Are you studying in 8th grade? If yes, then you must learn the Fun With Numbers unit. One of the most important concepts in that unit is Playing With Numbers. The name itself says that the topic is totally about the numbers. There are 4 different types of numbers which are natural numbers, whole numbers, integers, and rational numbers.
Natural numbers sometimes called the counting numbers which do not include 0 and include from 1 to n. Whole numbers are similar to the natural numbers which include zero. In integers, we have positive integers and negative integers and zero. And rational numbers are nothing but fractions in the form of a/b and b does not equal to zero.
Read further sections of this page to know completely about how to play games with numbers. You will see the definition of play with numbers, General form of numbers, Games with numbers, tests of divisibility, solved examples in the below sections.
Play with Numbers Definition
The name itself says that this chapter contains more information about numbers. There are various games to play with numbers. The name of the game is reversing the digits of a number, general form of the number, letters for digits, and tests of divisibility. The detailed process of all these games is mentioned below.
Number in General Form
You can represent any number in a general form easily by checking out the simple procedure. The only thing is to identify the position of each digit in the given number. And multiply the position of digit i.e tens digit 10 * number and add remaining digits. For example, take a two-digit number AB. Its general form is 10 * A + B. The simple thing is to perform the addition, multiplication operations and the result will be the original number.
Games with Numbers
Reversing the Digits:
Reverse the digits of the number, add the original number, and reversed number. Divide the sum by 11, the remainder will be automatically zero. You can play this game with either a two-digit number or a three-digit number. But for three-digit numbers, the procedure will be different.
Letters for Digits:
In this method, we are going two have two or more numbers and expressions in between them. Perform those arithmetical operations and by trial and error method get which number suits in expression that satisfies the equation. It is one of the tricky and easy games to play with numbers.
Tests of divisibility:
The test of divisibility means a list of numbers divisible by a particular number and leaves the remainder zero or not.
Number Puzzles:
Playing with number puzzles and games will increase your skills and knowledge in math numbers. You have to fill the given numbers in the grid or magic triangle or any other by satisfying the conditions provided.
Solved Examples
Example 1:
Write the following list of numbers in the generalized form.
a. 125 b. 76 c. 59 d. 895
Solution:
Given numbers are 125, 76, 59, 895
General form of 125 is as follows:
125 can be expressed as 100 + 20 + 5
1 * 100 + 2 * 10 + 5 is 125.
76 = 70 + 6
= 7 * 10 + 6
59 = 50 + 9
= 5 * 10 + 9
895 = 800 + 90 + 5
= 8 * 100 + 9 * 10 + 5
Example 2:
Prove that the following numbers satisfy the reversing the digits method?
a. 12 b. 756
Solution:
Given two-digit number is 12.
Reverse of 12 is 21.
12 + 21 = 33
11) 3 3 (3
– 3 3
= 0
Three digit number is 756
Reverse of 756 is 657
756 – 657 = 99
99) 9 9 (1
– 9 9
= 0
Example 3:
In a two-digit number, the digit in the units place is 4 times the digit in the tens place and the sum of the digits is equal to 10. What is the number?
Solution:
Let us take two digit number as ‘ab’
b = 4 * a
a + b = 10
Substitute b = 4a in the above equation.
a + 4 * a = 10
5a = 10
a = 2
Substitute a = 2 in the equation to get b value.
2 + b = 10
b = 10 – 2 = 8
∴ The number is 28.
Example 4:
Check is 195 divisible by 4 or not?
Solution:
Given divisor is 195 and dividend is 4
The last digit of 195 is 5, which is not divisible by 4.
Hence, 195 is not divisible by 4.
Example 5:
In the given 3 × 3 grid, arrange the digits from 1 to 9 (without repetition) such that the sum of the numbers surrounding any cell is a multiple of the number in the cell.
Solution:
The only way is provided here.
4 | 8 | 9 |
---|---|---|
1 | 3 | 7 |
5 | 6 | 2 |
Check out the games and learn hose to be perfect in mathematics.