A compatible number is similar to actual value in a calculation and applies to fetch the final result. This write-up explains the concept of utilizing the compatible numbers for easy arithmetic calculations.
Please remember :Compatible numbers help you to find an estimated answer if you are trying to find the percentage of an entity. You can convert the percent to a fraction and use rounding method to figure out estimation. |
Arithmetic is one of the oldest elementary streams of mathematics. It encompasses study of numbers, mostly the properties of operations such as subtraction, addition, division and multiplication. It is the elementary part of number theory that is considered to be one of the top divisions of modern mathematics, including analysis and Geometry.
Arithmetic operations
Addition, Subtraction, Division and Multiplication are the basic arithmetic operations. Although there are many advanced operations such as logarithmic functions and exponentiation. All the operations in Arithmetic are performed based on an order.
● Addition (+)
When you are required to find the sum of 100 + 200, you can answer ‘300’ quickly. However, finding the sum of 357 + 419 takes some seconds more, doesn’t it. Here is when you apply the concept of compatible numbers. In these type of calculations, you can use the rounding theory to round off both the numbers to the nearest compatible value.
Here, it is helpful to round off 357 to 355 or 350, and 219 as 420. By operating like this, you are actually decreasing a value by two and increasing the other by one. Hence, you will increase one in the final value.
In the simplest form, addition links two values that are called the addends into a single value, which is the sum of the values, such as 2 + 4 = 6 or 4 + 3 = 7. Adding more than two values is called as summation and encompasses methods to add finite numbers.
Addition is associative and commutative which exposes that the order of terms does not matter. 0 is the identity element of addition i.e, adding any number to 0 yields the same number.
● Subtraction (−)
Suppose there is a problem like 1017 - 421. The first step is rounding the numbers. Round 421 to 420 and 1017 to 1020 and subtract 420 from 1020. The value you get is 600 which is an estimated answer.
Subtraction is inverse of addition. Subtractions calculates the difference among the two values i.e, the minuend minus the subtrahend. When the minuend is greater than the subtrahend, the difference is positive, and if the minuend is smaller, the difference is negative, and 0 if both are equal.
Subtraction is neither associative nor commutative. Therefore, it is useful to consider subtraction and addition as addition of the minuend and opposite of the subtrahend, i.e, a - b = a + (-b).
● Multiplication (×)
Suppose you have to multiply 500 x 40. It’s simple, since you can quickly multiply 5 and 4, and add 3 zeros. But, what if it is 72 x 228. Here, you can round off 72 to 70 and 228 to 230 and multiply both. You get an estimated answer as 16100, where you get really close to the exact answer.
Multiplication also combines two values into a single number, being the second basic operation of arithmetic. The two original values are known as multiplier and multiplicand, or simply as factors.
Multiplication can be considered as a scaling operation. If the values are lying in a line, multiplication of a value(say x) larger than 1 is similar to expanding everything away from 0 in such a way that the value 1 is expanded to previous position of x.
Multiplication is also associative and commutative. The value of multiplicative identity is 1, which exposes that multiplying any value by 1 fetches the same value. The reciprocal of any value is the multiplicative inverse, which means that multiplying any value by the value itself fetches the multiplicative identity.
● Division (÷ or /)
It gets complicated to estimate quotients just like 2400/12. You can divide 24/12 and obtain 2, and add two zeros at the end of 2 as the final answer. But, what if it is something like 1546/117? Here you can round the numbers to 1500 and 100. Please note that both the divisor and the dividend are decreased. You get 15, which means that the answer is close to and less than 15, since we have decreased the values.
Division is the inverse of multiplication. It computes the quotient of two values, i.e, the dividend divided by the divisor. If any dividend is divided by 0, it is undefined and if the dividend is greater than the divisor, the quotient is larger than 1, else it is less than 1.When the quotient is multiplied by the divisor, it always fetches the dividend.
Division is neither associative, nor commutative. It is useful to consider division as multiplying the dividend by the number of times the reciprocal of the divisor, i.e, p÷q = p x 1/q.
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