All the solutions provided in McGraw Hill Math Grade 5 Answer Key PDF Chapter 3 Lesson 10 Quotients with Zeros will give you a clear idea of the concepts.
McGraw-Hill My Math Grade 5 Answer Key Chapter 3 Lesson 10 Quotients with Zeros
Example 1
Maya is saving to buy a television. The television costs $327. She plans to save money for 3 months. How much does Maya need to save each month to buy the television?
Let m represent the amount Maya needs to save each month. Find the unknown in the equation $327 ÷ 3 = m.
1. Divide the hundreds.
2. Divide the tens.
There are not enough tens to divide.
Place a 0 in the quotient.
3. Regroup the two tens as twenty ones. There are now 27 ones.
4. Divide the ones.
So, $327 ÷ 3 = ___. Since m = ___, Maya needs to save each month.
Check for Reasonableness Compare to the estimate ____ ≈ ____
Answer:
$109
Explanation:
Divide the hundreds.
300 ÷ 3 = 100
2. Divide the tens.
There are not enough tens to divide.
Place a 0 in the quotient.
Regroup the two tens as twenty ones. There are now 27 ones.
4. Divide the ones.
So, $327 ÷ 3 = 109.
Since m = 109, Maya needs to save each month.
Example 2
Find 5,231 ÷ 4.
1. Divide the thousands. Divide the hundreds.
2. Divide the hundreds.
3. Divide the tens.
There are not enough tens to divide. Place a 0 in the tens place.
4. Divide the ones.
The remainder is ____
So, 5,231 ÷ 4 = ____
Check Use multiplication to check your answer.
_____ × 4 = ____ and 5,228 + ____ = 5,231
Answer:
Quotient = 1307
Remainder = 3
Explanation:
Divide the thousands.
5000 ÷ 4 = 1250
Divide the hundreds.
200 ÷ 4 = 50
Divide the tens.
There are not enough tens to divide. Place a 0 in the tens place.
Divide the ones.
The remainder is 3
So, 5,231 ÷ 4 = 1307
Check Use multiplication to check your answer.
1307 × 4 = 5228
5,228 + 3 = 5,231
Guided Practice
Question 1.
Divide.
Answer:
Quotient = 210
Remainder = 2
Explanation:
Divide the hundreds.
800 ÷ 4 = 200
Divide the tens.
40 ÷ 4 = 10
The remainder is 2.
So, 842 ÷ 4 = 210
Check Use multiplication to check your answer.
210 × 4 = 840
840 + 2 = 842
Talk Math
Yolanda wants to find 936 ÷ 9. In which place-value position should she place a zero? Explain.
Answer:
104
Zero should be placed in tens place value.
Explanation:
Check Use multiplication to check your answer.
104 × 9 = 936
Independent Practice
Divide.
Question 2.
Answer:
209
Explanation:
Divided the hundreds.
400 ÷ 2 = 200
Divide the tens.
There are not enough tens to divide. Place a 0 in the tens place.
Divide the ones.
18 ÷ 2 = 9
So, 418 ÷ 2 = 209
Check Use multiplication to check your answer.
209 × 2 = 418
Question 3.
Answer:
105
Explanation:
Divided the hundreds.
200 ÷ 2 = 100
Divide the tens.
There are not enough tens to divide. Place a 0 in the tens place.
Divide the ones.
10 ÷ 2 = 5
So, 210 ÷ 2 = 105
Check Use multiplication to check your answer.
105 × 2 = 210
Question 4.
Answer:
1081
Explanation:
Divided the thousands.
4000 ÷ 4 = 1000
Divide the hundreds.
300 ÷ 4 = 75
Divided the tens.
20 ÷ 4 = 5
Divide the ones.
4 ÷ 14 = 1
So, 4,324 ÷ 4 = 1081
Check Use multiplication to check your answer.
1081 × 4 = 4324
Question 5.
Answer:
Quotient = 13
Remainder = 2
Explanation:
Question 6.
Answer:
Quotient = 3,106
Remainder = 1
Explanation:
Divided the thousands.
6000 ÷ 2 = 3000
Divide the hundreds.
200 ÷ 2 = 100
Divided the tens.
There are not enough tens to divide. Place a 0 in the tens place.
Divide the ones.
Remainder is 1.
Question 7.
Answer:
2,064
Explanation:
Divided the thousands.
6000 ÷ 3 = 2000
Divide the hundreds.
There are not enough hundreds to divide. Place a 0 in the tens place.
Divided the tens.
19 ÷ 3 = 6
Divide the ones.
Question 8.
840 ÷ 7 = ____
Answer:
120
Explanation:
Question 9.
627 ÷ 3 = ____
Answer:
209
Explanation:
Divided the hundreds.
600 ÷ 3 = 200
Divide the tens.
There are not enough hundreds to divide. Place a 0 in the tens place.
Divide the ones.
Question 10.
5,330 ÷ 5 = ____
Answer:
1066
Explanation:
Divided the thousands.
5000 ÷ 5 = 1000
Divide the hundreds.
300 ÷ 5 = 60
There are not enough hundreds to divide. Place a 0 in the tens place.
Divided the tens.
30 ÷ 5 = 6
Divide the ones.
Question 11.
8,017 ÷ 9 = ___
Answer:
Quotient = 809
Remainder = 7
Explanation:
Question 12.
413 ÷ 4 = ___
Answer:
Quotient = 103
Remainder = 1
Explanation:
Divided the hundreds.
400 ÷ 4 = 100
Divide the tens.
There are not enough hundreds to divide. Place a 0 in the tens place.
Divide the ones.
Question 13.
9,163 ÷ 3 = ____
Answer:
Quotient = 3045
Remainder = 1
Explanation:
Divided the thousands.
9000 ÷ 3 = 3000
Divide the hundreds.
There are not enough hundreds to divide. Place a 0 in the tens place.
Divided the tens and ones.
Problem Solving
Question 14.
Mathematical PRACTICE 2 Use Algebra There are 312 fish at the aquarium in 3 different fish tanks. Each tank has the same number of fish. How many fish are in each tank? Write an equation to find the unknown. Then find the unknown.
Answer:
312 ÷ 3 = x
x = 14 fishes.
So, the unknown number is 14.
Explanation:
Total fishes in aquarium = 312
Number of fish tanks 3.
Number of fishes in each tank = x
312 ÷ 3 = x
x = 14 fishes.
So, the unknown number is 14.
Question 15.
There are 1,620 minutes of music to be put on 9 CDs. If the same number of minutes fits on each CD, how many minutes of music fit on each CD?
Answer:
180 minutes.
Explanation:
Number of minutes of music to be put on 9 CDs = 1,620 minutes.
Total number of CDs = 9
Number of minutes of music fit on each CD,
1620 ÷ 9 = 180 minutes.
Question 16.
Gina spent 120 minutes helping her neighbors rake leaves in the last 4 days. She helped the same amount of minutes each day. How many minutes did she rake leaves each day?
Answer:
30 minutes.
Explanation:
Gina spent 120 minutes helping her neighbors rake leaves in the last 4 days.
She helped the same amount of minutes each day.
Number of minutes she rake leaves each day,
120 ÷ 4 = 30 minutes.
HOT Problems
Question 17.
Mathematical PRACTICE 1 Keep Trying Write two division problems that have zeros in the quotient. One of the problems should have a remainder and the other should not.
Answer:
First problem:
There are 9,163 minutes of music to be put on 3 CDs. If the same number of minutes fits on each CD, how many minutes of music fit on each CD?
Second problem:
There are 5,330 minutes of music to be put on 5 CDs. If the same number of minutes fits on each CD, how many minutes of music fit on each CD?
Explanation:
In first problem, the quotient has zero and remainder also as shown below,
In the second problem, the quotient is zero and remainder is also zero as shown below,
Question 18.
? Building on the Essential Question How can I know when to place a zero in the quotient?
Answer:
Zero placeholders can be used to continue dividing to get a more accurate quotient.
In long division where the divisor is larger than the current working dividend,
we need to put a zero in the quotient.
McGraw Hill My Math Grade 5 Chapter 3 Lesson 10 My Homework Answer Key
Practice
Divide.
Question 1.
Answer:
107
Explanation:
Check Use multiplication to check your answer.
107 × 8 = 856
Question 2.
Answer:
Quotient = 975
Remainder = 1
Explanation:
Check Use multiplication to check your answer.
975 × 3 = 2925
2925 + 1 = 2926
Question 3.
841 ÷ 4 = ____
Answer:
Quotient = 210
Remainder = 1
Explanation:
Check Use multiplication to check your answer.
210 × 4 = 840
840 + 1 = 841