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Our compatible numbers calculator is here to help you perform arithmetic calculations using compatible numbers. Our calculator will help you find compatible numbers for addition, subtraction, multiplication, and division.

If you are wondering what compatible numbers are and how to use compatible numbers to estimate arithmetic operations, you've come to the right place! In the article below, we shall discuss compatible numbers and their applications with examples.

What are compatible numbers?

We often encounter problems that require arithmetic calculations, like adding or subtracting the cost of items you want to buy. We may not always have a calculator at hand, so performing quick math in your head is valuable. The compatible number is a trick to help you make these mental calculations quickly if some error is acceptable.

A compatible number is a fair approximation of a true value, but is easier to use in quick mental arithmetic.

For example, say you have $150 and want to purchase three items that cost $79, $24, and $39, respectively. Adding 79+24+3979+24+39 in your head quickly can be tricky. However, you could approximate the addition as 80+25+40=14580+25+40 = 145, which is much faster and only slightly inaccurate. And just like that, you know that these items are within your budget!😉

In this example, the numbers (80, 25, 40) are the compatible numbers for (75, 24, 39). Each arithmetic operation can have different sets of compatible numbers. Let's look at each of them in the following sections.

Compatible numbers for addition

Adding two numbers is easier if they end with the digits 00 or 55. For example, adding 25+50=7525 + 50 = 75 is easier than adding 24+48=7224 + 48 = 72.

So when seeking compatible numbers for addition, rounding numbers to the nearest multiple of five or ten is the easiest option. For larger numbers, you could also round to the nearest hundred, thousand, or ten-thousand, etc. It depends on how much error is acceptable for your calculation.

🔎 For more on rounding numbers, visit our rounding calculator.

Let's see an example of compatible numbers for addition: 458+673458 + 673. Below, we've done it the old-fashioned way, carrying ones over as necessary.

11458+6731131\def\arraystretch{1.5} \begin{array}{c:c:c:c} &\textcircled{{1}}&\textcircled{{1}}\\ &4 & 5 & 8 \\ +&6 & 7 & 3 \\ \hline &11 & 3 & 1\\\hline \end{array}

This is quite a hassle to do in your head quickly. But, if we rounded to the nearest ten, we'd get the compatible numbers 460+670460 + 670, which are added as follows:

1460+6701130\def\arraystretch{1.5} \begin{array}{c:c:c:c} &\textcircled{{1}}&\kern{0.9em}\\ &4 & 6 & 0 \\ +&6 & 7 & 0 \\ \hline &11 & 3 & 0\\\hline \end{array}

This is much easier than the original calculation, and the error is small enough to be acceptable in most cases. Let's take a look at the compatible numbers we obtain by rounding our original numbers to the nearest hundred (i.e., 500+700500 + 700):

500+7001200\def\arraystretch{1.5} \begin{array}{c:c:c:c} &&\kern{0.9em}\\ &5 & 0 & 0 \\ +&7 & 0 & 0 \\ \hline &12 & 0 & 0\\\hline \end{array}

This calculation is even easier to do in our heads than rounding to the nearest ten, but there is a sizable error. Whether this is acceptable or not differs from case to case.

Similarly, "rounding" to the nearest multiple of five will give us numbers that are easy to add. 458+673458 + 673 becomes 460+675460 + 675:

1460+6751135\def\arraystretch{1.5} \begin{array}{c:c:c:c} &\textcircled{{1}}&\kern{0.9em}\\ &4 & 6 & 0\\ +&6 & 7 & 5 \\ \hline &11 & 3 & 5\\\hline \end{array}

See how easy it is to estimate using compatible numbers instead of performing the actual calculation?

Compatible numbers for subtraction

Similar to addition, subtracting numbers whose last digit is 00 is easier to do in our heads. Let's look at a compatible numbers example with the same numbers, 673458673 - 458:

676313458215\def\arraystretch{1.5} \begin{array}{c:c:c:c} &6\kern{0.4em} & \bcancel{7}^6 & \bcancel{3}^{13} \\ -&4 & 5 & 8 \\ \hline &2 & 1 & 5\\\hline \end{array}

We had to move a ten over to the 33 to obtain 1313 — So much effort for such a simple equation!

If we rounded to the nearest ten, we'd get the compatible numbers 670460670 - 460, which makes for a simpler subtraction:

670460210\def\arraystretch{1.5} \begin{array}{c:c:c:c} &6 & 7 & 0 \\ -&4 & 6 & 0 \\ \hline &2 & 1 & 0\\\hline \end{array}

Again, we can round to the nearest hundreds to get another set of compatible numbers 700500700 - 500, which makes it even simpler:

700500200\def\arraystretch{1.5} \begin{array}{c:c:c:c} &7 & 0 & 0 \\ -&5 & 0 & 0 \\ \hline &2 & 0 & 0\\\hline \end{array}

Notice that the error is more significant for this set.

There is another guideline we can use to obtain compatible numbers for subtraction - if the numbers have the same last digit, the last digits will cancel each other out to become zero, making the calculation easier. So, if we can approximate our terms to numbers with the same last digit, we can simplify our mental process.

As an example, for the same numbers 673458673 - 458, one set of compatible numbers would be 673453673 - 453:

673453220\def\arraystretch{1.5} \begin{array}{c:c:c:c} &6 & 7 & 3 \\ -&4 & 5 & 3 \\ \hline &2 & 2 & 0\\\hline \end{array}

Yet another set of compatible numbers would be 678458678 - 458:

678458220\def\arraystretch{1.5} \begin{array}{c:c:c:c} &6 & 7 & 8 \\ -&4 & 5 & 8 \\ \hline &2 & 2 & 0\\\hline \end{array}

Notice that the error remains the same for both sets!

Compatible numbers for multiplication

When choosing compatible numbers for multiplication, we need to remember that numbers ending with one or more zeros are easier to multiply.

Consider the numbers 47×1447 \times 14:

47×14188+470658\def\arraystretch{1.5} \begin{array}{cccc} &&4 & 7 \\ &\times & 1 & 4 \\ \hline &1& 8 & 8 \\ +&4&7&0\\\hline &6&5&8\\\hline \end{array}

Rounding the numbers to the nearest ten, we get the compatible numbers for multiplication 50×1050 \times 10 :

50×10500\def\arraystretch{1.5} \begin{array}{cccc} &&5 & 0 \\ &\times & 1 & 0 \\ \hline &5&0&0\\\hline \end{array}

The error is much bigger this time, which may or may not be acceptable for your purposes. Act accordingly!

Compatible numbers for division

Finding compatible numbers for division is similar to that of multiplication: choose numbers with one or more zeros in the last digits.

Dividing the numbers 47÷1447 \div 14 gives us 3.33.3, but getting there isn't easy:

3.314474250428\def\arraystretch{1.5} \begin{array}{c|ccc} &3.3\\ \hline 14&4 & 7 & \\ -&4&2\\ \hdashline &&5&0\\ -&&4&2\\ \hdashline &&&8 \end{array}

However, rounding the numbers to the nearest tens, we get 50÷1050 \div 10, which we can easily calculate: 50÷10=550 \div 10 = 5!

🙋 Another quick math trick is the divisibility test, which determines whether a dividend is divisible by the given divisor. You can learn more with our divisibility test calculator!

Using our compatible numbers calculator

Our compatible numbers calculator is simple to use:

  1. Select the arithmetic operation for which you seek compatible numbers. You can choose between:

    1. Addition
    2. Subtraction
    3. Multiplication
    4. Division
  2. Enter the numbers for which you seek compatible numbers. You must enter at least two numbers for our calculator to work.

    • For addition, subtraction, and multiplication, you can enter up to 10 numbers. Additional fields will appear as you enter values for existing fields.

    • In subtraction, enter the number you want to subtract from in the #1 position. The calculator will subtract in the following manner: #1 - #2 - #3 - #4 -....-#10.

    • If you seek compatible numbers for division, you can enter two numbers, with #1 being the dividend and #2 as the divisor.

  3. Our compatible numbers calculator will display different sets of numbers that you can use for your arithmetic operations.

🔎 Love having fun with numbers? The fun never stops here at Omni! Jump to our consecutive integers calculator, which will help you find nn consecutive numbers that sum up to a given number!

FAQ

What are compatible numbers for adding 66 and 58?

The compatible numbers for adding 66 and 58 are (70, 60) and (65, 60). To obtain this answer, follow these steps:

  1. Round the numbers to the nearest ten: 66 → 70; 58 → 60.
  2. Round the numbers to the closest multiple of five: 66 → 65; 58 → 60.
  3. Verify your results with our compatible numbers calculator.

What are compatible numbers for dividing 72 and 19?

The compatible numbers for dividing 72 and 19 are (70, 20). To arrive at this answer, follow this simple step:

  • Round the numbers to the nearest ten: 72 → 70; 19 → 20.

Our compatible numbers calculator will help you verify this result.

Are 72 and 32 compatible for subtraction?

Yes. Numbers that end with the same digit are compatible for subtraction since the last digits cancel each other out to leave behind a zero. Here, 72 and 32 have the same last digit (2), so they are compatible for subtraction.

What is the easiest method to find compatible numbers?

The easiest method to find compatible numbers for any arithmetic operation (addition, subtraction, multiplication, or division) is to round the numbers to their nearest ten. Numbers with zero in the last digit are easy to calculate quickly in our heads.

Krishna Nelaturu
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