How to Multiply Numbers Ending with 5 – Easy Shortcut for Students

Multiplication is a fundamental skill in mathematics, but some number combinations can appear tricky. Imagine being able to quickly multiply numbers like 35 x 35 or 65 x 65 in your head, almost instantly! This might sound like a magic trick, but it's actually a clever shortcut that makes multiplying numbers ending in 5 incredibly easy and fun, especially for students looking to sharpen their mental math abilities.

This guide will unveil a straightforward and reliable method for multiplying numbers that end with the digit 5. We'll explore how this shortcut works for both two-digit numbers multiplied by themselves, and even for multiplying two different numbers ending in 5. Get ready to impress your friends and teachers with your newfound math speed and boost your confidence in tackling multiplication problems!

How to Multiply Numbers Ending in 5 – Easy Shortcut for Students

Multiplying numbers that end in 5, especially when they are squared (multiplied by themselves), has a fantastic and easy shortcut that can turn a seemingly complex problem into a quick mental calculation.

Trick 1: Squaring Numbers Ending in 5 (e.g., 35 x 35, 75 x 75)

This trick is perfect for finding the square of any number ending in 5.

Steps:

1. Ignore the 5: Take the digit(s) before the 5.

2. Multiply by "Next Number": Multiply this digit (or number) by the next consecutive whole number.

3. Attach 25: Write "25" at the end of the result from Step 2.

Examples:

Trick 2: Multiplying Two Different Numbers Ending in 5 (When the "Tens" Digits Differ by an Even Number)

This trick works when both numbers end in 5, and their "tens" digits (or the numbers before 5) have an even difference (e.g., 25 and 45; difference between 2 and 4 is 2, which is even).

Steps:

1. Ignore the 5s: Take the numbers before the 5s from both numbers.

2. Multiply the "Before 5" Numbers: Multiply these two numbers together.

3. Find the Average of the "Before 5" Numbers: Add the two "before 5" numbers and divide by 2.

4. Square the Average: Multiply the average by itself.

5. Calculate Difference in Squared Averages: Find the difference between your squared average (from Step 4) and 25.

6. Combine: The final answer will be (Result from Step 2 * 100) + (Result from Step 5 or 25 if direct method applies).

Self-correction: The trick for different numbers ending in 5 can be more complex than "tens digits differing by an even number" is the only case. A simpler, more universal trick for Ax5 * Bx5 is (A * B * 100) + ((A+B)/2 * 50) + 25 if it holds. The most straightforward universal trick involves finding the sum of the tens digits. Let's simplify and use the common "add 50/subtract 50" approach if the tens digits are odd/even.

Let's use a simpler, more common and understandable trick for multiplying any two numbers ending in 5, which usually involves a bit more mental manipulation than just squaring. A very common shortcut for (10A+5) x (10B+5) relies on (A*B*100) + (A+B)*50 + 25.

Revised Trick 2 (More General): Multiplying Any Two Numbers Ending in 5

This trick works for any two numbers ending in 5.

Steps:

1. Ignore the 5s: Take the digits before the 5 from both numbers. Let them be 'A' and 'B'.

2. Multiply A and B: Calculate A x B.

3. Add A and B, then Halve: Calculate (A + B) / 2.

4. Combine and Adjust:

• If (A+B)/2 is a whole number (i.e., A+B is even), then the first part of your answer is (A x B) + (A+B)/2. The last two digits are "25".

• If (A+B)/2 is NOT a whole number (i.e., A+B is odd), then the first part of your answer is (A x B) + (A+B-1)/2. The last two digits are "75".

Examples:

Self-correction for Trick 2: The (A+B-1)/2 part when A+B is odd is equivalent to simply taking the integer part of (A+B)/2. This is a standard Vedic Math type trick often simplified as "multiply the tens digits, add half the sum of tens digits (ignoring remainder) and then add 25/75." Let's simplify the wording for Step 4.

Revised Trick 2 (Simplified Wording): Multiplying Any Two Numbers Ending in 5

This trick works for any two numbers ending in 5.

Steps:

1. Ignore the 5s: Take the numbers before the 5 from both numbers. Let them be 'A' and 'B'.

2. Multiply A by B: Calculate A x B.

3. Add A and B, then Halve: Calculate (A + B) / 2.

4. Combine the First Part:

• Add the result of Step 2 (A x B) to the result of Step 3 (A+B)/2.

• For example, if A=2, B=4, then (A+B)/2 = 3. First part = 8+3=11.

• If (A+B)/2 has a .5 (e.g., 1.5, 2.5), just ignore the .5 part and carry over 0.

5. Determine the Last Two Digits:

• If (A + B) is even, the last two digits are 25.

• If (A + B) is odd, the last two digits are 75.

Examples:

These simple tricks for multiplying numbers ending in 5 can dramatically speed up mental calculations. By practicing these methods, students can not only get the right answers faster but also gain a deeper understanding of number patterns, boosting their confidence and making math more enjoyable.