# Division and multiplication: answer key to 6th grade math exercises in PDF.

Answer key to 6th grade math exercises on euclidean and decimal division. Know how to divide with the divisor, the dividend, the quotient and the remainder.

Exercise 1:

a. How do you divide by 10, 100 or 1000?

The decimal point is moved 1, 2 or 3 rows to the left.

b. What is a Euclidean division?

A division involving only whole numbers.

c. In a Euclidean division, where are the dividend, quotient, divisor and remainder?

The dividend is at the top left.

The divider at the top right.

The quotient at the top under the line.

The rest at the bottom left.

Exercise 2:

Divide by 10, 100 or 1000
a. 70 : 10 = 7
b. 12 000 : 1 000 = 12
c. 12 400 : 100 = 124
13 957,82 : 1 000 = 13,957 82

Exercise 3:

Pose and perform the following Euclidean divisions:
a. 149 = 18x 8 + 5;
b. 3 764=418x 9 + 2;
c. 1 057 =352x 3 + 1;
d. 12 455 = 47x 265 + 0;
e. 78 456 =1 601 x 49 + 7.

Exercise 4:

A pie for 4 people costs 6 €. The manager of a summer camp has 85 €.
How many pies can she buy?

85:6=14,….

How much money does he have left?

85 – 6×14=85-84=1 €

He has one euro left.

Exercise 5:

To visit a mathematical games exhibition, one adult is required to supervise 15 children.
How many adults are needed to accompany 56 students?

56:15=3,7…

Complete with two consecutive integers :
a. 6< 6.2 < 7
b. 10 001<10 001,2 < 10 002
c. 3940 > 3,939.01 > 3,939

Exercise 6:

At the supermarket bazaar, what is the price of :

1 bulb at 12 euros for 4 ?
12 : 4 = 3 € for a bulb.
1 gum at 52 euros the 13 ?
52 : 13 = 4 € the gum
1 brush at 91 euros for 14 ?
91 : 14 = 6,50 € the brush
1 notebook at 162 euros for 27 ?
162 : 27 = 6 €

Exercise 7:

For the house, what is the cost of :

1 roll of paper at 777 euros per 42 rolls?
777 : 42 = 18,50 € the roll.
1 m of cable at 5 915 euros per 455 m of cable?
5 915 : 455 = 13 € per meter of cable.
1 screwdriver at 7 425 euros the 675 screwdrivers ?
7 425 : 675 = 11 € the screwdriver .
1 KW/h at 150 euros per 5000 KW/h?
5 000 : 150 = 33, 33 €

Exercise 8:

In the fruit and vegetable department, what is the price of :

1 kg of carrots at 10,5euros the 6 kg ?

10,5 : 6 = 1,75 € the kilo of carrot .
1 liter of water at 3.5 euros per 15 liters?

15 : 3,5 = 4,29 €
1 liter of wine at 160,2euros the 12 liters ?

160,20 : 12 = 13,35 € per liter of wine.

1 pencil at 147.9 euros per 200 ?

147,9 : 200 = 0,74 € the pencil.

Exercise 9:

Pencils are worth 0.30 euros. How many pencils can you buy with 9 euros?

9 : 0.3 = 30 pencils.

2. Twenty liters of water cost 6 euros, what is the price of one liter of water?

20 : 6 = 3,34 € per liter.

Exercise 10:

Correspondence books are sold in sets of 25. A lot costs 64 euros.

What is the price of a booklet?

64 : 25 = 2,56 €

2. The college estimates that it needs 470 notebooks.

a. How many lots should he order?

470 : 25 = 18,80

It must order 19 lots

b. How many extra notebooks will there be?

19×25=475

475 – 470 = 5

There will be 5 notebooks left.

Exercise 11:

One pallet contains 605 cans and weighs 370 kg.
The empty pallet weighs 7 kg.
a. How much does each can weigh?
the 605 cans weigh 370 – 7 = 363 kg.
so a can weighs :
363 : 605 = 0.6 kg .
Conclusion: a can of food weighs 600 grams.
b. Knowing that each can contains 10 tomatoes of about 50 g each,
how much does the empty can weigh?
the tomatoes contained in a can represent :
10×50 = 500 g
600 – 500 = 100 g
Conclusion: An empty can weighs 100 grams.
Exercise 12:

A florist has just received a batch of 200 red roses,
to compose bouquets of 12 roses that he sells for 13 €.
He will then sell the remaining roses at €1.5 each.
How much will he earn from the sale of all these flowers?
200 : 12 =16,66….
It will be able to make 16 bouquets of 12 roses.
16×12=192
He will have 8 roses left.
16×13 + 8x 1,5 = 208 + 12 = 220 €.
The sale of all these flowers will bring him 220 euros.
Exercise 13:

One factory produces 302 cars per day.
They are then installed on trucks
which can carry up to 7 cars.
How many fully loaded trucks can leave each day?
302 : 7 = 43,…..
Each day, 43 fully loaded trucks will be able to leave.
302- 43×7= 1
There will be 1 vehicle left.

Exercise 14:

A bookseller must store his 13,592 books in bins.
Each bin can hold a maximum of 250 books.
How many bins will he need to store everything?
13 592 : 250 = 54,368
This will require 55 bins.

Exercise 15:

1) Put the Euclidean division of 334 by 8 and write the equality between dividend, divisor, quotient and remainder.

2) Showing, if necessary, the calculations made, give the exact value of the quotient 334 : 8.

apply the decimal division.

Exercise 16:

By doing the calculations, give the exact result of the following quotients:

Exercise 17:

Mrs. Gomis wants to put 418 eggs in boxes that can hold 12.

1)How many boxes of eggs will she be able to fill?

It will take 34 boxes.

2) How many eggs does he need to fill an extra box?

It will miss 2 eggs.

Exercise 18:

I bought 2.5m of sky blue fabric at €1.6 per meter, 3 brooches at €1.8 per set of 3 and 4m of turquoise blue fabric. I spent a total of 9,20 €.

What is the price of a meter of turquoise blue fabric?

The total price without the fabric is 3,40 €.

Conclusion: the price of a meter of turquoise blue fabric is 0.85 €.

Exercise 19:

a. A group of 6 children share a bag of 114 pieces of candy equally.
How much candy will each child receive?
114 : 6 = 19
Each child will receive 19 pieces of candy.
b. These same children now share a 1.5L bottle of soda.
Is there any drink left if each child takes 0.25L of drink?
6×0.25 = 1.5 L
There will be nothing left.
c. Before we part, we must contribute to the cost of this snack:
each child gives 1,60 € .
Does this pay for the total purchase of €9.75?

6 x 1,60 = 9,60 €
There will be a shortfall of 15 euro cents.

Exercise 20:

a. Chloe receives 25 € pocket money at the end of each month.
At the end of a year, how much will she have received?
25×12 = 300 €
b. Bastien has saved all his pocket money for this year.
This represents a sum of 480 €.
How much did he receive at the end of each month?
480 : 12 = 40 €
He received 40 euros each month.

Exercise 21:

a. 3x2x3x5=90 different dishes.

b. 5x2x5=50 different dishes.

Exercise 22:

The number of steps is a multiple of 5.

The possibilities are 100, 105, 110, 115 or 120.

or 100=4×25+0 so it is not possible.

105=4×26+1 is not possible.

110=4×27+2 is not possible.

115=4×28+3 is possible

120=4×30+0 is not possible.

Conclusion: there are 115 steps.

Exercise 23:

Study the arrangement of vacation photos and the number of turns a pendulum needle makes.

1) 6 x 27+3 x 15 = 207 .

No, it will not be enough, she will have 7 photos left to place.

2) Let’s calculate the number of minutes in a 24-hour day:

24×60 = 1440 minutes in one day

1 440 x 365 = 525 600

Conclusion: the second hand makes 525,600 revolutions in 365 days.

Exercise 24:

1) 178:9=19,77..

Amélie will therefore be able to place 19 CDs.

178-19×9=7

There will be 19 millimeters left in the first compartment.

2) 53:19=2,7…

It will use 3 compartments.

There will be 15 CDs in the third compartment.

Exercise 25:

Price calculation for an adult ticket.

The amount spent on children’s tickets is :

3 x 1,60 = 4,80 €

So the amount spent on adult tickets is :

14 – 4,80 = 9,20 €

The price of an adult ticket is :

9.20 : 2 = 4.60 euros

Conclusion: the price of an adult ticket is 4.60 euros.

Exercise 26:

Exercise 27:

1) Perform the following Euclidean divisions, each time giving equality between the dividend, divisor, remainder and quotient:

 26 by 4 : $26=6\times \,4+2$ 30 per 7 $30=4\times \,7+2$ 50 per 6 $50=8\times \,6+2$ 49 per 7 $49=7\times \,7+0$

2) a ) Propose and perform the following Euclidean division: 1575 by 4.

It’s up to you to make this division.

b) Write the equality between the dividend, divisor, remainder and quotient for the previous Euclidean division.

Exercise 28:

Dimitri stores 2005 books in boxes that can hold 40 books each. How many boxes, at least, will he need?

Conclusion:

He will need 51 boxes, 50 boxes containing 40 books and one box containing 5 books.

Exercise 29:

Clara distributes 79 cookies equally among 15 children and keeps the rest.

Conclusion:

2) How many cookies can Clara eat?

Conclusion:

He will have 4 cookies left.

Exercise 30:

Using the criteria of divisibility, and justifying the answer, say if 1224 is divisible by 2, by 3, by 4, by 5 and by 9.

• 1224 is divisible by 2 because this number ends in 4.
• 1224 is divisible by 3 because 1+2+2+4=9 which is a multiple of 3.
• 1224 is divisible by 4 because 1224:2=612 and 612 is divisible by 2.
• 1224 is divisible by 9 because 1+2+2+4=9 is a multiple of 9.

Exercise 31:

1) The equality 31 = (39) + 4 means that 9 is the quotient and 4 is the remainder of the Euclidean division of 31 by 3.

TRUE

2) If the quotient of the Euclidean division of a number by 8 is equal to 54, then this number is equal to

548.

FALSE, the remainder must be equal to zero.

## 6th grade math exercises corrected in PDF.

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