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Grade 7:  The Learning Equation Math

12.02 Division of Decimals

Number Operations

Refresher pp 24-5

Learning Objectives:

The student will:

Area of a Rectangle

In the previous lesson the area of a rectangle was shown as the product of  the length and width of the rectangle.



Decimal Block Values

Any product can be shown as the area of a rectangle.  The length and width are the factors and the product is the area.

What if we know the area and width of the rectangle.  How can we calculate the length?

We will use the same blocks to illustrate decimal quotients.    You will need to understand the value of each type of block:




decmult4.gif (979 bytes) decmult5.gif (936 bytes) decmult6.gif (829 bytes)


To illustrate the quotient of:

7.68 2.4

we will need to know show the area and the width:

blank.gif (43 bytes)

?? units


decmult.gif (2778 bytes)

When the rectangle is created showing the area and width, the length of the rectangle is shown to be 3.2 units:

decmult2.gif (1621 bytes)


The following internet site(s) will give you the opportunity to build more rectangles to demonstrate decimal divsion..

Base 10 Blocks: Exploring Whole Decimal Numbers with Blocks


Base 10 Blocks: Exploring Whole Decimal Numbers with Blocks


Dividing Decimals - Long Division


Example Explanation



111.384 4.76

division.gif (24619 bytes)

complete solution



Division Bar


Dividend divisor = quotient

Place the dividend and divisor in the division bar:




Move the decimal of the divisor to the far right using a   ^.

Use the ^ to move the dividend divisor the same number of spaces to the right as you did the decimal in the divisor.

The ^ points to the location of the decimal when you divide as you did with whole number long division.


If you wish to see more step by step long division samples, complete the free registration, then link to:

Division of Decimals

use estimation strategies to justify and assess the reasonableness of calculations.

Rounding Review

You need good rounding skills to estimate calculations.  The following sites will give you practice rounding to a variety of place values:

A+ Math : Flashcards : Rounding Flashcards

BasketMath: Rounding Numbers - Q5



Estimate Calculation Strategies

Rounding numbers allows one to estimate calculations mentally.  One method is to round both numbers to the same place value, then complete the calculation using the rounded numbers.   When you are learning estimation skills, it is great to check your estimation on a calculator:

Scientific Calculator

The next example explains the method of round numbers to one non-zero digit.

Estimating the Quotient of Decimals

THE QUICKEST WAY to estimate the quotient of two decimals is to round both the divisor and dividend to one non-zero digit, and then divide the rounded decimals.

EXAMPLE: Estimate the quotient of 5.239 divided by 0.51 .

The first thing to do is round the two decimals so that each has one significant digit (non-zero digit). Rounding the divisor to one non-zero digit leaves 0.5 , and rounding the dividend to one non-zero digit leaves 5.   Now the division problem looks like this:

5 0.5

The decimal point in the divisor needs to be moved one place to the right, so that it is all the way to the right. Similarly the decimal point in the dividend is moved one place to the right; we need to add a 0 to the right of the 5 so this can be done. We can also get rid of the extraneous 0 to the left of the 5 in the divisor. The estimate concludes with:

50 5 = 10

modified source:  BMCC Math Tutorials -- Decimals -- Division of Decimals

add, subtract, multiply, and divide decimals (for more than two-digit divisors or multipliers, the use of technology is expected).

You can add, subtract, multiply, and divide decimals on a scientific calculator.  When you make your own examples, try estimating the answer before entering your values into the calculator.

Press Reload/Refresh if the calculator does not show properly.

Power Calculator Imput

wpeBD.jpg (813 bytes) = baseexponent

57.4 + 3.556 57.4 1203.h14.jpg (796 bytes) 3.556 equal.jpg (782 bytes) sumcalc.gif (1132 bytes)
57.4 - 3.556 57.4 1203.h11.jpg (777 bytes) 3.556 equal.jpg (782 bytes) difcalc.gif (1134 bytes)
57.4 x 3.556 57.4 1203.h12.jpg (794 bytes) 3.556 equal.jpg (782 bytes) prodcalc.gif (1157 bytes)
57.4 3.556 57.4 1206.h18.jpg (848 bytes) 3.556 equal.jpg (782 bytes) quotcalc.gif (1229 bytes)

Adding Decimals included in:   Multiplication of Decimals:  Grade 7 Lesson 12.01

Subtracting Decimals included in:   Multiplication of Decimals:  Grade 7 Lesson 12.01

Multiplication of Decimals:  Grade 7 Lesson 12.01

Division of Decimals:  Grade 7 Lesson 12.02



A+ Math Flash Cards - Choose dividing only




Decimal, whole number, quotient, divisor, dividend, multiplies, partitioning method, measurement method.


Prerequisite Skills:

Rounding Decimals/Whole Numbers


Rounding Decimals(Tenths)


Rounding Decimals(Hundredths)


Scientific Calculator

Estimating the Sum

Multiplying Decimals:  Grade 7 Lesson 12.01



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