Math Tricks and Tips
August 23, 2018
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Math Tricks and Tips | mathjokes.net
If you have a large number to multiply and one of the numbers is even, you can easily subdivide to get to the answer:
32 x 125, is the same as: 16 x 250 is the same as: 8 x 500 is the same as: 4 x 1000 = 4,000
Multiply by 6: Sometimes multiplying by 3 and then 2 is easy.
Multiply by 9: Multiply by 10 and subtract the original number.
Multiply by 12: Multiply by 10 and add twice the original number.
Multiply by 13: Multiply by 3 and add 10 times original number.
Multiply by 14: Multiply by 7 and then multiply by 2
Multiply by 15: Multiply by 10 and add 5 times the original number, as above.
Multiply by 16: You can double four times, if you want to. Or you can multiply by 8 and then by 2.
Multiply by 18: Multiply by 20 and subtract twice the original number
Multiply by 19: Multiply by 20 and subtract the original number.
Multiply by 24: Multiply by 8 and then multiply by 3.
Multiply by 27: Multiply by 30 and subtract 3 times the original number.
Multiply by 17: Multiply by 7 and add 10 times original number.
Multiply by 45: Multiply by 50 and subtract 5 times the original number
Multiply by 90: Multiply by 9 (as above) and put a zero on the right.
Multiply by 98: Multiply by 100 and subtract twice the original number.
Multiply by 99: Multiply by 100 and subtract the original number
use the conjunction (OR),
when the absolute value is less than a number you must use the conjunction AND.
To remember this just remember two words "GOR"-"LAND," which translate into "G(greater)OR" and "L(less than)AND."
When I introduce this topic I tell students that we are about to enter "GOR-LAND." (no political implications intended)
Always reduce computations to a single digit.
43 x 92 3956 Add the digits of multiplicand i.e. 4 + 3 = 7
Add the digits of multiplier i.e. 9 + 2 = 11 then reduce to a single digit 1 +1 = 2
Multiply 2 x 7 = 14 then reduce to a single digit 1 + 4 = 5
Add 3+9+5+6 = 23 then reduce to a single digit 2 + 3 = 5
Both numbers (5) are equal, therefore multiplication is correct
A=(pi)r*r ? Apple pies r round
C= (pi)d ? Cherry pie delight
I = p r t ? I "am" p-r-t
pronounced I am pretty
rt = d ? rt are d
pronounced retard
Quadratic formula : "X equals to negative b Plus or minus the square root, Of b squared minus four a c All over 2 a"
Supplementary and complimentary angles are angles that equal 90 degrees and 180degrees, but they get confused as to which is which.
They also know that 90 degree angles are right angles.
So I tell them that a compliment is the right thing to do, and right angles equal 90degrees, therefore complimentary angles are two angles that equal 90 degrees.
Then they know that 180 degrees is the other one, supplementary.
"Complementary" - early in the alphabet, so = 90degrees.
"Supplementary“ - later in the alphabet, so = 180degrees.
Isosceles triangles have 2 sides and angles equal.
Scalene triangles have 0 sides and 0 angles equal.
So, to remember them in that order, EIS, "Eat ice slowly"
Two given lines cut the coordinate axes in four concyclic points or not
just see whether the product of coefficients of x in both the equations is equal to that of coefficients of y.
If the given lines are
ax+by+c=0 and bx+ay+d=0
they cut the axes in concyclic points.
Convert 10 decameters to centimeters.
Set up the columns as shown below so that the ones column comes under deca.
Move the decimal point to the right of the column with centi.
Add zeros until you are under centimeters.
That is your answer.
Kilo hecta deca unit deci centi milli
1 0
Kilo hecta deca unit deci centi milli
1 0 0 0 0
i.e. 10 dam = 10 000 cm
“King Henry Died Monday Drinking Chocolate Milk"
Km Hm Dam M Dm Cm Mm
To convert...3.75 Hm = ______ Cm
It is 4 jumps to the right from Hm to Cm,
Simply move the decimal 4 jumps to the right.
3.75 Hm = 37,500. Cm
0.59 Dm = _______ HmI
It's 3 jumps to the left from Dm to Hm, Simply move the decimal 3 jumps to the left .
0.59 Dm = 0.00059 Hm
SQ (XYZ) is calculated like this.
STEP 1. Last digit = last digit of SQ(Z)
STEP 2. Second Last Digit = 2*Y*Z + any carryover from step1
STEP 3. Third Last Digit 2*X*Z+ Sq(Y) + any carryover from STEP 2
STEP 4. Fourth last digit is 2*X*Y + any carryover from STEP3
STEP 5 . In the beginning of result will be Sq(X) + any carryover from Step 4.
SQ (431)
STEP 1). Last digit = last digit of SQ(1) =1
STEP 2). Second Last Digit = 2*3*1 + any carryover from STEP1 = 6
STEP 3). Third Last Digit 2*4*1+ Sq(3) + any carryover from STEP2 = 2*4*1 +9= 17. so 7 and 1 carryover
STEP 4). Fourth last digit is 2*4*3 + any carryover (which is 1) = 24+1=25. So 5 and carry over 2.
STEP 5) . In the beginning of result will be Sq(4) + any carryover from Step 4. So 16+2 =18.
So the result will be 185761.
"Andrew Jackson was the 7th president, elected in 1828 to two terms. Then tack on the 45-90-45 right triangle.
pi - first eight digits of pi by K.Mahadevan,PGT
to get the first eight digits of pi, count the number of letters in each word of this phrase: May(3) I(1) have(4) a(1) large(5)container(9) of(2) coffee(6)
Final Difference % = X- Y – XY/100.
EXAMPLE 1. : The price of T.V set is increased by 40 % of the cost price and then decreased by 25% of the new price . On selling, the profit for the dealer was Rs.1,000 . At what price was the T.V sold.
From the above mentioned formula you get : Final difference % = 40-25-(40*25/100)= 5 %.
So if 5 % = 1,000 then 100 % = 20,000. C.P = 20,000 S.P = 20,000+ 1000= 21,000.
EXAMPLE 2 :
The price of T.V set is increased by 25 % of cost price and then decreased by 40% of the new price . On selling, the loss for the dealer was Rs.5,000 . At what price was the T.V sold?
From the above mentioned formula you get : Final difference % = 25-40-(25*45/100)= -25 %.
So if 25 % = 5,000 then 100 % = 20,000. C.P = 20,000 S.P = 20,000 – 5,000= 15,000.
TRY THESE
Now find out the difference in % of a product which was :
2. If A can finish work in X time and A and B together can finish work in S time then B can finish work in (XS)/(X-S) time.
3. If A can finish work in X time and B in Y time and C in Z time then they all working together will finish the work in (XYZ)/ (XY +YZ +XZ) time
4. If A can finish work in X time and B in Y time and A,B and C together in S time then : C can finish work alone in (XYS)/ (XY-SX-SY) B+C can finish in (SX)/(X-S) and A+ C can finish in (SY)/(Y-S)
TYPE 2 : Price of a commodity is decreased by r %. By how much % can the consumption be increased so that the expense remain the same.
Solution : TYPE1 : (100* r ) / (100+r) TYPE 2 : (100* r ) / (100-r)
Example
TYPE 1 : Price of a commodity is increased by 60 %. By how much % should the consumption be reduced so that the expense remain the same.
TYPE 2 : Price of a commodity is decreased by 60 %. By how much % can the consumption be increased so that the expense remain the same.
Solution : TYPE1 : (100* 60 ) / (100+60) = 37.5 %
TYPE 2 : (100* 60 ) / (100-60) = 150 %
2) Area of a trapezium = 1/2 * (sum of parallel sides) * height
= median * height where median is the line joining the midpoints of the oblique sides.
3) Let W be any point inside a rectangle ABCD . Then
4) Let ‘ a’ be the side of an equilateral triangle.
Then if three circles be drawn inside this triangle touching each other then each’s radius =
Suppose in 1999 population decreases by x% and then in 2000 by y% so the population in 2000 now is less that was in 1999.
In 1999 population increases by 10% and then in 2000 by 5% so the population in 2000 now is 10+5+(50/100)=+15.5% more that was in 1999.
If there is a decrease then it will be preceded by a negative sign and likewise.
Step 2: Form a Fibonacci sequence for ten numbers
Example, I choose number 5 for my first number
and 6 for my second number.
Then I add the numbers to get a Fibonacci sequence.
5+6 gives my 3rd number which is 11;
6+11 gives me my 4th number which is 17.
The entire sequence is as follows:
1st – 5,2nd – 6, 3rd – 11, 4th – 17,5th – 28,6th - 45 7th – 73,8th – 118, 9th – 191,10th – 309.
What is the sum of all these 10 numbers? (6 seconds)
The answer will also be 803.
Trick: Multiply 7th number by 11 and the answer is 803.
(It is true is any set of ten Fibonacci numbers)
General Tips for Studying Mathematics
- Go To Class regularly
- Get to Class On Time.
- LISTEN During Class.
- Take Good Notes.
- Ask Questions.
- Listen When Others Ask Questions.
- Review Notes After Class.
- Make a Set of Index Cards.
- Learn The (Proper) Notation.
- Get Into A Study Group.
- Note Due Dates.
- Budget Adequate Time For Studying/Homework.
- Do Homework After Each Class.
- Do Homework Without Notes and Book.
- Do More Homework.
- Practice, Practice, Practice.
- Persevere Keep Old Homework and Exam Papers.
- Don’t Forget Your Textbook.
- Seek Help If You Need It.
- Seek Help If You Need It . You should always do the best that you can
- and strive for the best grade that you can possible get.
Study Tips for Math
- Always read math problems completely before beginning any calculations. If you "glance" too quickly at a problem, you may misunderstand what really needs to be done to complete the problem.
- Whenever possible, draw a diagram. Even though you may be able to visualize the situation mentally, a hand drawn diagram will allow you to label the picture, to add auxiliary lines, and to view the situation from different perspectives.
- Do not feel that you must use every number in a problem when doing your calculations. Some mathematics problems have "extra" information. These questions are testing your ability to recognize the needed information, as well as your mathematical skills.
- Remain confident! Do not get flustered! Focus on what you DO know, not on what you do not know. You know a LOT of math!!
- If you are "stuck" on a particular problem, go on with the rest of the test. Oftentimes, while solving a new problem, you will get an idea as to how to attack that difficult problem.
- In certain problems, you may be able to "guess" at an approximate (or reasonable) answer. After you perform your calculations, see if your final answer is close to your guess.
Fear of Maths is only mental
- Instead of saying DIVIDE BY 2, say HALF/HALVE IT.
- Instead of saying MULTIPLY it by 2, say DOUBLE IT.
- Never use more than two digit numbers to prove the working of a method.
- Show the more interesting sides of maths, for example, show the beauty of the table of nine (which really looks cute, simple and well arranged).
- After these small things, leave the person to grow up inside herself, by herself.
- They’ll start with small victories, and keep gathering courage for bigger ones.
- Maths is easy and beautiful up to a certain level.
- Let’s all enjoy this beautiful, universal language.
Tough Multiplication
If you have a large number to multiply and one of the numbers is even, you can easily subdivide to get to the answer:
32 x 125, is the same as: 16 x 250 is the same as: 8 x 500 is the same as: 4 x 1000 = 4,000
Assorted Multiplication Rules
Multiply by 5: Multiply by 10 and divide by 2.Multiply by 6: Sometimes multiplying by 3 and then 2 is easy.
Multiply by 9: Multiply by 10 and subtract the original number.
Multiply by 12: Multiply by 10 and add twice the original number.
Multiply by 13: Multiply by 3 and add 10 times original number.
Multiply by 14: Multiply by 7 and then multiply by 2
Multiply by 15: Multiply by 10 and add 5 times the original number, as above.
Multiply by 16: You can double four times, if you want to. Or you can multiply by 8 and then by 2.
Multiply by 18: Multiply by 20 and subtract twice the original number
Multiply by 19: Multiply by 20 and subtract the original number.
Multiply by 24: Multiply by 8 and then multiply by 3.
Multiply by 27: Multiply by 30 and subtract 3 times the original number.
Multiply by 17: Multiply by 7 and add 10 times original number.
Multiply by 45: Multiply by 50 and subtract 5 times the original number
Multiply by 90: Multiply by 9 (as above) and put a zero on the right.
Multiply by 98: Multiply by 100 and subtract twice the original number.
Multiply by 99: Multiply by 100 and subtract the original number
INEQUALITIES
When solving absolute value inequalities: if the absolute value is greater than a number you mustuse the conjunction (OR),
when the absolute value is less than a number you must use the conjunction AND.
To remember this just remember two words "GOR"-"LAND," which translate into "G(greater)OR" and "L(less than)AND."
When I introduce this topic I tell students that we are about to enter "GOR-LAND." (no political implications intended)
Simple Multiplication Verification Method
How do you verify your multiplication? Here is a simple method.Always reduce computations to a single digit.
43 x 92 3956 Add the digits of multiplicand i.e. 4 + 3 = 7
Add the digits of multiplier i.e. 9 + 2 = 11 then reduce to a single digit 1 +1 = 2
Multiply 2 x 7 = 14 then reduce to a single digit 1 + 4 = 5
Add 3+9+5+6 = 23 then reduce to a single digit 2 + 3 = 5
Both numbers (5) are equal, therefore multiplication is correct
Formulas For Easy Remberence
A=(pi)r^2 ? Apple pies r squareA=(pi)r*r ? Apple pies r round
C= (pi)d ? Cherry pie delight
I = p r t ? I "am" p-r-t
pronounced I am pretty
rt = d ? rt are d
pronounced retard
Quadratic formula : "X equals to negative b Plus or minus the square root, Of b squared minus four a c All over 2 a"
Supplementary and Complimentary Angles
I teach middle school students. My students know thatSupplementary and complimentary angles are angles that equal 90 degrees and 180degrees, but they get confused as to which is which.
They also know that 90 degree angles are right angles.
So I tell them that a compliment is the right thing to do, and right angles equal 90degrees, therefore complimentary angles are two angles that equal 90 degrees.
Then they know that 180 degrees is the other one, supplementary.
"Complementary" - early in the alphabet, so = 90degrees.
"Supplementary“ - later in the alphabet, so = 180degrees.
Triangle Names
Equilateral triangles have 3 sides and 3 angles equal.Isosceles triangles have 2 sides and angles equal.
Scalene triangles have 0 sides and 0 angles equal.
So, to remember them in that order, EIS, "Eat ice slowly"
Two given lines cut the coordinate axes in four concyclic points or not
just see whether the product of coefficients of x in both the equations is equal to that of coefficients of y.
If the given lines are
ax+by+c=0 and bx+ay+d=0
they cut the axes in concyclic points.
Metric Measurement
ExampleConvert 10 decameters to centimeters.
Set up the columns as shown below so that the ones column comes under deca.
Move the decimal point to the right of the column with centi.
Add zeros until you are under centimeters.
That is your answer.
Kilo hecta deca unit deci centi milli
1 0
Kilo hecta deca unit deci centi milli
1 0 0 0 0
i.e. 10 dam = 10 000 cm
“King Henry Died Monday Drinking Chocolate Milk"
Km Hm Dam M Dm Cm Mm
To convert...3.75 Hm = ______ Cm
It is 4 jumps to the right from Hm to Cm,
Simply move the decimal 4 jumps to the right.
3.75 Hm = 37,500. Cm
0.59 Dm = _______ HmI
It's 3 jumps to the left from Dm to Hm, Simply move the decimal 3 jumps to the left .
0.59 Dm = 0.00059 Hm
TO FIND SQUARE OF A 3 DIGIT NUMBER
LET THE NUMBER BE XYZ.SQ (XYZ) is calculated like this.
STEP 1. Last digit = last digit of SQ(Z)
STEP 2. Second Last Digit = 2*Y*Z + any carryover from step1
STEP 3. Third Last Digit 2*X*Z+ Sq(Y) + any carryover from STEP 2
STEP 4. Fourth last digit is 2*X*Y + any carryover from STEP3
STEP 5 . In the beginning of result will be Sq(X) + any carryover from Step 4.
TO FIND SQUARE OF A 3 DIGIT NUMBER :
EXAMPLE :SQ (431)
STEP 1). Last digit = last digit of SQ(1) =1
STEP 2). Second Last Digit = 2*3*1 + any carryover from STEP1 = 6
STEP 3). Third Last Digit 2*4*1+ Sq(3) + any carryover from STEP2 = 2*4*1 +9= 17. so 7 and 1 carryover
STEP 4). Fourth last digit is 2*4*3 + any carryover (which is 1) = 24+1=25. So 5 and carry over 2.
STEP 5) . In the beginning of result will be Sq(4) + any carryover from Step 4. So 16+2 =18.
So the result will be 185761.
Special Numbers
e to 15 decimal places e=2.718281828459045..."Andrew Jackson was the 7th president, elected in 1828 to two terms. Then tack on the 45-90-45 right triangle.
pi - first eight digits of pi by K.Mahadevan,PGT
to get the first eight digits of pi, count the number of letters in each word of this phrase: May(3) I(1) have(4) a(1) large(5)container(9) of(2) coffee(6)
PROFIT AND LOSS :
Suppose the price is first increase by X% and then decreased by Y% , the final change % in the price is given by the following formula.Final Difference % = X- Y – XY/100.
EXAMPLE 1. : The price of T.V set is increased by 40 % of the cost price and then decreased by 25% of the new price . On selling, the profit for the dealer was Rs.1,000 . At what price was the T.V sold.
From the above mentioned formula you get : Final difference % = 40-25-(40*25/100)= 5 %.
So if 5 % = 1,000 then 100 % = 20,000. C.P = 20,000 S.P = 20,000+ 1000= 21,000.
EXAMPLE 2 :
The price of T.V set is increased by 25 % of cost price and then decreased by 40% of the new price . On selling, the loss for the dealer was Rs.5,000 . At what price was the T.V sold?
From the above mentioned formula you get : Final difference % = 25-40-(25*45/100)= -25 %.
So if 25 % = 5,000 then 100 % = 20,000. C.P = 20,000 S.P = 20,000 – 5,000= 15,000.
TRY THESE
Now find out the difference in % of a product which was :
- First increased by 20 % and then decreased by 10 %.
- First Increased by 25 % and then decrease by 20 %
- First Increased by 20 % and then decrease by 25 %.
- First Increased by 10 % and then decrease by 10 %.
- First Increased by 20 % and then decrease by 15 %.
TIME AND WORK:
1. If A can finish work in X time and B can finish work in Y time then both together can finish work in (X*Y)/ (X+Y) time.2. If A can finish work in X time and A and B together can finish work in S time then B can finish work in (XS)/(X-S) time.
3. If A can finish work in X time and B in Y time and C in Z time then they all working together will finish the work in (XYZ)/ (XY +YZ +XZ) time
4. If A can finish work in X time and B in Y time and A,B and C together in S time then : C can finish work alone in (XYS)/ (XY-SX-SY) B+C can finish in (SX)/(X-S) and A+ C can finish in (SY)/(Y-S)
PERCENTAGE
TYPE 1 : Price of a commodity is increased by r%. By how much % should the consumption be reduced so that the expense remain the same.TYPE 2 : Price of a commodity is decreased by r %. By how much % can the consumption be increased so that the expense remain the same.
Solution : TYPE1 : (100* r ) / (100+r) TYPE 2 : (100* r ) / (100-r)
Example
TYPE 1 : Price of a commodity is increased by 60 %. By how much % should the consumption be reduced so that the expense remain the same.
TYPE 2 : Price of a commodity is decreased by 60 %. By how much % can the consumption be increased so that the expense remain the same.
Solution : TYPE1 : (100* 60 ) / (100+60) = 37.5 %
TYPE 2 : (100* 60 ) / (100-60) = 150 %
Geometry
1) Apollonius theorem could be applied to the 4 triangles formed in a parallelogram.2) Area of a trapezium = 1/2 * (sum of parallel sides) * height
= median * height where median is the line joining the midpoints of the oblique sides.
3) Let W be any point inside a rectangle ABCD . Then
4) Let ‘ a’ be the side of an equilateral triangle.
Then if three circles be drawn inside this triangle touching each other then each’s radius =
Successive discounts
Suppose in 1999 population increases by x% and then in 2000 by y% so the population in 2000 now is more that was in 1999.Suppose in 1999 population decreases by x% and then in 2000 by y% so the population in 2000 now is less that was in 1999.
In 1999 population increases by 10% and then in 2000 by 5% so the population in 2000 now is 10+5+(50/100)=+15.5% more that was in 1999.
If there is a decrease then it will be preceded by a negative sign and likewise.
Fibonacci Addition Trick
Step 1: Choose two numbersStep 2: Form a Fibonacci sequence for ten numbers
Example, I choose number 5 for my first number
and 6 for my second number.
Then I add the numbers to get a Fibonacci sequence.
5+6 gives my 3rd number which is 11;
6+11 gives me my 4th number which is 17.
The entire sequence is as follows:
1st – 5,2nd – 6, 3rd – 11, 4th – 17,5th – 28,6th - 45 7th – 73,8th – 118, 9th – 191,10th – 309.
What is the sum of all these 10 numbers? (6 seconds)
The answer will also be 803.
Trick: Multiply 7th number by 11 and the answer is 803.
(It is true is any set of ten Fibonacci numbers)
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