Introduction to Estimation of Products
Imagine yourself in the market with your mom, you can’t take forever buying 5 kilograms of tomato costing Rs.32 each kilogram simply because you are struggling to calculate how much that would totally cost. Such a situation is a bit embarrassing.
And that’s why you need to learn the basics of how to estimate products to be able to do mental maths super fast (and easy) so you don’t lose your amazing tomato deals.
What you need to know, how it is done, is dealt with in detail in this article. Let’s dive right in!
What is Product Estimation?
The process of making complex multiplications easier by rounding off the multiplicand and multiplier to the nearest tens or hundreds to obtain an approximate or estimated product can be termed product estimation.
We know what a product is in maths. Now it is really important to be strong in your basic multiplication skills to be able to estimate the products at a much faster rate
Estimation
What are the Things I Should Know to Estimate Products?
There are 2 things one should master before one can master the art of estimating products. Let us now see how to estimate the product using the general rule
First thing, you should know basic multiplication tables from 1 to at least 9, to begin with. Though it is necessary to know till multiplication tables of 20, even till 15 will do.
Second thing, you should learn how to quickly round off numbers to the nearest tens or hundreds in such a way that only a few easy digits are left to multiply to obtain the estimated product.
Things to know to Get Started
How to Estimate Products?
There are a few steps that usually come under the general rules of estimating products. These might seem tedious to begin with but with a bit of practice and patience, it becomes much easier to estimate products
Step 1: Take the given multiplicand and multiplier and round them off to the nearest tens, hundreds, or thousands to make them into an easier number to multiply. For example, to multiply 29 and 76, we round these numbers off to their nearest place values. In this case, we round off 29 to 30 and 76 to 80.
Step 2: Arrange the estimated multiplicand and multiplier and multiply as usual to obtain the estimated product. Getting back to our example, 30 x 80 is the expression now. 3 x 8 is 24 which is pretty simple. Dealing with zeroes also becomes relatively easier with a bit of practice.
Step 3: Add the required zeroes and make sure they are right (getting the zeroes is the last thing we want to do during estimation)
The obtained estimated product is very close and approximate to the actual product which can be calculated later if required.
Solved Examples
Q1. Estimate the product of 37 and 72.
Ans: We round up 37 to the nearest tens which are 40 and 72 is rounded down to the nearest 10 which is 70.
Multiplying 40 x 70 we get 2800. Our estimated product is 2800.
Q2. Find the estimated product of 56 and 42.
Ans: Rounding off numbers 56 to 60 and 42 to 40 (nearest tens)
The product of 60 and 40 is 2400. The estimated product is found to be 2400
Q3. Estimate the product of 27 and 62.
Ans: We round up 27 to the nearest tens which are 30 and 62 is rounded down to the nearest 10 which is 60.
Multiplying 30 x 60 we get 1800. Our estimated product is 1800.
Q4. Find the estimated product of 49 and 38.
Ans: Rounding off numbers 49 to 50 and 38 to 40 (nearest tens)
The product of 50 and 40 is 2000. The estimated product is found to be 2000
Practice Problems
Q1. Find the estimated product of 44 and 54
Ans: 2000
Q2. Find the estimated product of 92 and 17
Ans: 1800
Q3. Find the estimated product of 35 and 58
Ans: 2400
Q4. Find the estimated product of 25 and 25
Ans: 900
Q5. Find the estimated product of 88 and 26
Ans: 2700
Summary
Quickly brushing through what we’ve learned up until now, knowing how to estimate products is important to gain speed and accuracy in multiplication. To be able to estimate products, one has to be good at rounding-off numbers and multiplication tables till 9.
The general rule of estimating products is as follows, rounding multiplicands and multipliers to the nearest tens, hundreds, and thousands and multiplying the rounded-off numbers. Adding and removing zeroes as per the expression gives us the estimated product which is closely approximate to the actual product.
FAQs on Estimate the Product
1. Why is it so important to learn estimating products?
We are in such a technological era filled with gadgets and smartphones. We are always having one form or the other of a calculator so why is learning about estimating products so important? Well, the answer to that is pretty simple. It is important to be prompt in mental maths in certain places where you can’t always pull out your smartphone. Market place calculations, on a shopping spree, these simple tricks help you go a long way with your fast and quick maths tricks!
2. How to estimate the product of 57 and 62.
We round up 57 to the nearest tens which are 60 and 62 is rounded down to the nearest 10 which is 60. Multiplying 60 x 60 we get 3600. Our estimated product is 3600.
3. How to know which number should be rounded off to a higher value or a lower value?
It’s not as complicated as it seems. Any number having a value higher than 5 in its one place is rounded up to the higher ten value. For example, the number 48 is rounded off to 50 which is the higher value as 8 in one place is higher than 5.
Similarly, any number having a value lower than 5 in its one place is rounded down to the lower ten value. For example, the number 43 is rounded off to 40 which is the lower value as 3 in one place is lower than 5. This general rule of estimation product can be used for hundreds, and thousands of places as well.
