Divisibility - 7

Category: Arithmetic

"Published in Newark, California, USA"

Divisibility by 7:

How do you know that a number is divisible by 7? Well, this method of checking and verifying a number is different or unique. You need to do this one. Double the last digit of a given number and then subtract it from the remaining digits. If the result is a multiple of 7 or 0, then the given number is divisible by 7. You can repeat the process if you wish until the result is a multiple of 7 or 0.

Example 1:

The first thing that we need to do is to inspect the given number if it is divisible by 7 or not. 

Double the last digit and then subtract it from the remaining digits as follows

 
Since -2 is not a multiple of 7, then the given number is not divisible by 7. There's a remainder of 3 in the division. The answer or a quotient must be a whole number itself. You should not have a fraction or a remainder in the final answer.  

Example 2:

The first thing that we need to do is to inspect the given number if it is divisible by 7 or not. 

Double the last digit and then subtract it from the remaining digits as follows

Since 7 is a multiple of 7, then the given number is divisible by 7. There's no remainder or a fraction in the division.

Example 3:

The first thing that we need to do is to inspect the given number if it is divisible by 7 or not. 

Double the last digit and then subtract it from the remaining digits as follows

Since the result of this process is 0, then the given number is divisible by 7. There's no remainder or a fraction in the division.

You should consider in studying the divisibility of a number because you will use these principles later when you will study higher Math subjects that involves the division of a number, simplifying fractions, and even factoring. 

This method can also be used for negative integers as long as the result of a process is a multiple of 7. Again, there should be no remainder or a fraction in the division.  
   

Divisibility - 6

Category: Arithmetic

"Published in Newark, California, USA"

Divisibility by 6:

How do you know that a number is divisible by 6? Well, a number is divisible by 6 if it is both divisible by 2 and 3. In short, an even number that is divisible by 3.

Example 1:

The first thing that we need to do is to inspect the given number if it is divisible by 6 or not. 

Since the given number is not an even number and besides, the sum of the digits is not a multiple of 3 as shown below

then the given number is not divisible by 6. There's a remainder of 1 in the division. The answer or a quotient must be a whole number itself. You should not have a fraction or a remainder in the final answer. 

Example 2:

The first thing that we need to do is to inspect the given number if it is divisible by 6 or not. 

Since the given number is not an even number but the sum of the digits is a multiple of 3 as shown below

  

 
then the given number is not divisible by 6. There's a remainder of 3 in the division. The answer or a quotient must be a whole number itself. You should not have a fraction or a remainder in the final answer. 

Example 3:

The first thing that we need to do is to inspect the given number if it is divisible by 6 or not. 

Although the given number is an even number but the sum of the digits is not a multiple of 3 as shown below

then the given number is not divisible by 6. There's a remainder of 4 in the division. The answer or a quotient must be a whole number itself. You should not have a fraction or a remainder in the final answer. 

Example 4:

The first thing that we need to do is to inspect the given number if it is divisible by 6 or not. 

Since the given number is an even number and the sum of the digits is a multiple of 3 as shown below

then the given number is divisible by 6. There's no remainder or a fraction in the division.

You should consider in studying the divisibility of a number because you will use these principles later when you will study higher Math subjects that involves the division of a number, simplifying fractions, and even factoring. 

This method can also be used for negative integers as long as the given number is both divisible by 2 and 3. Again, there should be no remainder or a fraction in the division.  
  

Divisibility - 5

Category: Arithmetic

"Published in Newark, California, USA"

Divisibility by 5:

How do you know that a number is divisible by 5? Well, a number is divisible by 5 if the last digit of a number ends with 5 or 0. 

Example 1:

The first thing that we need to do is to inspect the given number if it is divisible by 5 or not. 

Since the last digit of a given number is not 5 or 0, then the given number is not divisible by 5. We know that a number ends with 5 or 0 is divisible by 5. There's a remainder of 2 in the division. The answer or a quotient must be a whole number itself. You should not have a fraction or a remainder in the final answer. 

Example 2:

The first thing that we need to do is to inspect the given number if it is divisible by 5 or not. 

Since the last digit of a given number is 5, then the given number is divisible by 5. There's no remainder or a fraction in the division.

Example 3:

The first thing that we need to do is to inspect the given number if it is divisible by 5 or not. 

Since the last digit of a given number is 0, then the given number is divisible by 5. There's no remainder or a fraction in the division.

You should consider in studying the divisibility of a number because you will use these principles later when you will study higher Math subjects that involves the division of a number, simplifying fractions, and even factoring. 

This method can also be used for negative integers as long as the last digit is either 5 or 0. Again, there should be no remainder or a fraction in the division.   
 

Rate, Distance, Time - Problem, 6

Category: Algebra, Mechanics, Physics

"Published in Newark, California, USA"

The local train is 25 miles down the track from Central Station when the express leaves the station. The local train travels at a rate of 50 mi/hr and the express travels travels at a rate of 80 mi/hr. Let n represent the number of hours since the express train left Central Station.

(a) Write an expression that represents the express train's distance from Central Station in n hours.

(b) When will the express train catch up with the local train?

Solution:

To illustrate the problem, it is better to draw the figure as follows

Photo by Math Principles in Everyday Life

Initially, the local train is already left from Central Station which is 25 miles apart. The time traveled by the local train is

 

 

   
If the express train leaves from Central Station which is faster than the local train, then the express train will catch up the local train at time n.

Photo by Math Principles in Everyday Life

(a) The distance traveled by the express train is
 

 

 

 

 
(b) Finally, the express train will catch up the local train at
 

 

 

 

 

 

 

 

or

Divisibility - 4

Category: Arithmetic

"Published in Newark, California, USA"

Divisibility by 4:

How do you know that a number is divisible by 4? Well, a number is divisible by 4 if the last two digits of a number are multiples of 4 or divisible by 4. Also, if the last two digits of a number are 0. You need to remember or memorize the multiplication table for this one.  

Example 1:

The first thing that we need to do is to inspect the given number if it is divisible by 4 or not. Let's examine the last two digits of a given number which is 82. 

Since 82 is not a multiple of 4, then the given number is not divisible by 4. We know that 80 is divisible by 4. There's a remainder of 2 in the division. The answer or a quotient must be a whole number itself. You should not have a fraction or a remainder in the final answer. 

Example 2:

 
The first thing that we need to do is to inspect the given number if it is divisible by 4 or not. Let's examine the last two digits of a given number which is 48. 

Since 48 is a multiple of 4, then the given number is divisible by 4. There's no remainder or a fraction in the division.

Example 3:

The first thing that we need to do is to inspect the given number if it is divisible by 4 or not. Since the last two digits of a given number are 0, then the given number is divisible by 4. There's no remainder or a fraction in the division.

You should consider in studying the divisibility of a number because you will use these principles later when you will study higher Math subjects that involves the division of a number, simplifying fractions, and even factoring. 

This method can also be used for negative integers as long as the last two digits are multiples of 4 or 0. Again, there should be no remainder or a fraction in the division.