Mental Math Hacks:
How to Solve "Missing Digits" Instantly
Have you ever seen someone look at a math problem like 48 × 5 and shout "240" before you could even reach for your phone?
They aren't "human computers." They just know a few simple tricks. In our Missing Digits game, knowing these tricks is the difference between guessing blindly and solving it in seconds.
Hack 1: The "Last Digit" Rule
This is the single most powerful tool for solving missing digit puzzles. You don't need to calculate the whole number; you only need to calculate the Last Digit (The Ones Place).
💡 Example:
_ 3 × 7 = _ _ 1
You have a number ending in 3 multiplied by 7.
What is 3 × 7? It's 21.
That means the answer MUST end in 1.
If you see a puzzle where the answer ends in a specific number, work backward. If the answer ends in 5, one of the multipliers must be a 5.
Hack 2: The "Times 5" Trick
Multiplying by 5 is notoriously easy if you change your perspective.
The Trick: Multiplying by 5 is the same as multiplying by 10 and dividing by 2.
- Problem: 48 × 5
- Step 1: Cut 48 in half (24).
- Step 2: Add a zero (240).
In a puzzle, if you see _ _ × 5 = 2 4 0, just ignore the 5. Look at the 240. Double it (480), remove the zero, and you have your answer: 48.
Hack 3: The "9 Rule" (Sum of Digits)
This is magic. If you multiply any number by 9, the digits of the answer will almost always add up to 9 (or a multiple of 9).
- 9 × 4 = 36 (3 + 6 = 9)
- 9 × 15 = 135 (1 + 3 + 5 = 9)
- 9 × 121 = 1089 (1 + 0 + 8 + 9 = 18, and 1 + 8 = 9)
How to use it: If you have _ 9 × 3 = _ _ _, you can quickly check your guess by summing the digits of the result. If they don't sum to 9, your guess is wrong.
Hack 4: Estimation (The Ballpark)
Before you do math, use common sense.
9 _ × 9 _ = 8 _ _
Is this possible? No. Because 90 × 90 is 8100 (a 4-digit number). The result shows only 3 digits. Therefore, the numbers in the blanks must be small. This allows you to eliminate 7, 8, and 9 immediately without doing any calculation.
❓ Frequently Asked Questions
What is the fastest way to check if my answer is correct?
Use the "Last Digit Rule." Multiply only the ones-place digits and compare that to the ones-place of the result. If they don't match, your answer is wrong.
Does the "9 Rule" work for division too?
Yes! If a number is divisible by 9, its digits will sum to 9 (or a multiple of 9). This can help you verify if a division answer is correct.
How can I practice mental math daily?
Play our Missing Digits game every day! It gives you a new puzzle to solve and tracks your streak.
Practice Your New Powers
Go to the Missing Digits game and try to solve today's puzzle in under 30 seconds using the "Last Digit Rule."
▶ PLAY MISSING DIGITS