expression \(\frac{6}{x}\) is x since the letter is x, and the operation is division since fractions mean division.
Result
The variable is x and the operation is division.
Page 142 Exercise 3 Answer
An algebraic expression is a type of math expression that has at least one variable and at least one operation.
In the expression
\(15+\frac{1}{2} n\)n is the variable and the operation is addition, so the given expression is an algebraic expression.
Result
The expression has the variable n and the operation addition.
Page 142 Exercise 4 Answer
The expression 2(3+4) can be described as a product of two factors, where one factor is 2 and the second factor is the sum 3 + 4.
Result
Yes, one factor is 2 and the second factor is 3 + 4.
Page 142 Exercise 5 Answer
In the expression 2(3+4) we have two factors, one is 2 and the other is 3 + 4. The other factor, 3 + 4 is the sum of two terms.
Result
3 + 4 is the sum of two terms.
Page 142 Exercise 6 Answer
The given situation is “five less than y”, which can be written as an algebraic expression: y − 5.
y − 5
Page 142 Exercise 7 Answer
The given situation is “six times the quantity two x plus three y”, which can be written as an algebraic expression:6 × (2x + 3y).
Result
6 × (2x + 3y)
Page 142 Exercise 8 Answer
The expression
\(\frac{w}{4}+12.5-7 z\)has three terms.
A term is a part of an expression that is separated by a plus or a minus sign. Thus, the given expression has the following terms: \(\frac{w}{4}\), 12.5, and 7z.
The first term, \(\frac{w}{4}\), is written as a fraction and represents the quotient of w divided by 4.
The second term, 12.5, is a constant numerical value.
The third term, 7z, is a product of two factors. A coefficient, the number that is multiplied by a variable, in this case the variable z, is 7. So, 7 is the coefficient of z.
Result
Three terms since the terms are the parts of the expression that are separated by a plus or a minus sign.
Page 142 Exercise 9 Answer
In the expression
\(\frac{w}{4}+12.5-7 z\)which has three terms of \(\frac{w}{4}\), 12.5, and 7z, the third term of 7z, has a coefficient.
When a term is a product of two factors, a variable and a constant numerical value , a coefficient is the number that is multiplied by a variable. In this case, the variable is z and the coefficent is 7. So, 7 is the coefficient of z.
Result
7z has a coefficient since it has a number multiplied by a variable.
Page 142 Exercise 10 Answer
In the expression
\(\frac{w}{4}+12.5-7 z\)which has three terms of \(\frac{w}{4}\), 12.5, and 7z, the second term of 12.5 is a constant numerical value since it has no variable.
Result
12.5
Page 143 Exercise 11 Answer
The given situation is “12 times a number g”, which can be written as an algebraic expression: 12 × g.
Result
12 × g
Page 143 Exercise 12 Answer
The given situation is “p pennies added to 22 pennies”, which can be written as an algebraic expression: p + 22.
Result
p + 22
Page 143 Exercise 13 Answer
The given situation is “22 divided by a number s”, which can be written as an algebraic expression: 22 ÷ s, which can also be written as \(\frac{22}{s}\).
Result
22 ÷ s or \(\frac{22}{s}\)
Page 143 Exercise 14 Answer
The given situation is “\(12 \frac{3}{4}\) less than the product of 7 and a number x”, which can be written as an algebraic expression:
7x − \(12 \frac{3}{4}\)
Result
7x − \(12 \frac{3}{4}\)
Page 143 Exercise 15 Answer
The expression
5 − g
has two terms.
A term is a part of an expression that is separated by a plus or a minus sign. Thus, the given expression has the following terms: 5 and g.
The first term is a constant numerical value and the second term is a variable. The operation is subtraction.
Result
The given expression has two terms.
Page 143 Exercise 16 Answer
The expression
3 + \(\frac{1}{2}\)b
has two terms.
A term is a part of an expression that is separated by a plus or a minus sign. Thus, the given expression has the following terms: 3 and \(\frac{1}{2}\)b.
The first term is a constant numerical value and the second term is a product of a coefficient \(\frac{a}{b}\) and a variable b.
Result
The given expression has two terms.
Page 143 Exercise 17 Answer
The expression
\(\frac{v}{3}\) + 3⋅ 5
has two terms.
A term is a part of an expression that is separated by a plus or a minus sign. Thus, the given expression has the following terms: \(\frac{v}{3}\) and 3 ⋅ 5.
The first term is a constant numerical value and the second is a product of two numbers.
Result
The given expression has two terms.
Page 143 Exercise 18 Answer
The expression
16.2 − (3 ⋅ 4) + (14 ÷ 2)
has three terms.
A term is a part of an expression that is separated by a plus or a minus sign. Thus, the given expression has the following terms: 16.2, (3 ⋅ 4), and (14 ÷ 2).
The first term is a constant numerical value, the second term is a product of two numbers, and the third term is a quotient of two numbers.
Result
The given expression has three terms.
Page 143 Exercise 19 Answer
In the expression
5.3t – (20 ÷ 4) + 11
there are three terms: 5.3t, (20 ÷ 4), and 11.
The second term, (20 ÷ 4), is a quotient of two numbers, 20 and 4.
Result
The second term (20 ÷ 4) is a quotient of two numbers, 20 and 4.
Page 143 Exercise 20 Answer
In the expression
5.3t – (20 ÷ 4) + 11
there are three terms: 5.3t, (20 ÷ 4), and 11.
The first term, 5.3t, is a product of a variable t, and a constant numerical value, 5.3.
Result
The first term 5.3t is a product of a variable t, and a constant numerical value, 5.3.
Page 143 Exercise 21 Answer
To following expression shows how much longer is the round-trip to San Diego, which is 1,012 miles, than the round-trip to San Jose, which is 236 miles:
1012 − 236.
Result
The expression has two terms.
Page 143 Exercise 22 Answer
A truck driver made 5 round-trips to Los Angeles and some round-trips to San Diego. Let the number of round-trips to San Diego be x.
Each round trip to Los Angeles is 770 miles and each round trip to San Diego is 1,012. The following expression then shows how many miles he drove in all:
5 ⋅ 770 + x ⋅ 1012
The second term, x ⋅ 1012, describes how many miles he drove to San Diego, while x stands for how many trips he made to San Diego.
Result
The expression is 5 ⋅ 770 + x ⋅ 1012. The second term, x ⋅ 1012, describes how many miles he drove to San Diego, while x stands for how many trips he made to San Diego.
Page 144 Exercise 23 Answer
The expression is:
y ÷ 3(4 – 2) + 5.5
The given expression has the following parts: y, 3(4 – 2), and 5.5.
The first part, y, is a variable.
The second part, 3(4 – 2), is a product of the numbers 3 and 4 – 2. This second factor of the product is a difference of 4 and 2.
The third part, 5.5, is a constant numerical value.
Result
Page 144 Exercise 24 Answer
In one year a florist sells f flowers, so in 6 years he sells 6 ⋅ f flowers.
The expression 6 ⋅ f shows how many flowers a float in the parade may use.
Result
6 ⋅ f
Page 144 Exercise 25 Answer
The expression abc is a product of three variables, however it has only one term since a term is a part of an expression that is separated by a plus or a minus sign. Thus, Anthony is wrong.
Page 144 Exercise 26 Answer
In a 5-day period Yuri walked the same number of poodles and the same number of bulldogs each day as he did on Monday, when he walked p puddles and b bulldogs. This means he walked p + b dogs each of the 5 days. The following expression shows how many dogs were walked in this 5-day period:
5 ⋅ (p+b).
Result
5 ⋅ (p+b)
Page 144 Exercise 27 Answer
There are two baskets of apples and each has 12 apples, so we will multiply 2 by 12.
There is no exact number of students, so let’s mark the number of students with n. They equally shared two baskets of apples thus we will divide the product 2 ⋅ 12 by n.
The following expression represents the given situation:
(2⋅12) ÷ n.
Result
(2⋅12) ÷ n where n is the number of students.
Page 144 Exercise 28 Answer
A regular octagon has 8 sides which are all equal length, in this case s. The following two expressions represent the perimeter P of the figure.
P = s + s + s + s + s + s + s + s
P = 8 ⋅ s
The first expression uses addition to represent the perimeter, and the second expression uses multiplication to express the same.
Result
s + s + s + s + s + s + s + s and 8 ⋅ s
Page 144 Exercise 29 Answer
Four more than the product 3 times the number of c cats can be represented by the following expressions:
4 + 3c,
3 ⋅ c + 4,
(3×c) + 4.
The expression (4+3)c doesn’t represent four more than the product 3 times the number of c cats. The sum 4 + 3 is in brackets so it takes priority over multiplication. The result is then 7c which is not equal to 4 + 3c.
Result
(4+3)c
Page 144 Exercise 30 Answer
The phrase “Four less than w divided by 4.”could be represented by the algebraic expression
\(\frac{w}{4}\) – 4.
The other phrases couldn’t be represented by the given algebraic expression.
“The quotient of four and a number w” could be represented by
\(\frac{4}{w}\)The difference between a number w and 4″ and Four less than a number w” could be represented by
w − 4.
Result
four less than w divided by 4