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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,….

**She can buy 14 pies.**

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…**

**It will take 4 adults.**

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?**

**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 €

**She will receive 300 euros.**

** 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 : |
30 per 7 |
50 per 6 |
49 per 7 |

**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.

1) How many cookies does each child receive?

**Conclusion: **

Each child receives 5 cookies.

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:

Answer with TRUE or FALSE. If you answer FALSE, justify your answer.

**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.

After consulting the **answers to this exercise on euclidean and decimal division** in the sixth grade, you can return to the **exercises in the sixth grade****.**

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