Estimating Products

Estimating a product means rounding each factor to a number that multiplies easily, then multiplying those. Rounding both factors up makes the estimate too high; both down, too low. Below: how to round for estimation, how to judge the direction of the error, and worked examples.

Multiplication is meant to help you find the product or the answer to the multiplication problem. However, at times you wish to receive a result ‘close enough’ yet not exact. An example of the reason for estimating is to spot serious errors in your calculations.

It’s possible to use estimation to compare something, as well as check out your work, and assist with tougher problems. You can merely use estimation for those issues.

There are \(2\) skills required to estimate products: Using rounding as well as multiplying by zeroes. Here is a better way to show you how this is done.

Related Topics

• Estimating and Rounding
• Rounding Numbers
• How to Round Decimals?

How do you do estimating of products?

Using Rounding

Whenever something gets rounded, you adjust the numerals so it is simpler to use them whenever you’re doing a calculation. It’s possible to round a number to the closest ten, as well as the closest hundred, and so on.

STEP one: Whenever you round to the closest ten, check out the numeral on the right of the tens position.

STEP two: If the number is five or higher, raise the numeral in the tens spot by one, then change the numeral in the one’s spot to \(0\).

STEP three: If the number is lower than \(5\), leave it in the tens spot as it is, and then change the numeral in the one’s spot to \(0\).

STEP four: Now it’s possible to multiply the subsequent numerals by each other.

Multiplying using Zeroes

If you want to multiply numbers using zeroes, first you must multiply the numbers without a zero together. After that, write down the number of zeroes you get in the problem and move them to the end of the solution.

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Estimating Products, Example 1:

Estimate the product.

\(32 × 47=\)____

Solution:

First, round \(32\) to the closest ten. Check out the numeral on the right of the tens position. It is \(2\) and this number is lower than \(5\). So, \(32\) is rounded down to \(30\). Do the same for \(47\). Then \(47\) is rounded up to \(50\). Now multiply two result together: \( 30 × 50= 1,500\)

Estimating Products, Example 2:

Estimate the product.

\(74 × 65=\)____

Solution:

First, round \(74\) to the closest ten. Check out the numeral on the right of the tens position. It is \(4\) and this number is lower than \(5\). So, \(74\) is rounded down to \(70\). Do the same for \(65\). Then \(65\) is rounded up to \(70\). Now multiply two result together: \( 70 × 70= 4,900\)

Exercises for Estimating Products

Estimate the products.

1. \(\color{blue}{41 ×57}\)
2. \(\color{blue}{66 × 82 }\)
3. \(\color{blue}{93×28 }\)
4. \(\color{blue}{ 72 × 35 }\)

1. \(\color{blue}{2,400}\)
2. \(\color{blue}{5,600 }\)
3. \(\color{blue}{2,700 }\)
4. \(\color{blue}{ 2,800 }\)