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**Arithmetic** with corrected 3rd grade math exercises are always worth considering. Thus, the notion of multiple and divisors of a whole number is very important. Also, with this chapter, you will know the prime factor decomposition of any positive integer. In addition, the student will need to know the definition of an integer and then also know how to determine the value of the greatest common divisor (GCD) of two integers.

Arithmetic is a part of mathematics that studies numbers and operations on numbers. This is why most students prefer it to geometry. In the third grade, students study arithmetic and its applications in various contexts in detail.

We will end this series of exercises with real-life problems that are similar to those available in your third grade textbook.

## Series of exercises on arithmetic

### Exercise #1:

Write the number as an irreducible fraction.

Hint: one can give the prime decomposition of the numbers 325 and 1,053 and then calculate the PGCD of the numbers 1,053 and 325.

### Exercise #2:

1.Give the prime factor decomposition of the numbers 630 and 924.

2. write the fraction in irreducible form, giving details of all the calculations.

### Exercise #3:

A philatelist owns 1,631 French stamps and 932 foreign stamps. He wishes to sell his entire collection by making identical lots, i.e. with the same number of stamps and the same distribution of French and foreign stamps

1. Calculate the maximum number of batches that can be made.

2. How many French and foreign stamps will there be in each lot?

### Exercise #4:

1/ Determine the PGCD of the numbers 108 and 135.

2/ Mark with 108 red and 135 black balls. He wants to make packages so that :

– All packages contain the same number of red marbles;

– All packages contain the same number of black marbles;

– All red and all black marbles are used.

a. What is the maximum number of packages it can achieve?

b. How many red marbles and black marbles will there be in each package?

### Exercise #5:

1.Give the prime factor decomposition of the numbers 325 and 1053.

2. write in irreducible fraction form the number

### Exercise #6:

Determine the prime factor decomposition of 110 and 88.

Calculate the PGCD of 110 and 88.

A worker has metal plates 110 cm long and 88 cm wide. He was instructed to “cut out identical squares from these plates, as large as possible, so that there is no loss”.

What will be the length of the side of a square?

How many squares will he get per plate?

### Exercise #7:

For May^{1st}, Julie has 182 sprigs of lily of the valley and 78 roses.

She wants to make as many identical bouquets as possible using all the flowers.

How many identical bouquets can she make?

What will be the composition of each bouquet?

### Exercise #8:

A chocolate maker has just made 2,622 Easter eggs and 2,530 chocolate fish.

He wants to sell egg and fish assortments so that :

All packages have the same composition.

After packing, there are no eggs or fish left.

1) Help this chocolate maker to choose the composition of each package: give all the possibilities.

2) What is the most number of packages he can make?

### Exercise #9:

A batch of 161 red pencils and a batch of 133 black pencils are divided into packets so that all the pencils in a packet are the same color and all packets contain the same number of pencils.

a) How many pencils are in each package?

b) What is the number of packages of pencils of each color?

### Exercise #10:

A box of board games has the shape of a rectangular parallelepiped. The edges measure an integer number of centimeters; the faces have areas of 96 cm², 160 cm² and 240 cm².

What is the volume of the box?

### Exercise #11:

A trunk has the shape of a rectangular parallelepiped with dimensions 140 cm, 112 cm and 84 cm. We want to fill it with identical cubes whose edge measures a whole number of centimeters.

1) Calculate the edge of the largest possible cube.

2) Calculate the edges of the other cubes that could fill the trunk.

3) Calculate in each case the number of cubes needed to fill the trunk.

### Exercise #12:

The sides of a triangular lot measure 198 m, 254 m and 306 m. Trees are planted along the sides, equally spaced, with a tree at each top. The distance between two consecutive trees is measured by a whole number of meters.

What is the minimum number of trees that must be purchased?

Skills to learn about inequations and sign tables:

- Know the definition of a multiple and a divisor;
- Know how to apply the Euclidean division property;
- Decompose an integer into a product of prime numbers;
- Compute the greatest common divisor (GCD) of two positive integers;
- Make a fraction irreducible.
- These exercises are in accordance with the officialnational education programs.

In addition, you can consult the course on arithmetic and decomposition into prime factors in third grade.

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