Problem Solving and Proofs Archives - Page 5 of 9

Understanding If Then Statements and Counterexamples

December 8, 2012 GB High School Mathematics, Problem Solving and Proofs

If then statements are common in everyday conversations. If mom is going home this holiday season, then we are going to have a grand celebration. If you pass the exam, then I’m going to buy you a tablet. But how is if then statements related to mathematics?

If then statements can be seen in almost every field of mathematics. They are mostly found in mathematical proofs. You will have to familiarize yourself with its structure if you are going to be a mathematics major in the future.

In the statement “if a polygon is a square, then it is a rectangle,” we call the “a polygon is a square” the antecedent or the hypothesis, while “it is a rectangle” is called the consequent or conclusion. » Read more

Why The Addition Number Trick Works

November 21, 2012 GB High School Mathematics, Problem Solving and Proofs

In the Addition Number Trick, my latest post in the Mathematical Palette (sorry, this site is already gone), I shared about a number trick I learned when I was still in the elementary school. The trick involves (1) letting a friend write a number and then (2) predicting the sum of the five numbers, including the four numbers (3 – 6) that you are about to write in alternate. The order of writing is indicated by the circled numbers in the figure below.

To get the sum of the five numbers, subtract 2 from the first number and then affix it to the leftmost part (543 becomes 2541). Next, your friend and you will write the numbers in alternate, and you should make sure that each digit on the same place value add up to 9 (see detailed instructions). After adding the numbers, the sum should be correct. » Read more

5 comments addition number trick, math mind reading trick, sum prediction trick

Math Word Problems: Solving Number Problems Part 3

September 22, 2012 GB High School Algebra, High School Mathematics, Problem Solving and Proofs

This is the third part of the Solving Number Problems Series. The first part can be read here and the second part can be read here. In this post I will continue worked examples using problems which are slightly more complicated than the problems in the previous two parts. Without further ado, lets start with the seventh problem in the series.

PROBLEM 7

Twice a number added to $18$ is $5$ times that number. What is the number?

Solution

In the two previous posts, we have learned that if $n$ is a number, then twice that number is $2n$ . So, twice a number added to $5$ is represented by $2n + 5$ . Now, that number, the $2n + 5$ is five times that number of $5n$ . So, we can now set up the equation