All the solutions provided in McGraw Hill My Math Grade 3 Answer Key PDF Chapter 9 Lesson 6 Evaluate Expressions will give you a clear idea of the concepts.
McGraw-Hill My Math Grade 3 Answer Key Chapter 9 Lesson 6 Evaluate Expressions
When a symbol, such as ? and 
, or a letter, such as x or y, is used to stand for an unknown, it is called a variable.
Math in My World
Example 1
Santiago unpacked 5 more boxes of light bulbs than boxes of flashlights.
Write an expression using the variable x for the unknown
When you find the value of an expression by replacing the variable with a number, you evaluate the expression.
Answer: 5 + X
Explanation:
Given, Santiago unpacked 5 more boxes of light bulbs than boxes of flashlights.
Here, X is the variable
so, The expression will be 5 + X.
Example 2
The hardware store has 6 fewer step ladders than extension ladders. There are y extension ladders. Write an expression using the variable y. Then evaluate the expression if y = 10.
There are ____________ step ladders.
Answer: There are 4 step ladders
Explanation:
Given, The hardware store has 6 fewer step ladders than extension ladders.
There are y extension ladders.
Then the expression will be, y – 6
and, if y = 10.
then, 10 – 6 = 4
So, There are 4 step ladders.
Example 3
Owen looked at a set of 4 pliers. His dad looked at a set that had s times as many pliers plus 3 more. If s = 2, how many pliers were in the set Owen’s dad looked at?
Write an expression, then evaluate it.
1. Write the expression.
2. Replace s with 2.
3. When there are no parentheses, first multiply or divide, in order from left to right.
4. Then, add or subtract, in order from left to right.
So, if s = 2, then 3 + s × 4 = ____________. There were ___________ pliers in the set.
Answer: There were 11 pliers in the set.
Explanation:
Given, Owen looked at a set of 4 pliers.
His dad looked at a set that had s times as many pliers plus 3 more.
Then the expression will be 3 + S × 4
If s = 2,
3 + 2 × 4
there are no parentheses, first multiply or divide, in order from left to right.
The we get, 3 + 8 = 11
So, There were 11 pliers in the set.
Talk Math
Look back at Example 3. How would your answer be different if you evaluated the expression left to right? Explain.
Answer: There would be 20 Pliers..
Explanation:
In the example,
Given, Owen looked at a set of 4 pliers.
His dad looked at a set that had s times as many pliers plus 3 more.
Then the expression will be 3 + S × 4
If s = 2,
3 + 2 × 4
5 × 4 = 20
There would be 20 Pliers.
Guided Practice
Evaluate each expression if a = 2 and b = 5.
Question 1.
3 + a
3 + __________ = ____________
Answer: 5
Explanation:
Given, 3 + a and a = 2
The expression will be, 3 + 2
That is 5
So, 3 + a = 5.
Question 2.
11 – b
11 – ___________ = ____________
Answer: 6
Explanation:
Given, 11 – b and b = 5
The expression will be, 11 – 5
That is 6
So, 11 – b = 6.
Question 3.
b × 4
_____________ × 4 = _____________
Answer: 20
Explanation:
Given, b × 4 and b = 5
The expression will be, 5 × 4
That is 20
So, b × 4 = 20.
Question 4.
12 ÷ a + 4
Answer: 10
Explanation:
Given, 12 ÷ a + 4 and b = 5
The expression will be, 12 ÷ 2 + 4
= 6 + 4
That is 10
So, 12 ÷ a + 4 = 10.
Independent Practice
Algebra Evaluate each expression if z = 7 and y = 20.
Question 5.
(8 × z) – y
Answer: 36
Explanation:
Given, (8 × z) – y and z = 7 and y = 20.
The expression will be, ( 8 × 7 ) – 20
Solve with in the parentheses
That is 56 – 20 =36
So, (8 × z) – y = 36.
Question 6.
y + 3 × 4
Answer: 32
Explanation:
Given, y + 3 × 4 and y = 20.
The expression will be, 20 + 3 × 4
there are no parentheses, first multiply in order from left to right.
That is 20 + 12 =32
So, y + 3 × 4 = 32.
Question 7.
y ÷ 5
Answer: 4
Explanation:
Given, y ÷ 5 and y = 20.
The expression will be, 20 ÷ 5
That is 4
So, y ÷ 5 = 4.
Question 8.
6 × 4 – y
Answer: 4
Explanation:
Given, 6 × 4 – y and y = 20.
The expression will be, 6 × 4 – 20
there are no parentheses, first multiply in order from left to right.
That is 24 – 20 = 4
So, 6 × 4 – y = 4.
Question 9.
z – 5 + 7
Answer: -5
Explanation:
Given, z – 5 + 7and z = 7.
The expression will be, z – 5 + 7
there are no parentheses, first add in order from left to right.
That is 7 – 5 + 7 = -5
So, z – 5 + 7 = -5.
Question 10.
28 ÷ z × 6
Answer: 24
Explanation:
Given, 28 ÷ z × 6 and z = 7.
The expression will be, 28 ÷ 7 × 6
there are no parentheses, first Divide in order from left to right.
That is 4 × 6 = 24
So, 28 ÷ z × 6 = 24.
Algebra Draw a line to match the expression to its value if g = 2.
Answer: 
Explanation:
Given, G = 2
( 5 + 3 ) × g
( 5 + 3 ) × 2 = 8 × 2 = 16,
g × 5 – 5
there are no parentheses, first multiply in order from left to right.
2 × 5 – 5 = 10 – 5 = 5,
15 – 9 – g
15 – 9 – 2 = 4,
5 + ( 3 × g )
5 + ( 3 × 2 ) = 5 + 6 = 11,
g × ( 5 – 5 )
g × ( 5 – 5 ) = 2 × ( 5 – 5 ) = 0.
Algebra Circle yes or no to tell whether the expression is evaluated correctly if n = 12.
Question 16.
n ÷ 4 × 6
Answer: Yes
Explanation:
Given, n ÷ 4 × 6
if n = 12
12 ÷ 4 × 6
there are no parentheses, first Divide in order from left to right.
3 × 6 = 18
So, n ÷ 4 × 6 = 18
Question 17.
12 + n ÷ 4
Answer: No
Explanation:
Given, 12 + n ÷ 4
if n = 12
12 + 12 ÷ 4
there are no parentheses, first Divide in order from left to right.
12 + 3 = 15
So, 12 + n ÷ 4 = 15.
Question 18.
Did you circle no for either Exercise 16 or 17? Explain.
Answer: No for Exercise 17
Explanation:
Given, 12 + n ÷ 4
if n = 12
12 + 12 ÷ 4
there are no parentheses, first Divide in order from left to right.
12 + 3 = 15
So, 12 + n ÷ 4 = 15.
Problem Solving
Mathematical PRACTICE Use Algebra Write an expression for each. Then evaluate it.
Question 19.
Tomas has $10. Aisha has x more than Tomas. If x = $5, how much money does Aisha have?
Answer: Aisha have $15
Explanation:
Given, Tomas has $10. Aisha has x more than Tomas.
If x = $5,
The expression will be, 10 + X
10 + 5 = 15.
So, Aisha have $15.
Question 20.
There are 5 swing sets at a playground. Each swing set has v swings. If v = 3, what is the total number of swings?
Answer: The total number of swings are 15
Explanation:
Given, There are 5 swing sets at a playground. Each swing set has v swings.
If v = 3,
The expression will be, 5 × v
5 × v = 15
So, The total number of swings are 15
Question 21.
Jimena put 5 pencils and n pens in a pencil box for each of her 2 friends. If n = 3, how many pencils and pens did Jimena put in pencil boxes?
(5 + n) ___________; ______________
Answer: Jimena put 16 pencils and pens in a pencil box.
Explanation:
Given, Jimena put 5 pencils and n pens in a pencil box for each of her 2 friends.
If n = 3,
Then the expression will be, ( 5 + n ) × 2
( 5 + 3 ) × 2 = 8 × 2 = 16
So, Jimena put 16 pencils and pens in a pencil box.
HOT Problems
Question 22.
Mathematical PRACTICE Identify Structure Neil forgot to place the parentheses on the expression below. Place the parentheses so that the expression has a value of 2.
12 – 4 + 6
Why are the parentheses important in this expression?
Answer: the parentheses are important in this expression for easy evaluation
Explanation:
Given, 12 – 4 + 6
Neil forgot to place the parentheses on the expression below.
Place the parentheses so that the expression has a value of 2.
If, (12 – 4) + 6
8 + 6 = 14
Its not the required answer
Another way is , if ,12 – ( 4 + 6 )
12 – 10 = 2
Its the required answer,
So, the parentheses are important in this expression for easy evaluation
Question 23.
Building on the Essential Question When evaluating an expression with more than one operation and no parentheses, how should you proceed?
Answer: If there are no parentheses, first multiply or divide, in order from left to right.
Explanation:
Write the expression.
Replace s with value given.
When there are no parentheses, first multiply or divide, in order from left to right.
Then, add or subtract, in order from left to right.
So, If there are no parentheses, first multiply or divide, in order from left to right.
McGraw Hill My Math Grade 3 Chapter 9 Lesson 6 My Homework Answer Key
Practice
Algebra Evaluate each expression if c = 4 and d = 7.
Question 1.
15 – d
15 – __________ = ____________
Answer: 8
Explanation:
Given, 15 – d and d = 7
The expression will be, 15 – 7
That is 8
So, 15 – d = 8.
Question 2.
16 + c
16 + ___________ = ____________
Answer: 20
Explanation:
Given, 16 + c and c = 4
The expression will be, 16 + 4
That is 20
So, 16 + c = 20.
Question 3.
35 ÷ d
35 ÷ ____________ = _____________
Answer: 5
Explanation:
Given, 35 ÷ d and d = 7
The expression will be, 35 ÷ 7
That is 5
So, 35 ÷ d = 5.
Algebra Evaluate each expression if x = 14 and y = 6.
Question 4.
(x + y) ÷ 4
Answer: 5
Explanation:
Given, (x + y) ÷ 4 and x = 14 and y = 6.
The expression will be, (14 + 6) ÷ 4
Solve with in the parentheses
That is 20 ÷ 4 = 5
So, (x + y) ÷ 4 = 5.
Question 5.
x – 2 × 2
Answer: 10
Explanation:
Given, x – 2 × 2 and x = 14.
The expression will be, 14 – 2 × 2
there are no parentheses, first multiply in order from left to right.
That is 14 – 4 = 10
So, x – 2 × 2 = 10.
Question 6.
y + 24 ÷ 2
Answer: 18
Explanation:
Given, y + 24 ÷ 2 and y = 6.
The expression will be, y + 24 ÷ 2
there are no parentheses, first Divide in order from left to right.
That is 6 +12 = 18
So, y + 24 ÷ 2 = 18.
Problem Solving
Mathematical PRACTICE Model Math Write an expression for each situation. Then evaluate it.
Question 7.
Monica has 7 hats. Andrea has b fewer hats than Monica. If b = 5, how many hats does Andrea have?
Answer: Andrea have 3 hats.
Explanation:
Given, Monica has 7 hats. Andrea has b fewer hats than Monica.
The expression will be, 7 – b
If b = 5,
7 – 5 = 3
So, Andrea have 3 hats.
Question 8.
There are 4 shelves with canned dog food. Each shelf has t cans. Then Tracy adds 2 cans to only 1 of the shelves. If t = 8, how many cans are on the shelves altogether?
4 × t ____________; 4 × ______________
Answer: There are 40 shelves altogether.
Explanation:
Given, There are 4 shelves with canned dog food. Each shelf has t cans.
Then Tracy adds 2 cans to only 1 of the shelves.
The expression will be, 4 × ( t + 2 )
If t = 8,
4 × ( 8 + 2 )
4 × 10 = 40
So, There are 40 shelves altogether.
Question 9.
Valerie is making identical quilts for herself and her sister. For each quilt she buys 5 yards of solid fabric and w yards of printed fabric. If w = 4, how much fabric did Valerie buy to make both quilts?
(___________) × 2; ________________
Answer: Valerie bought 18 yards of fabric to make both quilts.
Explanation:
Given, Valerie is making identical quilts for herself and her sister.
For each quilt she buys 5 yards of solid fabric and w yards of printed fabric.
The expression will be, ( 5 + w ) × 2
If w = 4,
( 5 + 4 ) × 2
9 × 2 = 18
So, Valerie bought 18 yards of fabric to make both quilts.
Vocabulary Check
Question 10.
Explain what a variable is.
Answer: a variable is an alphabet or term that represents an unknown number or unknown value or unknown quantity. The variables are specially used in the case of algebraic expression or algebra.
Explanation:
For example, x+9=4 is a linear equation
where x is a variable, where 9 and 4 are constants.
Question 11.
What does it mean to evaluate an expression?
Answer: To evaluate an algebraic expression means to find the value of the expression when the variable is replaced by a given number.
Explanation:
To evaluate an expression,
we substitute the given number for the variable in the expression and
then simplify the expression using the order of operations.
Test Practice
Question 12.
Evaluate the expression h + 8 ÷ 4 if h = 16.
(A) 20
(B) 18
(C) 8
(D) 6
Answer: B
Explanation:
Given, h + 8 ÷ 4,
if h = 16.
The expression will be, 16 + 8 ÷ 4,
there are no parentheses, first Divide in order from left to right.
That is 16 + 2 = 18
So, h + 8 ÷ 4 = 18.