All the solutions provided in McGraw Hill Math Grade 5 Answer Key PDF Chapter 3 Lesson 4 Division Patterns will give you a clear idea of the concepts.
McGraw-Hill My Math Grade 5 Answer Key Chapter 3 Lesson 4 Division Patterns
Math in My World
Example 1.
A monarch butterfly can fly 240 miles in 3 days. Suppose it flies the same distance each day. How many miles can it fly each day?
Find 240 ÷ 3.
1. Since 240 is a multiple of 10, use the basic fact and continue the pattern.
2 4 ÷ 3 basic fact
2 4 
÷ 3 24 tens divided by 3 equals
2, 4 
÷ 3 24 hundreds divided by 3 equals 8 tens.
2, 4, 
÷ 3 24 thousands divided by 3 ect.
Answer:
24 miles everyday.
Explanation:
A monarch butterfly can fly 240 miles in 3 days.
Number of miles can it fly each day 240 ÷ 3.
Since 240 is a multiple of 10, use the basic fact and continue the pattern.
2 4 ÷ 3 basic fact
2 4 0 ÷ 3 = 24 tens divided by 3 equals
2, 4 0 0 ÷ 3 = 24 hundreds divided by 3 equals 8 tens.
2, 4, 0 0 0 ÷ 3 = 24 thousands divided by 3 etc.,
2. Circle the pattern above that matches the problem.
So, the butterfly can fly ____ miles each day.
Answer:
2 4 ÷ 3; 24 tens divided by 3 equals
Explanation:
A monarch butterfly can fly 240 miles in 3 days.
Number of miles can it fly each day 240 ÷ 3.
Example 2
A cow eats 900 pounds of hay over a period of 30 days. How many pounds of hay would the cow eat each day at this rate?
Let h represent the number of pounds of hay.
_____ ÷ ____ = h
One Way Use a fact family.
Use the family fact of 3, 3, and 9 to help represent the problem.
Another Way Use a pattern in the number of zeros.
You can cross out the same number of zeros in the dividend and the divisor to make the division easier.
900 ÷ 30 Cross out the same number of zeros in both the dividend and divisor.
90 ÷ 3 = 30 Divide. THINK: 9 tens ÷ 3 = 3 tens.
So, 900 ÷ 30 = ___. Since h = ____, the cow eats __ pounds each day.
Answer:
30 pounds.
Explanation:
900 ÷ 30 Cross out the same number of zeros in both the dividend and divisor.
90 ÷ 3 = 30 Divide.
THINK: 9 tens ÷ 3 = 3 tens.
So, 900 ÷ 30 = 30.
Since h = 30,
The cow eats 30 pounds each day.
Talk Math
Is the quotient 48 ÷ 6 equal to the quotient 480 ÷ 60? Explain.
Answer:
Yes, the quotient 48 ÷ 6 equal to the quotient 480 ÷ 60.
Explanation:
480 ÷ 60 Cross out the same number of zeros in both the dividend and divisor.
48 ÷ 6 = 8 Divide.
THINK: 48 tens ÷ 6 = 8 tens.
48 ÷ 6 = 8
480 ÷ 60 = 8
Guided Practice
Question 1.
Find 500 ÷ 5 mentally. 500 ÷ 5 = ____
Answer:
100
Explanation:
Independent Practice
Divide mentally.
Question 2.
800 ÷ 2 = ____
Answer:
400
Explanation:
Question 3.
900 ÷ 3 = ____
Answer:
300
Explanation:
Question 4.
150 ÷ 5 = ___
Answer:
30
Explanation:
As, there is zeros in ones, move to tens.
50 ÷ 5 = 10
100 ÷ 5 = 20
Add the quotients of tens and hundreds.
10 + 20 = 30
Question 5.
140 ÷ 7 = _____
Answer:
20
Explanation:
The digit in hundred is less then the divisor add the tens.
100 and 40 is written as 14 tens.
As, there is zeros in ones, divided 14 with 7.
14 ÷ 7 = 2
So, 140 ÷ 7 = 20
Question 6.
450 ÷ 9 = ___
Answer:
50
Explanation:
The digit in hundred is less then the divisor add the tens.
400 and 50 is written as 45 tens.
As, there is zeros in ones, divided 45 with 9.
45 ÷ 9 = 5
So, 450 ÷ 9 = 50
Question 7.
280 ÷ 4 = ___
Answer:
70
Explanation:
The digit in hundred is less then the divisor add the tens.
200 and 80 is written as 28 tens.
As, there is zeros in ones, divided 28 with 4.
28 ÷ 4 = 7
So, 280 ÷ 4 = 70
Question 8.
180 ÷ 60 = ___
Answer:
3
Explanation:
The digit in hundred is less then the divisor add the tens.
100 and 80 is written as 18 tens.
Cross out the same number of zeros in both the dividend and divisor.
18 ÷ 6 = 3
So, 180 ÷ 6 = 3
Question 9.
240 ÷ 30 = ___
Answer:
8
Explanation:
The digit in hundred is less then the divisor add the tens.
100 and 40 is written as 14 tens.
Cross out the same number of zeros in both the dividend and divisor.
24 ÷ 3 = 8
So, 240 ÷ 30 = 8
Question 10.
420 ÷ 70 = ____
Answer:
6
Explanation:
The digit in hundred is less then the divisor add the tens.
400 and 20 is written as 42 tens.
Cross out the same number of zeros in both the dividend and divisor.
42 ÷ 7 = 6
So, 420 ÷ 70 = 6
Algebra Mentally find each unknown.
Question 11.
1,800 ÷ 30 = k
k = ____
Answer:
k = 60
Explanation:
1,800 ÷ 30. Cross out the same number of zeros in both the dividend and divisor.
The digit in hundreds is less than the divisor.
So, 1 hundred and 8 tens is written as 18 tens.
Divided. 1,80 ÷ 3 = 60
Question 12.
2,000 ÷ 400 = z
z = ____
Answer:
z = 5
Explanation:
2,000 ÷ 400. Cross out the same number of zeros in both the dividend and divisor.
The digit in hundreds is less than the divisor.
So, 2 hundred and zero tens is written as 120 tens.
Divided. 20 ÷ 4 = 5
Question 13.
2,400 ÷ 300 = s
s = ____
Answer:
s = 8
Explanation:
2,400 ÷ 300. Cross out the same number of zeros in both the dividend and divisor.
The digit in hundreds is less than the divisor.
So, 2 hundred and 4 tens is written as 24 tens.
Divided. 24 ÷ 3 = 8
Problem Solving
Question 14.
Mathematical PRACTICE Make Sense of Problems A group of 10 people bought tickets to a reptile exhibit and paid a total of $130. What was the price of one ticket?
Answer:
$13
Explanation:
A group of 10 people bought tickets to a reptile exhibit and paid a total of $130.
The price of one ticket 130 ÷ 10 = 13
130 ÷ 10. Cross out the same number of zeros in both the dividend and divisor.
The digit in hundreds is less than the divisor.
So, 1 hundred and 3 tens is written as 13 tens.
Divided. 13 ÷ 1 = 13
Question 15.
The fastest team in a wheelbarrow race traveled 100 meters in about 20 seconds. On average, how many meters did the team travel each second?
Answer:
5 meters.
Explanation:
The fastest team in a wheelbarrow race traveled 100 meters in about 20 seconds.
Number of meters the team travel each second, 100 ÷ 20 = 5 meters.
100 ÷ 20. Cross out the same number of zeros in both the dividend and divisor.
The digit in hundreds is less than the divisor.
So, 1 hundred and 0 tens is written as 10 tens.
Divided. 10 ÷ 2 = 5
Question 16.
A video store took in $450 in DVD rentals during one day. If DVDs rent for $9 each, how many DVDs were rented?
Answer:
50 DVDs.
Explanation:
A video store took in $450 in DVD rentals during one day.
If DVDs rent for $9 each,
Number of DVDs were rented, 450 ÷ 9 = 5
The digit in hundreds is less than the divisor.
So, 4 hundred and 5 tens is written as 45 tens.
Divided. 450 ÷ 9 = 50
Question 17.
Daniela has a 160-ounce bag of potting soil. She puts an equal amount of soil in 4 pots. How much soil will she put in each pot?
Answer:
40 ounce.
Explanation:
Daniela has a 160-ounce bag of potting soil.
She puts an equal amount of soil in 4 pots.
Total soil she put in each pot, 160 ÷ 4 = 40
The digit in hundreds is less than the divisor.
So, 1 hundred and 6 tens is written as 16 tens.
Divided. 160 ÷ 4 = 40
Hot Problems
Question 18.
Mathematical PRACTICE 3 Find the Error Sonia is finding 5,400 ÷ 90 mentally. Find her mistake and correct it.
Answer:
540 ÷ 9 = 60
Explanation:
Given, 5400 ÷ 90
Cross out the same number of zeros in both the dividend and divisor.
540 ÷ 9 is correct.
But Sonia written as 54 ÷ 9 = 6, which is wrong.
Question 19.
? Building on the Essential Question How can patterns help me divide multiples of 10?
Answer:
A multiple of 10, use the basic fact to continue the pattern.
2 4 ÷ 3 basic fact
2 4 0 ÷ 3 24 tens divided by 3 equals
2, 4 0 0 ÷ 3 24 hundreds divided by 3 equals 8 tens.
2, 4, 0 0 ÷ 3 24 thousands divided by 3.
Explanation:
Divisibility rule for 10 states that any number whose last digit is 0, is divisible by 10.
when dividing numbers that have increasing place values,
divide the first digits of the dividend and divisor.
Then, if only the dividend has zeroes, add the same number of zeroes to quotient as in the dividend.
McGraw Hill My Math Grade 5 Chapter 3 Lesson 4 My Homework Answer Key
Practice
Divide mentally.
Question 1.
270 ÷ 3 = ____
Answer:
90
Explanation:
A multiple of 10, use the basic fact to continue the pattern.
2 7 ÷ 3 basic fact.
2 7 0 ÷ 3 27 tens divided by 3 equals.
2 7 0 ÷ 3 = 90
Question 2.
3,200 ÷ 80 = ___
Answer:
40
Explanation:
A multiple of 10, use the basic fact to continue the pattern.
Cross out the same number of zeros in both the dividend and divisor.
32 ÷ 8 basic fact equals 4
320 ÷ 8 32 tens divided by 8 equals 40
Question 3.
320 ÷ 8 = ____
Answer:
40
Explanation:
A multiple of 10, use the basic fact to continue the pattern.
32 ÷ 8 basic fact equals 4
320 ÷ 8 32 tens divided by 8 equals 40
Algebra Mentally find each unknown.
Question 4.
2,000 ÷ 10 = m
m = ____
Answer:
m = 200
Explanation:
2,000 ÷ 10. Cross out the same number of zeros in both the dividend and divisor.
The digit in hundreds is less than the divisor.
So, 2 hundred and zero tens is written as 20 tens.
Divided. 200 ÷ 1 = 200
Question 5.
8,100 ÷ 90 = b
b = ____
Answer:
b = 90
Explanation:
8100 ÷ 90. Cross out the same number of zeros in both the dividend and divisor.
The digit in hundreds is less than the divisor.
So, 8 hundred and one tens is written as 81 tens.
Divided. 810 ÷ 9 = 90
Question 6.
450 ÷ 9 = r
r = ____
Answer:
r = 50
Explanation:
450 ÷ 9.
The digit in hundreds is less than the divisor.
So, 4 hundred and 5 tens is written as 45 tens.
Divided. 45 ÷ 9 = 5
450 ÷ 9 = 50
Problem Solving
Question 7.
Mathematical PRACTICE 1 Make a Plan Peyton has collected 120 aluminum cans for recycling. If 20 cans will fit in each blue plastic bag, how many bags will she need to carry all the cans?
Answer:
6 bags.
Explanation:
Peyton has collected 120 aluminum cans for recycling.
If 20 cans will fit in each blue plastic bag,
Number of bags she need to carry all the cans,
120 ÷ 20
Cross out the same number of zeros in both the dividend and divisor.
The digit in hundreds is less than the divisor.
So, 1 hundred and 2 tens is written as 12 tens.
Divided. 12 ÷ 2 = 6
Question 8.
There are 5,000 sheets of paper in 25 boxes. If each box contains the same number of sheets of paper, how many sheets of paper are in each box?
Answer:
200 sheets of paper.
Explanation:
There are 5,000 sheets of paper in 25 boxes.
Total sheets of paper in each box,
5000 ÷ 25
The digit in hundreds is less than the divisor.
So, 5 hundred and zero tens is written as 50 tens.
Divided. 50 ÷ 25 = 2
500 ÷ 25 = 20
5000 ÷ 25 = 200
Question 9.
Richard measured his rectangular living room. The room has an area of 200 square feet, and the length is 20 feet. The width is found by dividing the area by the length. What is the width of Richard’s living room?
Answer:
10 feet.
Explanation:
Richard room has an area of 200 square feet, and the length is 20 feet.
The width of Richard’s living room, 200 ÷ 20
Cross out the same number of zeros in both the dividend and divisor.
The digit in hundreds is less than the divisor.
So, 2 hundred and zero tens is written as 20 tens.
Divided. 20 ÷ 2 = 10
Question 10.
The average polar bear weighs 1,200 pounds. The average grizzly bear weighs 800 pounds. The average black bear weighs 400 pounds. The average polar bear weighs how many times more than the average black bear?
_______________________
The average grizzly bear weighs how many times more than the average black bear?
_______________________
Answer:
The average polar bear weighs 3 times more than the average black bear.
The average grizzly bear weighs 2 times more than the average black bear.
Explanation:
The average polar bear weighs 1,200 pounds.
The average grizzly bear weighs 800 pounds.
The average black bear weighs 400 pounds.
The average polar bear weighs how many times more than the average black bear,
1200 ÷ 400
Cross out the same number of zeros in both the dividend and divisor.
The digit in hundreds is less than the divisor.
So, 1 hundred and 2 tens is written as 12 tens.
Divided. 12 ÷ 4 = 3 times.
The average grizzly bear weighs how many times more than the average black bear,
800 ÷ 400
Cross out the same number of zeros in both the dividend and divisor.
Divided. 8 ÷ 4 = 2 times.
Test Practice
Question 11.
An elementary school has 320 students. All of the students are going on a field trip. If 40 students can ride a bus, how many buses are needed?
A. 6 buses
B. 7 buses
C. 8 buses
D. 9 buses
Answer:
Option(C)
Explanation:
An elementary school has 320 students.
If 40 students can ride a bus,
Number of buses needed for a trip,
320 ÷ 40
Cross out the same number of zeros in both the dividend and divisor.
The digit in hundreds is less than the divisor.
So, 3 hundred and 2 tens is written as 32 tens.
Divided. 32 ÷ 4 = 8 buses.