Addition of 5 consecutive Numbers

Addition of 5 consecutive numbers can be done by various methods but the simplest one is to multiply the highest number by 5 and subtract 10 from the result obtained.

Addition : – 13+14+15+16+17 =  ?

Solution : – Here the highest number is 17

Multiply it by 5: 17 *5 =85

 Subtract 10 : 85 – 10 = 75

Addition : – 66+67+68+69+70 = ? 

Solution : – Here the highest number is 70 

Multiply it by 5:  70× 5 = 350         Subtract 10 : 350 – 10 = 340 

Now the question you may ask : If there are more consecutive numbers then what strategy shall you see use to find the total ? 

  I am giving here some points and expect you to generalize a rule to add consecutive numbers on your own. 

• If there are 4 consecutive numbers ; multiply the highest by 4 and substract 6                    ( 1 1/2 × 4 ) 
• If there are 5 consecutive numbers; multiply the highest by 5 and substract 10 ( 2 × 5 ) 
• If there are 6 consecutive numbers; multiply the highest by 6 and substract 15                  ( 2 1/2 × 6 ) 
• If there are 7 consecutive numbers; multiply the highest by 7 and substract 21 ( 3 × 7 ) 
• If there are 8 consecutive numbers; multiply the highest by 8 and substract 28                 (3 1/2 × 8 )

You can add consecutive numbers more smartly if you understand the two cases.

Case 1:-  If there are odd numbers Addition

of consecutive terms. 

Rule : – Multiply the middle term by the number of terms. 

Addition: –     12+13+14+15+16+17+18+19+ 20 =? 

Solution : – Since there are 9 terms so the middle term =16        Multiply it by 9 = 16 × 9 = 144 

Case 2 : – If there are even numbers of consecutive terms.         

Rule : – Take the mean of the two middle terms and multiply it with the number of terms.

Addition : –     23+24+25+26+27+28+29+30   = ? 

Solution : – You can see that there are 8 consecutive numbers to be Addition.

The two middle numbers are obviously 26 and 27  Take the mean of the two = 26.5  Multiply it with the number of terms = 26.5 × 8 = 212                                 

I am hopeful that you would have generalized the rule to add the consecutive numbers. Leave this apart and learn some        interesting methods to add fast.

Mathematics can sometimes seem daunting with its complex formulas and intricate problem-solving techniques. However, there are several math tricks and shortcuts that can make calculations easier and more efficient. These tricks can help in various mathematical operations, such as addition, subtraction, multiplication, and division. By mastering these tricks, you can save time, improve mental math skills, and gain a deeper understanding of mathematical concepts.

One useful math trick is the technique of rounding. Rounding allows you to approximate numbers to a more manageable value while still maintaining reasonable accuracy. For example, when adding or subtracting large numbers, you can round them to the nearest tens or hundreds place to simplify the calculation. This technique is particularly helpful when performing mental math or estimating the outcome of a mathematical operation.

Another helpful trick is the concept of “casting out nines.” This technique involves summing the digits of a number until only a single digit remains. If the final digit is nine, then the original number is divisible by nine. For instance, consider the number 738. Adding the digits 7 + 3 + 8 equals 18, and adding the digits of 18 gives 9. Therefore, 738 is divisible by nine. Casting out nines can be a quick and simple way to test divisibility by nine and identify errors in calculations.

Multiplication can also be made easier using certain tricks. One such technique is the “multiplying by powers of 10.” To multiply any number by 10, 100, 1000, and so on, you can simply move the decimal point to the right by the same number of zeros. For instance, to multiply 25 by 100, you move the decimal point two places to the right, resulting in 2500. This trick is useful for quick mental calculations involving multiples of 10.

Furthermore, the distributive property of multiplication can be a valuable trick when multiplying two-digit numbers. For example, when multiplying 14 by 12, you can break it down into (10 + 4) multiplied by (10 + 2). By distributing the multiplication, you get (10 * 10) + (10 * 2) + (4 * 10) + (4 * 2), which simplifies to 100 + 20 + 40 + 8, resulting in 168. This method can simplify complex multiplication problems by breaking them down into smaller, more manageable parts.

In conclusion, math tricks can be valuable tools for simplifying calculations, improving mental math skills, and gaining a deeper understanding of mathematical concepts. From rounding and casting out nines to techniques for multiplication, these tricks can save time and make math more approachable. By incorporating these tricks into your mathematical toolkit, you can become a more confident and efficient problem solver.