Justify the number trick using algebra.
Take any four consecutive integers and add the highest and lowest number. Show that the sum is always equal to the sum of the two middle numbers.
Important Questions on Algebraic Expressions and Equations Puzzles and Tricks
Justify the number trick using algebra. Take any five consecutive integers and add the highest and lowest number. Show that the sum is always double the middle numbers and the same as the sum of the other two middle values.
Find two numbers that differ by , where the sum of the smaller one and four the larger one is .
Use the algebra to justify why the number tricks always work.
If you take two-digit number and subtract the number crated when you reverse its digits, you always get nine times the difference in the digits.
Use the algebra to justify why the number tricks always work.
Show that the mean of a set containing an odd number of consecutive integers is always the middle integer in the set.
Find the three consecutive numbers such that three times the lowest one plus five times the middle one is equal to less than ten time the largest one.
You are creating a number trick of your own. You will ask a volunteer to select a number and then you will:
• ask them to multiply the number by two.
• choose an even number and ask your volunteer to add this number to the one in your head.
• say divide the result by 2 and subtract your original number.
What is the result? Justify your answer using algebra.
