Multiplication & division
A library has 3,425 fiction books and 2,318 nonfiction books.
How many books does the library have altogether?
Answer: 5,743 books
3,425 + 2,318 = 5,743
Question:
Maya has 45 more stickers than Noah. Noah has 72 stickers.
How many stickers does Maya have?
Answer: 117 stickers
72 + 45 = 117
Question:
A farmer has 6 baskets with 25 apples in each basket.
He gives away 40 apples.
How many apples does he have left?
Answer: 110 apples
6 × 25 = 150
150 − 40 = 110
A library has 3,425 fiction books and 2,318 nonfiction books.
How many books does the library have altogether?
Answer: 5,743 books
3,425 + 2,318 = 5,743
Question:
A student says:
“If I have 5 groups of 12, I should multiply 5 + 12 to find the answer.”
Is the student correct?
Answer: No.
When there are 5 equal groups of 12, multiply:
5 × 12 = 60
A teacher has 144 stickers and divides them equally among 8 students.
How many stickers does each student receive?
Answer: 18 stickers
144 ÷ 8 = 18
Question:
A large box contains 3 times as many books as a small box.
The small box contains 24 books.
How many books are in the large box?
Answer: 72 books
24 × 3 = 72
A teacher buys 9 packs of pencils. Each pack contains 12 pencils.
She gives 18 pencils to each of her 4 students.
How many pencils does she have left?
Answer: 36 pencils
First:
9 × 12 = 108 pencils
Then:
18 × 4 = 72 pencils given away
Finally:
108 − 72 = 36 pencils
Question:
A stadium has 4,500 seats. During a game, 1,275 seats are empty.
How many people are in the stadium?
Answer: 3,225 people
4,500 − 1,275 = 3,225
Question:
A student solves:
156 − 48 = 108
Is the student correct?
Answer: Yes!
156 − 48 = 108
Question:
A bakery makes 12 trays of cookies. Each tray contains 36 cookies.
The bakery packs all the cookies equally into 9 boxes.
How many cookies go into each box?
Answer: 48 cookies
First:
12 × 36 = 432 cookies
Then:
432 ÷ 9 = 48 cookies
Question:
A school sold 1,250 tickets for a play.
There were 350 more adult tickets than student tickets.
How many student tickets were sold?
Answer: 450 student tickets
Think of the bar model:
Remove the extra 350:
1,250 − 350 = 900
Split the remaining 900 into two equal parts:
900 ÷ 2 = 450
So 450 student tickets were sold.
Question:
A store has 8 boxes with 45 toys in each box.
The store sells 125 toys.
How many toys are left?
Answer: 235 toys
8 × 45 = 360
360 − 125 = 235
Question:
A school collected 2,845 cans in October. In November, they collected 1,375 more cans than in October.
How many cans did they collect in November?
Answer: 4,220 cans
2,845 + 1,375 = 4,220
A student says:
“If Sara has 3 times as many stickers as Mia, and Mia has 20 stickers, then together they have 60 stickers.”
Is the student correct?
Answer: No.
Sara has:
20 × 3 = 60 stickers
But they have 60 + 20 = 80 stickers altogether.
Question:
A theater has 15 rows with 28 seats in each row.
If 84 seats are reserved for performers and staff, how many seats are available for everyone else?
Answer: 336 seats
15 × 28 = 420
420 − 84 = 336
Question:
Ava and Ben have the same amount of money.
Ava spends $18.
Ben earns $42.
Afterward, Ben has twice as much money as Ava.
How much money did they each have at the beginning?
Answer: $78 each
Think of the final amounts as:
The difference between them is:
$18 + $42 = $60
So 1 part = $60.
Ava ended with $60.
She had spent $18, so:
$60 + $18 = $78
Answer: They each started with $78.
A school is taking students on a field trip.
There are 84 students and 12 teachers.
Each bus can hold 24 people.
What is the least number of buses needed?
Answer: 4 buses
Total people:
84 + 12 = 96
Then:
96 ÷ 24 = 4
So the school needs 4 buses.
Question:
A zoo had 6,250 visitors on Saturday and 1,875 fewer visitors on Sunday.
How many visitors came to the zoo over both days?
Answer: 10,625 visitors
Sunday:
6,250 − 1,875 = 4,375
Total:
6,250 + 4,375 = 10,625
Question:
A student solves this problem:
A school has 240 students. There are 4 times as many students in Grade 4 as in Grade 3. How many students are in Grade 3?
The student says 60 students.
Is the student correct?
Answer: Yes!
The bar model has 5 equal parts:
240 ÷ 5 = 48
Wait! That means the student is not correct.
The correct answer is 48 students.
Check:
48 × 4 = 192
192 + 48 = 240
Question:
A warehouse has 2,400 bottles.
The bottles are packed into boxes with 12 bottles in each box. The boxes are then divided equally among 8 stores.
How many boxes does each store receive?
Answer: 25 boxes
First:
2,400 ÷ 12 = 200 boxes
Then:
200 ÷ 8 = 25 boxes
Question:
Liam has 4 times as many trading cards as Zoe.
Together, they have 250 cards.
How many cards does Zoe have?
Answer: 50 cards
Think of the bar model:
Together:
5 equal parts = 250
250 ÷ 5 = 50
So Zoe has 50 cards.
Liam has:
50 × 4 = 200 cards
Question:
A sports club has 360 members.
There are twice as many adult members as child members.
The club charges adults $15 and children $10 for a special event.
If every member attends, how much money will the club collect?
Answer: $4,800
Think of the members as 3 equal parts:
360 ÷ 3 = 120 children
Adults:
120 × 2 = 240 adults
Money from adults:
240 × $15 = $3,600
Money from children:
120 × $10 = $1,200
Total:
$3,600 + $1,200 = $4,800
Question:
A school has 8,450 pencils.
It gives 2,375 pencils to the fourth grade and 1,825 pencils to the fifth grade.
How many pencils are left?
Answer: 4,250 pencils
8,450 − 2,375 = 6,075
6,075 − 1,825 = 4,250
Question:
Two students solve this problem:
A school has 425 students. There are 75 more students in fourth grade than fifth grade. How many students are in each grade if these are the only two grades?
Who is correct?
Answer: Noah is correct.
Since fourth grade has 75 more students:
Try Noah's numbers:
250 − 175 = 75
And:
250 + 175 = 425
So Noah's answer works.
Emma's numbers have the difference going in the wrong direction:
200 − 225 = −25
Therefore:
Fourth grade = 250 students
Fifth grade = 175 students