Hey Everyone,
So recently in school I've been practicing my Number Sense like crazy (the ability to do math in your head). Don't know what Number Sense is? Look here: LINK
So where I live (and I'm pretty sure everywhere else in the USA) in our Science and Math UIL Competitions we have a test called the Number Sense Test, where we have 10 minutes to answer as many of the 80 questions on the test in our head without being allowed to write a thing but the answer. This test is known to have a variety of math difficulties from basic math, to pre-calculus level math.
In this guide I will be teaching you how you can improve your Number Sense skills allowing you to do many complex and simple math equations in your head with ease allowing you to work faster, and more accurately, allowing you to excel in your learning and math skills.
Multiplying ANY number by 11
Alright, so this is probably one of the easiest things to learn in Number Sense:
Step 1: The last digit on the right of the number is the first digit towards your answer.
Step 2: The sum of the last digit and the one next to it will give you the next digit in the answer. If the sum is greater than or equal to 10, carry over to step 3.
Step 3: repeat the addition of consecutive digits until the final digit of the number is reached. If you need to, add carryovers from the previoius steps.
Step 4: The very last digit you will write down will the the digit furthest to the left (plus any carryover).
I'm guessing you probably didn't get everything I just said so here's a few examples:
EX. A: 36 x 11 = _________
Step 1: The first digit you write down is 6, because it's the last digit in the number being multiplied by 11.
Step 2: 3 + 6 = 9, simple enough right? 9 will be the 2nd number you write down. You now have 96 written down.
Step 3: The last digit you write down is 3, because it is the digit farthest to the left.
Answer: 396
Simple enough right? So now, let's take things a bit further.
EX. B: 76 X 11 = _________
Step 1: The first digit you write down is 6, because it's the last digit in the number being multiplied by 11.
Step 2: 7 + 6 = 13. 3 will be the 2nd number you write down, carry over the 1. You now have 36 written down.
Step 3: The last digit you write down is 8, because it is the digit farthest to the left plus the carried over 1.
Answer: 836
Ok, so you got 2 digit numbers down. Let's take it further.
EX. C: 385 x 11 = _______
Step 1: The first digit you write down is 5, because it's the last digit in the number being multiplied by 11.
Step 2: 5 + 8 = 13. 3 will be the 2nd number you write down, carry over the 1. You now have 35 written down.
Step 3: 3 + 8 + (1) = 12. 2 will be the 3nd number you write down, carry over the 1. You now have 235 written down.
Step 4: The last digit you write down is 4, because it is the digit farthest to the left plus the carried over 1.
Answer: 4235
Ready to take this TO THE EXTREME!!!
EX. 7PM: 8235153251324534 x 11 = ______________
Step 1: I'm not going to bother writing all of the steps... after all, this is all about doing this all in your head. But 4 is the 1st number you write down.
Answer: 90586685764569874 (and yes, I really did do that all in my head)
So recently in school I've been practicing my Number Sense like crazy (the ability to do math in your head). Don't know what Number Sense is? Look here: LINK
So where I live (and I'm pretty sure everywhere else in the USA) in our Science and Math UIL Competitions we have a test called the Number Sense Test, where we have 10 minutes to answer as many of the 80 questions on the test in our head without being allowed to write a thing but the answer. This test is known to have a variety of math difficulties from basic math, to pre-calculus level math.
In this guide I will be teaching you how you can improve your Number Sense skills allowing you to do many complex and simple math equations in your head with ease allowing you to work faster, and more accurately, allowing you to excel in your learning and math skills.
Multiplying ANY number by 11
Alright, so this is probably one of the easiest things to learn in Number Sense:
Step 1: The last digit on the right of the number is the first digit towards your answer.
Step 2: The sum of the last digit and the one next to it will give you the next digit in the answer. If the sum is greater than or equal to 10, carry over to step 3.
Step 3: repeat the addition of consecutive digits until the final digit of the number is reached. If you need to, add carryovers from the previoius steps.
Step 4: The very last digit you will write down will the the digit furthest to the left (plus any carryover).
I'm guessing you probably didn't get everything I just said so here's a few examples:
EX. A: 36 x 11 = _________
Step 1: The first digit you write down is 6, because it's the last digit in the number being multiplied by 11.
Step 2: 3 + 6 = 9, simple enough right? 9 will be the 2nd number you write down. You now have 96 written down.
Step 3: The last digit you write down is 3, because it is the digit farthest to the left.
Answer: 396
Simple enough right? So now, let's take things a bit further.
EX. B: 76 X 11 = _________
Step 1: The first digit you write down is 6, because it's the last digit in the number being multiplied by 11.
Step 2: 7 + 6 = 13. 3 will be the 2nd number you write down, carry over the 1. You now have 36 written down.
Step 3: The last digit you write down is 8, because it is the digit farthest to the left plus the carried over 1.
Answer: 836
Ok, so you got 2 digit numbers down. Let's take it further.
EX. C: 385 x 11 = _______
Step 1: The first digit you write down is 5, because it's the last digit in the number being multiplied by 11.
Step 2: 5 + 8 = 13. 3 will be the 2nd number you write down, carry over the 1. You now have 35 written down.
Step 3: 3 + 8 + (1) = 12. 2 will be the 3nd number you write down, carry over the 1. You now have 235 written down.
Step 4: The last digit you write down is 4, because it is the digit farthest to the left plus the carried over 1.
Answer: 4235
Ready to take this TO THE EXTREME!!!
EX. 7PM: 8235153251324534 x 11 = ______________
Step 1: I'm not going to bother writing all of the steps... after all, this is all about doing this all in your head. But 4 is the 1st number you write down.
Answer: 90586685764569874 (and yes, I really did do that all in my head)
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