Estimating Product and Quotient

The procedure of estimating product and quotient are in the following examples.


Estimating Product:

Working Rules for Estimating Product:

Step I: Round off each factor to its nearest greatest value.

Step II: Multiply the rounded off factors.


Solved Examples on Estimating Product:

1. Estimate the product 73 × 524

Solution:

Round off each factor to its nearest greatest value.

                       524         →         500

                        73          →     ×  100

Estimated value of 73 × 524 =  50000


2. Estimate the product 8 × 765

Solution:

Round off each factor to its nearest greatest value.

                       765         →         800

                         8          →     ×    10

Estimated value of 8 × 765   =   8000

Estimating Product


Estimating Quotient:

Working Rules for Estimating Product:

Step I: First round off the dividend to the nearest multiple of the divisor so that divisor becomes easy.

Step II: Then divide the dividend by the divisor to get the quotient.


Solved Examples on Estimating Product:

1. Estimate 546 ÷ 7.

Solution:

For 546 ÷ 7,

Let's round off the dividend 546 to the multiple of 7.

Let us say 525 or 560.

Its clear that dividend 546 is closer to 560, so the dividend 546 should be rounded off to 560.

Now, the estimated value of 546 ÷ 7

                                      = 560 ÷ 7

                                      = 80.


2. The estimated value of 1758 ÷ 88 is

(i) 25

(ii) 20

(iii) 30

(iv) 40


Solution:

1758 should be rounded off to 1800 and 88 be rounded off to 90.

Now, the estimated value of 1758 ÷ 88 = 1800 ÷ 90 = 20.

So, the option (ii) is correct, which is the required answer. i.e. answer (ii).

Estimating Quotient


Solved Examples to Estimate Product and Quotient:

1. Estimate the product 958 × 387 by rounding off each factor to its greatest place.

Solution:

Clearly, each factor is a three digit number. So, we round off each factor to nearest hundreds.

958 rounds off as 1000

387 rounds off as 400

Therefore estimated product = 1000 × 400 = 400000


2. Estimate the product to the nearest hundreds.

(i) 42 × 37

(ii) 67 × 62

(iii) 99 × 91

(iv) 147 × 51

(v) 193 × 47


Solution:

(i) 42 × 37 = 40 × 40 = 1600

(ii) 67 × 62 = 70 × 60 = 4200

(iii) 99 × 91 = 100 × 90 = 9000

(iv) 147 × 51 = 150 × 50 = 7500

(v) 193 × 47 = 190 × 50 = 9500


3. Find the estimated quotient 2838 ÷ 125 by rounding off the numerator and denominator to the nearest hundreds.

Solution:

We find that

2838 rounds off to nearest hundreds 2800

125 rounds off to nearest hundreds as 100

Therefore, estimated quotient = 2800 ÷ 100 = 28.


4. Estimate the quotient to the nearest tens.

(i) 87 ÷ 9

(ii) 163 ÷ 11

(iii) 461 ÷ 7

(iv) 1223 ÷ 17


Solution:

(i) 87 ÷ 9 = 90 ÷ 10 = 9 = 10

(ii) 163 ÷ 11 = 160 ÷ 10 = 16 = 20

(iii) 451 ÷ 7 = 460 ÷ 10 = 46 = 50

(iv) 1223 ÷ 17 = 1220 ÷ 20 = 61 = 60


Worksheet on Estimating Product and Quotient:

1. Estimate the following Products:

(i) 53 × 127

(ii) 128 × 780

(iii) 22 × 425

(iv) 8 × 472


Answer:

1. (i) 5,000

(ii) 80,000

(iii) 8,000

(iv) 4,000


2. Estimate the following Quotient:

(i) 295 ÷ 15

(ii) 1254 ÷ 10

(iii) 4295 ÷ 7

(iv) 1215 ÷ 11


Answer:

2. (i) 15

(ii) 130

(iii) 430

(iv) 120


3. What is the estimated product of 7 × 988?

Solution:

The number 7 rounded off to the nearest tens is 10.

The number 988 rounded off to the nearest thousands is 1000.

Therefore estimated product = 10 × 1000 = 10000.

Estimate

Estimate to Nearest Tens

Estimate to Nearest Hundreds

Estimate to Nearest Thousands

Estimating Sum and Difference

You might like these



Numbers Page

6th Grade Page

From Estimating Product and Quotient to HOME PAGE




Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.



New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.




Share this page: What’s this?

Recent Articles

  1. What is Area in Maths? | Units to find Area | Conversion Table of Area

    Jul 17, 25 01:06 AM

    Concept of Area
    The amount of surface that a plane figure covers is called its area. It’s unit is square centimeters or square meters etc. A rectangle, a square, a triangle and a circle are all examples of closed pla…

    Read More

  2. Worksheet on Perimeter | Perimeter of Squares and Rectangle | Answers

    Jul 17, 25 12:40 AM

    Most and Least Perimeter
    Practice the questions given in the worksheet on perimeter. The questions are based on finding the perimeter of the triangle, perimeter of the square, perimeter of rectangle and word problems. I. Find…

    Read More

  3. Formation of Square and Rectangle | Construction of Square & Rectangle

    Jul 16, 25 11:46 PM

    Construction of a Square
    In formation of square and rectangle we will learn how to construct square and rectangle. Construction of a Square: We follow the method given below. Step I: We draw a line segment AB of the required…

    Read More

  4. Perimeter of a Figure | Perimeter of a Simple Closed Figure | Examples

    Jul 16, 25 02:33 AM

    Perimeter of a Figure
    Perimeter of a figure is explained here. Perimeter is the total length of the boundary of a closed figure. The perimeter of a simple closed figure is the sum of the measures of line-segments which hav…

    Read More

  5. Formation of Numbers | Smallest and Greatest Number| Number Formation

    Jul 15, 25 11:46 AM

    In formation of numbers we will learn the numbers having different numbers of digits. We know that: (i) Greatest number of one digit = 9,

    Read More