McGraw Hill My Math Grade 5 Chapter 2 Lesson 4 Answer Key Multiplication Patterns

All the solutions provided in McGraw Hill Math Grade 5 Answer Key PDF Chapter 2 Lesson 4 Multiplication Patterns will give you a clear idea of the concepts.

McGraw-Hill My Math Grade 5 Answer Key Chapter 2 Lesson 4 Multiplication Patterns

Example 1
Pet Paws is ordering more goldfish to sell at their store. Each goldfish costs $2. Use the table to determine the cost of 10, 100, and 1,000 goldfish. Describe the pattern in the number of zeros when
multiplying the cost, $2, by powers of ten.



The number of zeros in the product increases when the power of ten increases. Each successive power of ten adds
_______ zero to the product.
How many zeros are in the product of 7 and 100? _____
How many zeros are in the product of 21 and 1o? _____
How many zeros are in the product of 12 and 1,000? _____
Answer:
The number of zeros in the product increases when the power of ten increases. Each successive power of ten adds another zero to the product.
How many zeros are in the product of 7 and 100? 2 zeros
How many zeros are in the product of 21 and 1o? 1 zero
How many zeros are in the product of 12 and 1,000? 3 zero

Example 2
Find 13 × 10² mentally.
Answer:
1300

Explanation:
Given,
13 × 10²
13 × 10 × 10
1300

Question 1.
Write 10² without exponents.
13 × 10² = ____
13 × ____
Answer:
1300

Explanation:
Given 10²
10² = 100
13 × 10²
13 × 100 = 1300

Question 2.
Count the number of zeros in the power of 10.

Compare the number of zeros to the exponent of 10². They are the _____
Answer:
Two zeros.

Explanation:
The number of zeros to the exponent of 10². They are the two zeros.

Question 3.
Write the zeros to the right of 13.
1, 3 ___ ____
So, the product is
_________
Answer:
1300

Explanation:
Given,
1, 3 0 0
The product is 13 × 100

Example 3
Find 40 × 7,000 mentally.
Answer:
280000

Explanation:
The multiplication of 40 × 7,000 = 280000

Question 1.
Write the basic multiplication fact.
4 × ____
Answer:
4 × 7 = 28

Explanation:
Given multiplicand is 4 and the multiplier is 7.
By multiplying both multiplicand 4 and multiplier 7, we get the value as 28.

Question 2.
Count the number of zeros in each factor.

There are a total of ___ zeros
Answer:
There are a total of 4 zeros.

Explanation:
Given,
40 × 7000
The number of zeros in each factor is 4 zeros.

Question 3.
Write the zeros to the right of the product from step 1.
28, ___, ___ ___ ____
So, the product is ____
Answer:
28000.

Explanation:
Given,
28, 0, 0, 0, 0
so, the product is 28000.

Talk Math
Explain how you could find the product of 29 and 10³ mentally.

Answer:
29000

Explanation:
The product of 29 and 10³
29 × 10 × 10 × 10
29000

Guided Practice

Find each product mentally.

Question 1.
8 × 10²
10² = ____
so, 8 × 10² = ____
Answer:
800

Explanation:
Given,
10² = 100
8 × 10² = 800

Question 2.
14 × 2,000
basic multiplication fact:
___ × ____ = 28
total number of zeros = ____
So, 14 × 2,000 = _____
Answer:
28000

Explanation:
Given,
14 × 2 = 28
Total number of zeros = 3
so, 14 × 2,000 = 28000

Independent Practice

Find each product mentally.

Question 3.
13 × 1,000 = ____
Answer:
13000

Explanation:
The given number is 13 × 1,000
By multiplying the given number the answer is 13000.

Question 4.
37 × 10² = ____
Answer:
3700

Explanation:
The given question is 37 × 10²
37 × 10 × 10
3700

Question 5.
9,000 × 3 = ____
Answer:
27000

Explanation:
The given question is 9,000 × 3
9 × 3 × 1000
27000

Question 6.
8 × 10² = ____
Answer:
800

Explanation:
The given question is 8 × 10²
8 × 10 × 10
800

Question 7.
21 × 10¹ = ___
Answer:
210

Explanation:
The given question is 21 × 10¹
21 × 10
210

Question 8.
9 × 50 = ____
Answer:
450

Explanation:
The given question is 9 × 50
450

Algebra Find the missing number.

Question 9.
× 10⁴ = 70,000
= ___
Answer:
Given,
× 10⁴ = 70,000
Let the blank be x
x × 10⁴ = 70,000
x × 10000 = 70,000
Cancel zeros from both sides
x = 7

Question 10.
300 × = 120,000
= ___
Answer:
Given,
300 × = 120,000
300 × x = 120,000
cancel common factors from both sides
3 × x = 1200
x = 1200 ÷ 3
x = 400

Question 11.
100 × = 900
= ___
Answer:
Given,
100 × = 900
Let us assume the box as x
100 × x = 900
Cancel the common factors from both sides
x = 9

Question 12.
× 10² = 4,400
= ___
Answer:
Given,
× 10² = 4,400
Let us assume the box is x
x × 10² = 4,400
x × 10 × 10 = 4400
Cancel the common factors from both sides
x = 44

Problem Solving

Question 13.
Each box contains 10² pencils. The school store has 15 boxes of pencils. How many pencils does the school store have?
Answer:
1500

Explanation:
Given,
The school store has 15 boxes of pencils
Each box contains 10² pencils.
The school has 15 × 10²
15 × 10 × 10 = 1500

Question 14.
Mathematical PRACTICE 8 Explain to a Friend Guilia runs an average of 15 minutes each day. She has a goal of running 10² minutes in 7 days. Will she complete her running goal in 7 days? Explain to a friend.
Answer:
Yes, she will complete her running goal.

Explanation:
15 miles each day for 7 days is 105 miles, 5 more than her original goal.

Question 15.
A group of friends bought 7 tickets to a dog show for $30 each. How much did they spend on the tickets?
Answer:
$210

Explanation:
A dog show for $30 each
A group of friends bought 7 tickets
$30 × 7
$210

Hot Problems

Mathematical PRACTICE 2 Use Number Sense Find each missing exponent.

Question 16.
40 × 10 = 4,000
= ____
Answer:
x = 2

Explanation:
Given,
40 × 10 = 4,000
40 × 10^x = 4000
10^x = 4000 ÷ 40
10^x = 100
10^x = 10²
x = 2

Question 17.
32 × 10 = 32,000
= ____
Answer:
x = 3

Explanation:
Given,
32 × 10 = 32,000
32 × 10^x = 32000
10^x = 32000 ÷ 32
10^x = 1000
10^x = 10³
x = 3

Question 18.
80,000 = 10 × 8
= ____
Answer:
x = 3

Explanation:
Given,
80,000 = 10 × 8
80,000 = 10^x × 8
10^x = 80000 ÷ 8
10^x = 1000
10^x  = 10³
x = 3

Question 19.
10,000 = 10 × 10
= ____
Answer:
x = 3

Explanation:
Given,
10,000 = 10 × 10
10000 = 10 × 10^x
10^x = 10000 ÷ 10
10^x = 1000
10^x = 10³
x = 3

Question 20.
? Building on the Essential Question How can patterns be used to determine products of a number and a power of 10?
Answer:
Patterns can be used to determine products of a number of a power of 10 by following it to obtain easily the answer. When you multiply a number by a power of ten, you just have to write the number and then add the corresponding number of zeroes to the end which will be the same number as the power used.

McGraw Hill My Math Grade 5 Chapter 2 Lesson 4 My Homework Answer Key

Practice

Find each product mentally.

Question 1.
70 × 500 = ___
Answer:
35000

Explanation:
Given,
70 × 500
35000

Question 2.
320 × 10² = ____
Answer:
32000

Explanation:
Given,
320 × 10²
320 × 10 × 10
32000

Question 3.
56 × 10³ = ___
Answer:
56000

Explanation:
Given,
56 × 10³
56 × 10 × 10 × 10
56000

Question 4.
10² × 72 = ____
Answer:
7200

Explanation:
Given,
10² × 72
10 × 10 × 72
7200

Question 5.
80 × 3,000 = ___
Answer:
240000

Explanation:
Given,
80 × 3,000
240000

Question 6.
10³ × 31 = ____
Answer:
31000

Explanation:
Given,
10³ × 31
10 × 10 × 10 × 31
1000 × 31
31000

Problem Solving

Question 7.
To protect themselves from extreme hot or cold temperatures, American Alligators dig burrows in the mud. Suppose there are 20 alligators, each with 50 feet of burrows. What is the total length of all the burrows?
Answer:

Answer:
1000 feet in length.

Explanation:
Given,
There are 20 alligators
And each with 50 feet of burrows.
The total length of all the burrows is 50 × 20 = 1000 burrows.

Question 8.
Paulita reads an average of 20 pages each day. She has 6 days to read 10² pages. Will she finish her reading in 6 days? Explain.
Answer:
She can finish in 5 days.

Explanation:
Paulita reads an average of 20 pages each day.
She has 6 days to read 10 squared = 10² = 10 × 10 = 100 pages
10 squared / 20 pages each day = 10² ÷ 20
= 100 ÷ 20
= 5 days.

Question 9.
Mathematical PRACTICE 1 Make Sense of Problems Explain how using basic facts can help you find 10 × 20 × 30 × 40 mentally.
Answer:
240000.

Explanation:
you just do 1 × 2 × 3 × 4
and then equals 24
so now we have 24 and then we add 4 zeros because their are 4 zeros in the equation so the answer is 240000.

Vocabulary Check

Fill in the blank with the correct term or number to complete the sentence.

Question 10.
Numbers like 10, 100, 1,000, and so on are called _______
Answer:
Numbers like 10, 100, 1,000, and so on are called powers of ten and they are easy to represent as exponents.

Test Practice

Question 11.
A music store sold 10³ CDs and 10² CD players. If each CD costs $12 and each CD player costs $35, what was the store’s total earnings?
A. $15,500
B. $24,500
C. $36,200
D. $47,000
Answer:
$15,500

Explanation:
10³ CDs = 1000 at $12 each = $12000
+10² players = 100 at $35 each = $3500
Total = $15500
103(12) + 102 (35) = $4806
The store’s total earnings is $15,500.