From this page, you will learn about Estimating Product and Quotient. Estimation is nothing but taking the values that are approximate to the original number. This Estimating value helps your child to improve mental math. Estimation of products is nothing but rounding the given factors to the required place value.
You can get the approximate value of the product of numbers with an estimation of products. The quotient means the number of times a division is completed fully, and the remainder is the quantity that doesn’t go fully into the divisor. Here, you will learn about how to estimate the quotient of two numbers easily by referring to the solved example questions.
Do Refer:
Estimating Product and Quotient – Definitions
Estimating Product: It is a process of rounding the given factors to the required place values. In estimating product, first, we need to round off the multiplier and the multiplicand to the nearest tens, hundreds, or thousands and then multiply that rounded numbers.
Estimating Quotient: Estimating Quotient means it’s not doing the division on the actual numbers. First, you need to round off the dividend and divisor to the nearest 10 and continue the division process we will get the estimated quotient value.
How to Estimate Product and Quotient?
The below are the steps to estimating the quotient of two given numbers. The steps are:
Step 1: If the numbers have two or more digits, then round off the numbers to the nearest tens, hundreds, and or thousands.
Step 2: Next, divide those numbers to get the quotient.
Step 3: The obtained quotient is called the estimated quotient of the given numbers.
The following are the steps to find out given numbers of products using Estimation of Products. The steps are as follows:
Step 1: First, take the given number. Next, we have to estimate the multiplier and the multiplicand to the nearest tens, hundreds, or thousands.
Step 2: Finally multiply the rounded numbers and get the obtained number.
Advantages of Estimating Product and Quotient
There are many benefits of estimating product and quotient. A few of advantages are listed below,
- Estimating product and quotient helps to improve mental math.
- Your fluency in mathematical calculations will be improved.
- You can easily understand the concept of rounding off numbers in the number system by learning the concept of estimation.
Problems on Estimating Product and Quotient
Problem 1:
Estimate quotient when 1140 is divided by 40
Solution:
Given the value is 1140 and 30.
Now, we have to find the estimating quotient value.
First, round off 1140 to the nearest 100 that is 1200.
Now, divide 1200 by 30
So, the value is
1200 ÷ 30 = 40
Therefore, estimating the quotient of given numbers is 40.
Problem 2:
Estimate the products of 43 and 67.
Solution:
As, given in the question the values are 43, 67.
Now, estimate the given numbers to the nearest tens, hundreds, or thousands.
The number 43 is between 40 and 50. But the 43 is near to 40 compared to 50. Therefore, 43 is rounded down to 40.
Next, the number 67 is between 60 and 70. But the 67 is near to 70 compared to 60. Therefore, 67 is rounded up to 70.
So, Multiply 40 and 70.
40 × 70 = 2800.
Hence, the estimated product is 2800.
Problem 3:
Estimate the following product to the Nearest Ten and Hundred. The product value is 242 × 368
Solution:
As given in the question, the product value is 242 x 368
Now, we have to find the nearest tens value and hundreds value.
(i) The given numbers are 242 and 368.
Now, estimate the given numbers to the nearest hundreds.
So, the number is 242, in between 200 and 300. But the 242 is near to 200 compared to 300. Therefore, 242 is rounded down to 200.
Next, the number 368 is between 300 and 400. But the 368 is near to 400 compared to 300. Therefore, 368 is rounded up to 400.
Multiply 200 and 400.
200 × 400 = 80,000.
Therefore, the estimated product is 80,000.
(ii) The given numbers are 242 and 368.
Now, estimate the given numbers to the nearest tens, hundreds, and thousands.
The number is 242 between 240 and 250. But the 242 is near to 240 compared to 250. Therefore, 242 is rounded down to 240.
Next, the number is 368 between 360 and 370. But the number 368 is near 370 compared to 360. Therefore, 368 is rounded up to 370.
Multiply 240 and 370.
240 × 370 = 88,800.
Thus, the estimated product is 88,800.
Problem 4:
Find the estimated value of 5160 ÷392.
Solution:
As given in the question, the value is 5160 ÷392
Now, let us round 5160 and 392 separately and then divide to get the estimated value.
First, take the value 5160,
It is a four-digit number. So, we can round off this to a maximum of the nearest 1000′s.
Now try to round off evenly by 100′s. Let us round off 5160 to 100′s.
First the digit to the hundreds place. Next, determine the digit to its right. If the digit is 5 or greater than 5, then add 1 to it and place zeros in tens place and units place. If the digit is less than 5, then leave it as it is.
So, 6 is greater than 5 then the value is 5200.
Next, the given value is 392. 9 is greater than 5. So, we have to increase 1 by hundreds place digit and zeros in the units place and tens place digit. The value is 400.
Thus, estimating the numbers 5160 and 392 to the nearest hundreds is 5200, and 400.
Now divide 5200 by 400, the quotient value is 13.
Therefore the estimated quotient value is 13.
Problem 5:
Estimate the product 93 × 46. Write the value.
Solution:
Given numbers are 93 and 46.
Now, estimate the given numbers to the nearest tens, hundreds, and thousands.
The number 93 is between 90 and 100. But the 93 is near to 90 compared to 100. Therefore, 93 is rounded down to 90.
Next, the number 46 is between 40 and 50. But the number 46 is near to 50 compared to 40. Therefore, 46 is rounded up to 50.
Now, Multiply 90 and 50.
90 × 50 = 4500.
Therefore, the estimated product is 4500.
FAQs on Estimating Product and Quotient
1. How can you check if a quotient is reasonable or not using the Estimation?
The following are used for estimation to check if a quotient is reasonable or not:
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- First, Round off the divisor and dividend to the nearest 10 or 100 depending on the number of digits.
- Next, we have to divide the rounded dividend by divisor to get the estimated quotient.
- Finally, compare the estimated value and exact answers to check whether the answer is reasonable or not.
2. What is a quotient?
Quotient means the answer to a division problem. In the division parts, you have to divide the dividend to get the quotient.