The ** multiplication ** is that operation that consists of calculating the ** product ** (result) that is obtained by adding the same number (**factor or multiplicand**) so many times as the value of the other number (**factor or multiplicator or multiplier**).

Multiplication is used when we have to ** replace the calculation of certain repetitive additions ** (for example: 2 + 2 + 2 + 2 = 8) by a more efficient method (2 x 4 = 8).

In general, multiplication is considered the ** inverse operation ** of ** division**.

#### Know the terms of multiplication

Do you know what ** multiplications ** are and what are they for? Can you tell what its symbol "x" means? Do you know the differences between the ** multiplicand**, the ** multiplier ** and the ** product **? Don't worry, through the ** lesson ** we explain each of the ** elements of multiplication**.

SPANISH

ENGLISH

__The elements of multiplication (multiplicand and multiplier) that are multiplied together are called "factors" or "coefficients":__

- The ** multiplicand ** is the element that tells us "*how many times*" we are going to add or multiply the multiplier digit (in this example, it is 24). It is at the top of any multiplication.

- The ** multiplier ** represents the element that multiplies each of the numbers in the multiplicand and we will take as a reference its multiplication table (in this case, the table of 7). It is located at the bottom of the multiplication and is always written to the right of the multiplication sign ("x")

- The **multiplication sign** determines the multiplicative operation and is read "*multiplied by*" or "*times*", in the following example, it would be "24 multiplied by 7" or "24 times 7". It is represented by a cross "x" (relative to the Cross of Saint Andrew) or by using a point at half height (•)

- The ** equal sign ** is the equality symbol and is read "*equals*". In our example, we will read the multiplication as "24 times 7 equals 168"

- The ** product ** contains the result of applying the multiplication algorithm (24 x 7 = 168)

#### Recognize the concept of multiplication as a repeated addition of equal addends

We must understand that, mathematically, ** multiplying a certain quantity by a number ** consists of * adding said quantity as many times as the number indicates*.

In other words, multiplications are those mathematical operations that are carried out to calculate the result (also called "**product**") of adding the same number ("**multiplicand**") so many times as indicated by the other number ("**multiplier**").

__In the following example we can see that multiplying 5 times 3 (that is 5x3) is also equivalent to adding 3 times the number 5 (meaning 5+5+5), obtaining in both cases the same result (product):__

#### Multiply natural numbers without carrying: 3 digits by 2 digits

__Look at the solved multiplication that we propose and you will learn how to calculate a multiplication of three digits in the multiplicand by two digits in the multiplier without regrouping.__

LET'S MULTIPLY 621 x 23

1st) We start by multiplying the ** ones of the multiplier (table of 3) from right to left and for each of the multiplicand digits**:

3 x 1 = 3 ones

3 x 2 = 6 tens

3 x 6 = 18 hundreds

We will write the __ results__ below the horizontal dividing line and ** aligning them according to their place value from the ones**.

2nd) We start a new line and ** write a zero to the right ** to __ align the figures from the tens__, we will repeat the process of multiplying again from right to left.

3rd) We will multiply the ** tens of the multiplier (table of 2) by each of the digits of the multiplicand**:

2 x 1 = 2 ones

2 x 2 = 4 tens

2 x 6 = 12 hundreds

We will write the __ results__ below the horizontal dividing line and ** aligning them according to their place value from the tens**.

4th) We will write a ** horizontal dividing line**, we will draw the ** sign of the addition (+) ** and then ** we will add the products ** obtained with the previous multiplications from right to left.

Finally, we will write the ** result of the sum below the horizontal dividing line**.

You've got it! The solution: 621 x 23 = 14,283

#### Solve multiplication word problems without carrying with natural numbers: 3 digits x 2 digits

We offer you a series of ** multiplication word problems ** of three figures by two figures (without regrouping) for you to continue improving. We also provide you with video lessons where we ** explain in a simple way ** what is the ** procedure for its resolution**. Time to practice!

SPANISH

ENGLISH

#### Multiply natural numbers with carrying: 3 digits by 2 digits

__We show you a solved example that will help you learn step by step how to solve three-digits multiplication in the multiplicand by two-digits in the multiplier and regrouping.__

LET'S MULTIPLY 472 x 56

1st) We start by multiplying the ** ones of the multiplier (table of 6) from right to left and for each of the multiplicand digits**.

If the result of the multiplication of two digits is equal to or greater than 10 (for example, 8 x 4 = 32), __ we will move the digit on the left (in this example it would be 3) to the next column__ to ** add it ** to the result of the next multiplied number.

** 6 x 2 = 12 ones**, that is, __ 1 ten__ and 2 ones

** 6 x 7 = 42 tens ** + __ 1 ten__ = 43 tens, that is, __ 4 hundreds__ and 3 tens

** 6 x 4 = 24 hundreds** + __ 4 hundreds__ = 28 hundreds

2nd) We start a new line and ** write a zero to the right ** to __ align the figures from the tens__, we will repeat the process of multiplying again from right to left.

3rd) We will multiply the ** tens of the multiplier (table of 5) by each of the digits of the multiplicand**.

Remember, if the result of each multiplication is greater than or equal to 10, __ we will move the digit on the left to the next column__ to ** add it ** to the result of the next multiplication.

** 5 x 2 = 10 ones**, that is, __ 1 ten__ and 0 ones

** 5 x 7 = 35 tens ** + __ 1 ten__ = 36 tens, that is, __ 3 hundreds__ and 6 tens

** 5 x 4 = 20 hundreds ** + __ 3 hundreds__ = 23 hundreds

4th) We will write a ** horizontal dividing line**, we will draw the ** sign of the addition (+) ** and then ** we will add the products ** obtained with the previous multiplications from right to left.

Finally, we will write the ** result of the sum below the horizontal dividing line**.

You've got it! The solution: 472 x 56 = 26,432

#### Solve multiplication word problems with carrying with natural numbers: 3 digits x 2 digits

We propose you our ** multiplication word problems ** of three figures by one figure (regrouping) so that you continue to improve. In addition, we provide you with video lessons where we ** explain in a practical way ** what is the ** procedure for its correct resolution**.

SPANISH

ENGLISH

#### Multiply natural numbers without carrying: 4 digits by 2 digits

__Look at the practical example that we provide you with using a multiplication without carrying of 4-digits in the multiplicand and 2-digits in the multiplier.__

LET'S MULTIPLY 4,213 x 32

1st) We start by multiplying the ** ones of the multiplier (table of 2) from right to left and for each of the multiplicand digits**:

2 x 3 = 6 ones

2 x 1 = 2 tens

2 x 2 = 4 hundreds

2 x 4 = 8 thousands

We will write the __ results__ below the horizontal dividing line and ** aligning them according to their place value from the ones**.

2nd) We start a new line and ** write a zero to the right ** to __ align the figures from the tens__, we will repeat the process of multiplying again from right to left.

3rd) We will multiply the ** tens of the multiplier (table of 3) by each of the digits of the multiplicand**:

3 x 3 = 9 ones

3 x 1 = 3 tens

3 x 2 = 6 hundreds

3 x 4 = 12 thousands

We will write the __ results__ below the horizontal dividing line and ** aligning them according to their place value from the tens**.

4th) We will write a ** horizontal dividing line**, we will draw the ** sign of the addition (+) ** and then ** we will add the products ** obtained with the previous multiplications from right to left.

Finally, we will write the ** result of the sum below the horizontal dividing line**.

You've got it! The solution: 4,213 x 32 = 134,816

#### Solve multiplication word problems without carrying with natural numbers: 4 digits x 2 digits

We provide you with a variety of ** multiplication word problems ** of four figures by two figures (without regrouping) so that you can continue to improve your __ calculation skills__ and __ solving word problem situations__.

SPANISH

ENGLISH

#### Multiply natural numbers with carrying: 4 digits by 2 digits

__We show you a solved example that will help you learn step by step how to solve 4-digits multiplication in the multiplicand by 2-digits in the multiplier and regrouping.__

LET'S MULTIPLY 3,956 x 97

1st) We start by multiplying the ** ones of the multiplier (table of 7) from right to left and for each of the multiplicand digits**:

If the result of the multiplication of two digits is equal to or greater than 10 (for example, 8 x 4 = 32), __ we will move the digit on the left (in this example it would be 3) to the next column__ to ** add it ** to the result of the next multiplied number.

** 7 x 6 = 42 ones**, that is, __ 4 tens__ and 2 ones

** 7 x 5 = 35 tens ** + __ 4 tens__ = 39 tens, that is, __ 3 hundreds__ and 9 tens

** 7 x 9 = 63 hundreds ** + __ 3 hundreds__ = 66 hundreds, that is, __ 6 thousands__ and 6 hundreds

** 7 x 3 = 21 thousands** + __ 6 thousands__ = 27 thousands

** write a zero to the right ** to __ align the figures from the tens__, we will repeat the process of multiplying again from right to left.

3rd) We will multiply the ** tens of the multiplier (table of 9) by each of the digits of the multiplicand**.

Remember, if the result of each multiplication is greater than or equal to 10, __ we will move the digit on the left to the next column__ to ** add it ** to the result of the next multiplication.

** 9 x 6 = 54 ones**, that is, __ 5 tens__ and 4 ones

** 9 x 5 = 45 tens ** + __ 5 tens__ = 50 tens, that is, __ 5 hundreds__ and 0 tens

** 9 x 9 = 81 hundreds ** + __ 5 hundreds__ = 86 hundreds, that is, __ 8 thousands__ and 6 hundreds

** 9 x 3 = 27 thousands ** + __ 8 thousands__ = 35 thousands

** horizontal dividing line**, we will draw the ** sign of the addition (+) ** and then ** we will add the products ** obtained with the previous multiplications from right to left.

Finally, we will write the ** result of the sum below the horizontal dividing line**.

You've got it! The solution: 3,956 x 97 = 383,732

#### Solve multiplication word problems with carrying with natural numbers: 4 digits x 2 digits

We present you various ** multiplication word problems ** of four figures by two figures (regrouping) so that you can continue developing your __ calculation skills__, your __ logical-mathematical reasoning and the resolution of problems__.

SPANISH

ENGLISH

#### Multiply natural numbers by 10, 100, 1,000 and so on

__ Do you know how to multiply a number by the unit followed by zeros? __ We will explain it to you below!

First, watch the ** video explanation ** and learn with simple steps to ** multiply ** any ** natural number ** by the ** unit followed by zeros**: 10, 100, 1,000, 10,000, 100,000 and so on.

SPANISH

ENGLISH

__The procedure is very simple__: only ** as many zeros are added to the end ** as there are in the number we have multiplied by, as shown in the examples.

#### Mentally calculate simple operations: Multiplication

Here are some ** mental math activities ** to test your memory and show that you already know all the ** multiplication tables**.

#### Applying the Commutative Property of Multiplication

One of the __ most important fundamental properties __ of multiplication is "**commutativity**":

A x B = B x A

The ** Commutative Property of Multiplication ** states that "*the order in which the factors are multiplied does not alter the product*".

In other words, when we multiply two numbers (factors) with each other, the order in which they are multiplied will not matter because the result (product) will always be the same.

SPANISH

ENGLISH

#### Apply the Associative Property of Multiplication

Another of the __ fundamental properties__ of multiplication is "**associativity**", where the use of ** parentheses ** tells us in what order we must solve the multiplications :

A x ( B x C ) = ( A x B ) x C

The ** Associative Property of Multiplication ** determines that "*when three or more numbers are multiplied, the result is the same regardless of the order in which the factors are multiplied*".

In other words, when we multiply three or more numbers (factors) with each other, the order in which they are multiplied will not matter because the result (product) will always be the same.

SPANISH

ENGLISH

Do you want access to more Fourth Grade learning?

Select more ** exercises**, ** worksheets** and ** activities ** of ** Mathematics ** for each of the 4 learning blocks of the Educational Curriculum (*"Numbers and Operations", "Quantities and Measurements", "Geometric and Spatial Reasoning" and "Data Analysis and Probability"*) aimed at improving the logical-mathematical competencies and skills that are developed throughout ** "Grade 4" or "Year 5"**:

##### NUMBERS AND OPERATIONS

##### QUANTITIES AND MEASUREMENTS

##### GEOMETRIC AND SPATIAL REASONING

##### DATA ANALYSIS AND PROBABILITY

If a child cannot learn the way we teach, perhaps we should teach how he learns

Gabriela Mistral