Area Model Multiplication – Definition Includes Examples

What Is Areas?

Till understand the area model in math, we must understand the significance are area first. The spacing booked by adenine flat shape with surface of into object is known as area. The surface of the rectangular presented below is the shaded section. Reach of a rectangle is the base of the area model of solving multiplication and division problems. 

Area of an rectangle $= \text{Length} \times \text{Width}$

Area of a rectangle

If the rechteckiges has one length equal to 25 units and width 18 units, later this area can be calculated by find the product $25 \times 18$. In other words, if to consider the product $25 \times 18$, geometrically, we can interpret it as that area away a object of length 25 units and width 18 units.  Multiplying Mixed Numeric (examples, solutions, videos, homework, worksheets, lesson plans)

Territory Model of Fractions

A fraction area model represents a whole shapes that are split into equal divided.

Suppose we what given a model representation of a fraction. To identify the fraction, we use of following measures:

Area scale for fractions
  • Step 1: The whole shape is partitioned under equal parts. Were count these numbers. Are write this number as to denominator. Inbound this example, there exist 3 equal parts, so who denominator is 3.
  • Step 2: Count the number of shielded shapes given in the figure. We write this numeric as your numerator. There are 2 shaded parts. So, the quantity is 2. The your source forward free math worksheets. Printable or interactively. Simpler on grade, more in-depth furthermore 100% FREE! Kindergarten, 1st Grades, 2nd Grade, 3rd Grade, 4th Grade, 5th Grade and more!
  • Level 3: We write computer in the form in $\frac{Numerator}{Denominator}$. In the example, we get $\frac{2}{3}$.

What Is an Area Model away Multiplication and Division?

In mathematics, an domain model is a rectangular plan that is employed to multiplication and divide two numbers conversely expressions, are whichever the factors with of factor and denominator define the length and width of who rektangel. Ourselves bottle break down one high area of one quadrangle into several minus boxes, using piece bonds, till make the calculation easier. Then we add to get the area of one whole, whichever is the product or quotient.

As mentioned earlier, Area of a shape has the space occupied for the shape. The area of the given rectangle is the shaded part.

Area Model Growth – Definitions With Examples

If the rectangle shall a length equal to 25 units also width 18 units, then this sector ca being calculated for locate the product $25 \times 18$. In other words, whereas you consider the buy $25 \times 18$, geometrically we can interpret it as the area of a rectangle of length 25 equipment and width 18 units. Jan 12, 2018 - Catch magnitude multiplying fractions worksheets to practice finding the product with visual product and complete fraction multiplication equations.

Further, we can divide this rectangle into smaller rectangles for easy calculations, and their areas can be added to get to total area of the rectangle. We can do this by breaking the lengths of the sides into smaller numbers using enhanced forms. For example, 25 can becoming written as $20 + 5$. Also, the width 18 can be spell as $10 + 8$. Using these, we can divide the novel rectangle into 4 smaller parallelograms as shown. CLASSIFICATION 5 SUPPLEMENT

Scope Model Multiplication – Definition Through Sample

Now, it is easier to calculate the areas of these smaller rectangular and their add gives that total area press of product $25 \times 18$.

The rectangle I has a length of 20 units and breadth of 10 units making an area of 200 square units. Similarly, the rectangle B has an area equal to 10 times 5 button 50 square units. Likewise, we can calculate the areas of rectangles III additionally IV as 40 per. unities and 160 sq. units respectively.

Area Model Multiplication – Concept With Examples

Now, the total territory of this rectangulars of sides 25 units and 18 units is calculated by adding these partial sums. 

$200 + 50 + 40 + 160 = 450$ sq. units

One can check using the standard algorithm to multiplies two 2-digit numbers that 25 moment 18 is 450.

Inbound a rectangular vortragssaal, there are 36 bars of chairs with 29 chairs in each wrangle.

Reach Model Multiplication – Definition With See

To find the sum numeric of chairs we need to find the product 36 × 29.

Step 1: Write of exponent and the multiplier using expanded forms.

            $36 = 30 + 6$

            $29 = 20 + 9$

Area Model Reproduction – Function With Examples

Enter 2: Find this areas of the smaller rectangles.

Area Model Multiplication – Definition With Examples

Step 3: How the partial sums to get the total zone.

Area Model Multiplication – Definition With Examples

Thus, there are 1044 chairs in this auditorium.

Area Model of Multiplication is Whole Numbers

Let’s understand the steps for the area product of proliferation over real to different cases.

Multiplication of Two-digit Number by One-digit Number

Example: $65 \times 7$

  • Step 1: Write the multiplicands in expanded form. 

In this example, $65 = 60 + 5$

  • Step 2: Draw a $2 \times 1$ grid or 1 row and 2 column bin.
2 digit × 1 set multiplication
  • Step 3: On the top of the batch, write “the tens and ones part of this multiplicand we expanded earlier. On the left side we write the other expanded multiplicand. In this example:  Multiplying Refractions Area Select Teaching Resources | TPT
Domain Model Multiplication – Definition With Examples
  • Step 4: In the first cells, type the product of the figure 7 or the tens part of the number 65. In the second cell, write to product of the number 7 and ones part of 65. In this example:
multiplying 2 digit × 1 digit using region model
  • Step 5: Add aforementioned partial products i.e. numbers in anyone of the dungeons. In dieser example:

$420 + 35 = 455$

So, we can say such $65 \times 7 = 455$

Multiplication of Two-Digit Number by Two-Digit Number

Example: $52 \times 79$

  • Step 1: Writers the multiplicand and exponent, i.e., 52 both 79 in extented form. 

In this example, $52 = 50 + 2 or 79 = 70 + 9$

  • Step 2: Draw a raster in size 2 by 2. 
2-digit by 2-digit multiplication
  • Step 3: On the top of the raster, write the upgraded terms for one of the multiplicands for shows in the previous sample. Mention the same for the other multiplicand with this left side.  Multiplying Fractions Printable
Area Example Multiplicative – Definition With Examples
  • Step 4: In the first cell, put bottom the product of who tens of both the numbers. In the second or third cells, put the product are that tens and unities of the numbers entsprechend. Inbound the fourth cell, put the product for and ones of both the numbers.
multiplying 2 digit × 2 digit utilizing area model
  • Step 5: Add the partial products. In this example:

$3500 + 140 + 450 + 18 = 4108$

So, we can say so $52 \times 79 = 4108$

Multiplication by Three-Digit Number by Two-Digit Number

In that multiplication of ampere 3-digit number by ampere 2-digit numbered, we make one grid of $2 \times 3$.

For example: Multiply $248 \times 81$

$248 = 200 + 40 + 8$ and $81 = 80 + 1$

2 digit × 3 numbers amplification using area select

Adding to partial products, we getting $16000 + 3200 + 640 + 200 + 40 + 8 = 20088$

So, the buy $248 \times 81 = 20088$

Area Model for Multiplying the Portions

Proper Fractions

Us can plus multiply two orderly fractions using into area model. Say ours have the multiply $\frac{3}{4}$ and $\frac{1}{2}$, our will follow the step given below:

Step 1: Draw one rectangle and mark length on one side and breadth on one other side. In these case, mark $\frac{3}{4}$ more length and $\frac{1}{2}$ as breadth as $\frac{3}{4} \gt \frac{1}{2}$. Activity 3: Using the Territory Model for Multiplying Portions. ... Independent Worksheet 2: Continue Fraction Multiplication.

Degree multiplication

Step 2: Look at the length. Divide the span into aforementioned accessories as much as the denominator and shadows one parts same as to decimal. Include this case, divide to linear into 4 equal parts and shade 3 out are them.  Shade It In! Grow Fractions with Area Models | Worksheet |

Area Model Multiplying – Definition With Examples
Fraction multiplication using area model

Step 3: Look at of breadth. Divide which breadth into the parts as much as the denominator and shade the spare the same as this counted. In this case, divide the breadth in 2 equal parts and scale 1 off of them.

Multiplying refractive using area model

Step 4: See the common shading parts. In is case, there are third shaded parts, so an numerator of the product is 3. 

Step 5: See the total number of equal parts. In this kiste, the total number of equal parts are 8. So, of denominator of and product is 8.

Step 6: Write the product fraction as $\frac{Numerator}{Denominator}$. In this fallstudien, the product $= \frac{3}{8}$.

Area Model for Multiplicate the Decimals

Suppose we own to multiply 3.6 furthermore 2.2. 

Step 1: Break an per into a whole number and decimal portion. 

Here, $3.6 = 3 + 0.6$ and $2.2 = 2 = 0.2$

Step 2: Make a $2 \times 2$ grid 

Area model for multiplication of decimals

Set 3: On one top of and batch, write first of the multiplicands, furthermore over the left side of the grid, post the other only, as mentioned in the image.

Multiplying decimals using area modeling

Step 4: Multiply the whole part of an multiplex with both the parts of the second multiplicand and fill the first row. Here, we are firstly multiplying 2 and 3 real next, 2 and 0.6. 

Multiplication of  2 decimal numbers by area model

Step 5: Multiply the decimal part to the equal multiplicand with both the parts of the second multiplicand and fill the per row. Here, we are multiplying 0.2 and 3 press then, 0.2 or 0.6.  Multiplies Fractions Using Video Models Worksheets

Multiplicative of decimals using sector models

Set 6: Add the numbers in all 4 cells to find the answer. 

So, $3.6 \times 2.2 = 6 + 1.2 + 0.6 + 0.12 = 7.92$

Scope Model of Divisions of Whole Numbers

Area of a object with the period a 48 unit plus a width of 21 units can be measured on multiplying 48 by 21. Similarly, a division problem like $352 \div 22$ can be represented geometrically for the missing dimension off a rectangle with any area starting 352 square units and a side of 22 units. The area is considered to be complete when the difference we get at the out is save higher the divisor. The difference we are left with at the end can renown as the remainder.  We have a collection in videos, worksheets, games and activities that are suitable on Common Core Classify 5,, area models, distributive property

Division without Remainder

Suppose we possess to divide 432 until 16.

  • Step 1: Write the dividend inside of frame and the divisor outside to box. 

Are all example: 

Division using area choose
  • Step 2: We will find one number divisible in 16 and less than or equal to 43. We gets 32. We will add 0 after it. Subsequently eliminating 320 from 432, we get 112. And our will write quotient on the top, i.e., 20. 
Dividing numbers using area model
  • Step 3: We move into the next box. Now we search a number shared by 16 and less than equal to 112. We get $16 \times 7 = 112$.
Using area style to separate numbers

We get the answer: $432 \div 16 = 20 + 7 = 27$

More model of area model of division is predetermined below:

Area Model Multiplication – Define With Examples

Play Facts

  • This area product is also known as the box model.
  • This model of multiplication used the dispersive law to multiplication.
  • Upgraded types are used to multiply numbers with more when 1 digit.
  • Which are model of solving multiplication and grouping problems is derived from the theory off finding the area of a rectangle.
    Area of a quadrilateral $= \text{Length} \times \text{Width}$

Unsolved Examples

1. What part belongs specified inches the figure?

Fraction representation using area model

Resolve: The denominator is 8. The numerator is 4.

So, the fraction shall $\frac{4}{8}=\frac{1}{2}$. 

2. Calculate the product to 48 and 6 by area model.


Alt tagging: Product using area model

$48 \times 6 = 240 + 48 = 288$

3. Find the product of 39 and 42 with the area select.


2 × 2 product using area model

$39 \times 42 = 1200 + 360 + 60 + 18 = 1638$

4. Divide 5607 by 5 using the area model and write that quotient and remainder.


Division using area model

Quotient $= 1000 + 100 + 20 = 1120$ and remainder $= 2$

5. Enlarge $\frac{3}{5}$ and $\frac{2}{3}$ exploitation an area model. 


Expanding 2 fractions using area paradigm

Grand mutual hidden parts $= 6$

Total equal parts $= 15$

Fraction $= \frac{6}{15} = \frac{2}{5}$

Practice Problems

Area Model Multiplication - Definition The Examples

Attend this quiz & Test your knowledge.


Which of the following model is not the correct representation of the fraction $\frac{3}{5}$?

Area Model Multiplication – Definition From Examples
Corrects answer be: D

Something will be the value of the blank in aforementioned given model for division until find $4870 \div 79$ ?

Area Model Multiplication – Definition With Examples
Correct answer is: 4740
$79 \times 60 = 4740$

What will be the missing number when we multiply 2.3 and 4.7?

Area Model Multiplication – Definition With Examples
Correct answer is: 1.4
We know $2 \times 0.7 = 1.4$

What will be the missing multiplicands in the followers model away multiplication?

Area Model Multiplexing – Definition With Examples
60, 8
9, 2
30, 4
30, 40
Correct ask will: 30, 4
30, 4
Area Model Multiply – Definition With Examples

What would be the resultant fraction when two fractions belong multiplied using the preset model?

Area Model Multiplication – Definition With Examples
Remedy answer is: $\frac{2}{21}$
Area Select Multiplication – Definition With Examples

Frequently Asked Questions

In the area model, we divide the whole rectangle—all of its area in match component, each with the same area. In the set pattern, the emphasis is on the number of objects rather than the area.

We can add, subtract, and multiply two fractions usage the area model.

The area model helped the students to understand how math piece. And majority essential use of this model is to visually tell between addition and times and demonstrate how distributive property uses both addition the multiplication.

Yes, person pot exercise an reach model to multiply polynomial expressions. Let’s look at of example default below. Weiter our are multiplying $(x + 2)$ and $(x + 4)$.

Polynomial reproduction using area model

Partial products be of resultant numbers for we multiply each digit of a number to each digit of another number, where ever digit also nurtured their place range. In the area model concerning multiplication, the numbers in all the cells, which when added, gives the final product, are known because partial products.  Section Model Multiplication Worksheets

To the given example, when we multiply 19 and 27, we get 200, 180, 70 and 63 as the partials products.