Examine why they work ?
Choose a number. Double it. Add nine. Add your original number. Divide by three. Add four. Subtract your original number. Your result is seven.

In a three-digit number, when the tens and the hundreds digit are interchanged the new number is 54 more than three times the original number. If 198 is added three times the original number. If 198 is added to the number, the digits are reversed. The tests difit exceeds the hundreds digit by twice as that of the tens digit exceeds the unit digit. Find the originall number.

(b) Explain rational number in your own words.

State whether the following statements are true or false. Justify your answers. (iii) Every real number need not be a rational number

Write down any three-digit number (for example, 425). Examine why they work ? Make a six-digit number by repeating these digits in the same order (425425). Your new number is divisible by 7, 11, and 13.

Add the following: 8 and -12 using number line

Add the following: -3 and -5 using number line

The sum of three numbers is 20. If we multiply the third number by 2 and add the first number to the result we get 23. By adding second and third numbers to 3 times the first number we get 46. Find the numbers using Cramer's rule.

Express 2310 as a product of prime factors. Also see how your friends have factorized the number. Have they done it same as you? Verify your final product with your friend’s result. Try this for 3 or 4 more numbers. What do you conclude?