All the solutions provided in McGraw Hill Math Grade 4 Answer Key PDF Chapter 2 Lesson 9 Solve Multi-Step Word Problems will give you a clear idea of the concepts.
McGraw-Hill My Math Grade 4 Answer Key Chapter 2 Lesson 9 Solve Multi-Step Word Problems
Math in My World
Example 1
The music club had $390 in their account. At the concert, they earned $472. Afterwards, they had to pay $75 to rent the stage and $102 for the rental equipment. How much is in their account now?
Write an equation.
When more than one step is involved, add and subtract in order from left to right.
So, the account now has $685
Answer: An estimate is $400 + $500 – $100 – $100 = $700
This is close to the actual amount, which is $685.
Explanation:
Given, The music club had $390 in their account. At the concert, they earned $472.
Afterwards, they had to pay $75 to rent the stage and $102 for the rental equipment.
The ones they are earning are the add ups and the ones they are spending are to be subtracted
Let the variable be y , which we have to find out,
So, We can write the equation as 390 + 472 – 75 – 102 = y .
y = 862 -75 – 102
y = 787 – 102
y = 685,
Thus, The amount left with them is $685
To check for an estimate, round the numbers to the nearest hundreds we get,
$400 + $500 – $100 – $100 = $700
This is close to the actual amount, which is $685. So, the answer is reasonable.
Example 2
Twenty people got on the bus at the first stop. At the second stop, 14 people got off the bus, and 5 people got on the bus. At the third stop, 2 people got off the bus, and some people got on the bus. Then there were 24 people on the bus. How many people got on the bus at the third stop?
Write an equation.
The letter b can be used as a variable to represent the unknown.
Find the unknown.
So, 15 people got on the bus at the third stop.
Answer: Totally, 15 people got on the bus at the third stop.
Explanation:
Given, Twenty people got on the bus at the first stop.
At the second stop, 14 people got off the bus, and 5 people got on the bus.
At the third stop, 2 people got off the bus, and some people got on the bus.
Then there were 24 people on the bus
Here the people who are on the bus are the add ups and the ones who got off are to be subtracted
Let the variable be b.
The equation will be 20 – 14 + 5 – 2 + b = 24
6 + 5 – 2 + b = 24
11 – 2 + b = 24
9 + b = 24
b = 24 – 9
b = 15
So, 15 people got on the bus at the third stop.
Talk Math
Can you use any letter of the alphabet for a variable? Explain
Answer: Yes, Any letter or symbol can represent a variable, or unknown, as they’re sometimes called; it makes no difference whether you use a, k or x.
A variable is a symbol, often a letter, that is used to represent an unknown, or a number that is not known.
Guided Practice
Question 1.
Algebra Savannah had $15. She earned $20. Then, she bought a gift for 8. How much money does she have left? Write an equation to solve the problem. Use a variable for the unknown.
Answer: he have left with $27.
Explanation:
Given, Savannah had $15. She earned $20. Then, she bought a gift for 8.
Now, write up an equation for the money she has and earned as add ups , And her expenses as subtracts
We have to find how much money she left which will be the unknown variable Let the unknown variable be y,
Then, $15 + $20 – $8 = y
y = $35 – $8
y = $27
So, She have left with $27.
Independent Practice
Algebra Write an equation to solve each problem. Use a variable for the unknown.
Question 2.
Bailey had 75 beads. She used 20 of them on a necklace and 12 of them on a bracelet. Then she bought 25 more beads. How many beads does Bailey have now?
Answer: Bailey has 68 beads.
Explanation:
Given, Bailey had 75 beads. She used 20 of them on a necklace and 12 of them on a bracelet.
Then she bought 25 more beads.
The ones she had will be add ups and she used will be subtracts
To know , How many beads does Bailey have now , Let the Unknown variable be y
The equation will be, 75 – 20 – 12 + 25 = y
y = 55 – 12 + 25
y = 43 + 25
y = 68
So, Bailey has 68 beads.
Question 3.
Alex had $30. He spent $13 on a game and $5 on a poster. Then, he earned $8 doing chores for a week. How much money does Alex have now?
Answer: Alex has $20
Explanation:
Given, Alex had $30. He spent $13 on a game and $5 on a poster.
Then, he earned $8 doing chores for a week.
The money he had and earned will be the add ups and the money he spent will be the subtract,
To know ,How much money does Alex have now? Let the Unknown variable be y
Then, y = $30 – $13 – $5 + $8
y = $17 – $5 + $8
y = $12 + $ 8
y = $20
So, Alex has $20.
Question 4.
Hunter had 16 jars of paint. He used 2 of them on a painting. He bought 8 more jars. Then, he used some of the jars to make another painting. Now, Hunter has 15 jars of paint. How many jars did he use for the second painting?
Answer: He used 7 jars of paint for the second painting.
Explanation:
Given, Hunter had 16 jars of paint. He used 2 of them on a painting.
He bought 8 more jars. Then, he used some of the jars to make another painting.
Now, Hunter has 15 jars of paint.
To know, How many jars did he use for the second painting? Let the Unknown variable be y
Then, 16 – 2 + 8 – y = 15
We can write it as , y = 16 – 2 + 8 – 15
y = 14 + 8 – 15
y = 22 – 15
y = 7
So, He used 7 jars of paint for the second painting.
Question 5.
A restaurant served food to a large party. The manager is listing the total costs, shown below.
The total cost is $1,317. How much did the side dishes cost?
Answer: The cost of the side dishes are $327
Explanation:
Given, The total cost is $1,317
To know, How much did the side dishes cost? Let the Unknown variable be y
The prices of the items are the add ups and the total cost will be the subtract
Then, 452 + 388 + 150 – y = 1,317
We can write it as , y = 452 + 388 + 150 – 1,317
y = 1,317 – 990
y = 327
So, The cost of the side dishes are $327
Problem Solving
Use a number cube to complete each number puzzle.
Question 6.
Roll a number cube 4 times. Write one number in each box. Find the greatest value of the variable.
+ – + = b
b = ____
Answer: b = 9
Explanation:
Given, Roll a number cube 4 times
6 + 2 – 4 + 5 = b
b = 8 – 4 + 5
b = 4 + 5
b = 9.
Question 7.
Roll a number cube 6 times. Write one number in each box. Find the greatest value of the variable.
+ – + + – = y
y = ____
Answer: y = 9
Explanation:
Given, Roll a number cube 6 times.
5 + 3 – 2 + 6 + 1 – 4 = y
y = 8 – 2 + 6 + 1 – 4
y = 6 + 6 + 1 – 4
y= 13 – 4
y = 9.
HOT problems
Question 8.
Mathematical PRACTICE 1 Make Sense of Problems Victoria had some money in her wallet. She went to the mall and spent $8 on a stuffed animal, $7 on lunch, and $13 on a gift for her mom. Then her brother gave her $10. She bought a book for $15. Now she has $12. How much money did Victoria originally have in her wallet?
Answer: Victoria originally have $45 in her wallet.
Explanation:
She went to the mall and spent $8 on a stuffed animal, $7 on lunch, and $13 on a gift for her mom.
Then her brother gave her $10.
She bought a book for $15. Now she has $12.
To know, How much money did Victoria originally have in her wallet? Let the Unknown variable be y
Then, y – 8 – 7 – 13 +10 – 15 = 12
we can write it as y = 8 + 7 + 13 – 10 + 15 + 12
y = 28 – 10 + 15 + 12
y = 18 + 15 + 12
y = 45
So, Victoria originally have $45 in her wallet.
Question 9.
? Building on the Essential Question How can I use variables to describe real-world problems? Explain.
Answer: You can use a variable expression to describe a real world situation where one or more quantities have an unknown value or can change in value. To write a variable expression for a real world situation: Figure out which quantity in the situation is unknown and define a variable to represent the unknown quantity.
Fluency Practice
Add.
Question 1.
Answer: 92,987
Explanation:
To estimate
Given, 53,035 + 39,952
round to the nearest hundred we get
53,000 + 40,000 = 93,000
So, 93,000 is nearest to 92,987
Question 2.
Answer: 1,57,461
Explanation:
To estimate
Given, 94,225 + 63,236
round to the nearest hundred we get
94,000 + 63,000 = 157,000
So, 157,000 is nearest to 1,57,461
Question 3.
Answer: 1,19,601
Explanation:
To estimate
Given, 82,427 + 37,174
round to the nearest hundred we get
82,000 + 37,000 = 119,000
So, 119,000 is nearest to 1,19,601
Question 4.
Answer: 50,481
Explanation:
To estimate
Given, 32,472 + 18,009
round to the nearest hundred we get
32,000 + 18,000 = 50,000
So, 50,000 is nearest to 50,481
Question 5.
Answer: 1,35,164
Explanation:
To estimate
Given, 72,259 + 62,905
round to the nearest hundred we get
72,000 + 63,000 = 1,35,000
So, 1,35,000 is nearest to 1,35,164
Question 6.
Answer: 69,801
Explanation:
To estimate
Given, 52,372 + 17,429
round to the nearest hundred we get
52,000 + 17,000 = 69,000
So, 69,000 is nearest to 69,801
Question 7.
Answer: 77,744
Explanation:
To estimate
Given, 63,141 + 14,603
round to the nearest hundred we get
63,100 + 14,600= 77,700
So, 77,700 is nearest to 77,744
Question 8.
Answer: 59,099
Explanation:
To estimate
Given, 20,407 + 38,692
round to the nearest hundred we get
20,400 + 38,700 = 59,100
So, 59,100 is nearest to 59,099
Question 9.
Answer: 4,19,870
Explanation:
To estimate
Given, 367,028 + 52,842
round to the nearest hundred we get
367,000 + 52,900 = 4,19,900
So, 4,19,900 is nearest to 4,19,870
Question 10.
Answer: 5,03,437
Explanation:
To estimate
Given, 482,952 + 20,485
round to the nearest hundred we get
483,000 + 20,500 = 5,03,500
So, 5,03,500 is nearest to 5,03,437
Question 11.
Answer: 2,21,990
Explanation:
To estimate
Given, 137,953 + 84,037
round to the nearest hundred we get
138,000 + 84,000 = 2,22,000
So, 2,22,000 is nearest to 2,21,990
Question 12.
Answer: 9,06,182
Explanation:
To estimate
Given, 813,448 + 92,734
round to the nearest hundred we get
813,400 + 92,700 = 9,06,100
So, 9,06,100 is nearest to 9,06,182
Question 13.
Answer: 9,34,223
Explanation:
To estimate
Given, 103,374 + 824,849
round to the nearest hundred we get
103,300 + 824,800 = 9,28,100
So, 9,28,100 is nearest to 9,34,223
Question 14.
Answer: 7,45,110
Explanation:
To estimate
Given, 372,555 + 372,555
round to the nearest hundred we get
372,500 + 372,500 = 7,45,000
So, 7,45,000 is nearest to 7,45,110
Question 15.
Answer: 9,60,514
Explanation:
To estimate
Given, 218,662 + 741,852
round to the nearest hundred we get
218,600 + 741,900 = 9,60,500
So, 9,60,500 is nearest to 9,60,514
Question 16.
Answer: 8,46,009
Explanation:
To estimate
Given, 359,751 + 486,258
round to the nearest hundred we get
359,700 + 486,300 = 8,46,000
So, 8,46,000 is nearest to 8,46,009
Question 17.
Answer: 3,72,586
Explanation:
To estimate
Given, 118,577 + 254,009
round to the nearest hundred we get
118,500 + 254,000 = 3,72,500
So, 3,72,500 is nearest to 3,72,586
Question 18.
Answer: 9,91,110
Explanation:
To estimate
Given, 888,888 + 102,222
round to the nearest hundred we get
888,900 + 102,200 = 9,91,100
So, 9,91,100 is nearest to 9,91,110
Question 19.
Answer: 9,75,269
Explanation:
To estimate
Given, 328,805 + 646,464
round to the nearest hundred we get
328,800 + 646,400 = 9,75,264
So, 9,75,264 is nearest to 9,75,269
Question 20.
Answer: 5,89,542
Explanation:
To estimate
Given, 335,533 + 254,009
round to the nearest hundred we get
335,500 + 254,000 = 5,87,500
So, 5,87,500 is nearest to 5,89,542
Fluency Practice
Subtract.
Question 1.
Answer: 26,071
Explanation:
Given, 63,581 – 37,510 = 26,071
To check , we can add the subtrahend to the result
That is 26,071 + 37,510 = 63,581
Question 2.
Answer: 10,003
Explanation:
Given, 72,510 – 62,507 = 10,003
To check , we can add the subtrahend to the result
That is 10,003 + 62,507 =72,510
Question 3.
Answer: 66,564
Explanation:
Given, 82,404 – 15,840 = 66,564
To check , we can add the subtrahend to the result
That is 66,564 + 15,840 =82,404
Question 4.
Answer: 15
Explanation:
Given, 43,524 – 43,509 = 15
To check , we can add the subtrahend to the result
That is 15 + 43,509 =43,524
Question 5.
Answer: 13,693
Explanation:
Given, 42,824 – 29,131 = 13,693
To check , we can add the subtrahend to the result
That is 13,693 + 29,131 = 42,824
Question 6.
Answer: 14,220
Explanation:
Given, 34,108 – 19,888 = 14,220
To check , we can add the subtrahend to the result
That is 14,220 + 19,888 = 34,108
Question 7.
Answer: 730
Explanation:
Given, 13,546 – 12,816 = 730
To check , we can add the subtrahend to the result
That is 730 + 12,816 = 13,546
Question 8.
Answer: 16,306
Explanation:
Given, 45,850 – 29,544 = 16,306
To check , we can add the subtrahend to the result
That is 16,306 + 29,544 = 45,850
Question 9.
Answer: 2,90,333
Explanation:
Given, 237,482 – 52,851 = 2,90,333
To check , we can add the subtrahend to the result
That is 2,90,333 + 52,851 = 237,482
Question 10.
Answer: 2,89,000
Explanation:
Given, 321,123 – 32,123 = 2,89,000
To check , we can add the subtrahend to the result
That is 2,89,000 + 32,123 = 321,123
Question 11.
Answer: 53,916
Explanation:
Given, 137,953 – 84,037 = 53,916
To check , we can add the subtrahend to the result
That is 53,916 + 84,037 = 137,953
Question 12.
Answer: 3,25,542
Explanation:
Given, 338,200 – 12,658 = 3,25,542
To check , we can add the subtrahend to the result
That is 3,25,542 + 12,658 = 338,200
Question 13.
Answer: 1,22,124
Explanation:
Given, 825,385 – 703,261 = 1,22,124
To check , we can add the subtrahend to the result
That is 1,22,124 + 703,261 = 825,385
Question 14.
Answer: 4,35,859
Explanation:
Given, 651,851 – 215,992 = 4,35,859
To check , we can add the subtrahend to the result
That is 4,35,859 + 215,992 = 651,851
Question 15.
Answer: 47,610
Explanation:
Given, 453,166 – 405,556 = 47,610
To check , we can add the subtrahend to the result
That is 47,610 + 405,556 = 453,166
Question 16.
Answer: 14,610
Explanation:
Given, 212,894 – 198,284 = 14,610
To check , we can add the subtrahend to the result
That is 14,610 + 198,284 = 212,894
Question 17.
Answer: 2,07,439
Explanation:
Given, 489,255 – 281,816 = 2,07,439
To check , we can add the subtrahend to the result
That is 2,07,439 + 281,816 = 489,255
Question 18.
Answer: 90,038
Explanation:
Given, 258,914 – 168,876 = 90,038
To check , we can add the subtrahend to the result
That is 90,038 + 168,876 = 258,914
Question 19.
Answer: 1,85,999
Explanation:
Given, 545,248 – 359,249 = 1,85,999
To check , we can add the subtrahend to the result
That is 1,85,999 + 359,249 = 545,248
Question 20.
Answer: 1,16,283
Explanation:
Given, 605,060 – 488,777 = 1,16,283
To check , we can add the subtrahend to the result
That is 1,16,283 + 488,777 = 605,060.