How To Solve Math Problems Faster

Math problems act as a medium for school students to not only enhance their reasoning and thinking ability but it also prepares them for basic problem-solving skills requirement in daily life.

Problem-solving is the heart of math learning and the education curriculum from the Buddhist era has also highlighted that math learning and students’ quality are both correlated and important.

A research study published by Journal of Social Sciences in 2009, showcased that factors that directly and indirectly affect a student’s problem-solving problem ability are his/her own attitude towards the subject along with the teacher’s behavior.
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Hence, for a child to get really good at problem solving, he/she needs to be supported or mentored by a quality math problem solver.

Now talking about the child’s own attitude towards the subject we can all agree that there are two types of students. One who loves math, second who is scared of it. Even if you love math, there is so much for you to read ahead in this blog. And those who fear math, after reading this blog, try solving the hardest question and see the results yourself.

So are you ready to learn math after now? We are going to help you learn some quick and easy math problem-solving techniques. In a recent survey, a report suggests that 37% of teens aged between 13-17 find math as the most difficult subject.

Now, are you one of these students who also feel math is a ghost? It haunts you with difficulty, but you don’t know how to tackle it smartly? Of course, how will you; did anyone tell you that math requires this:

PPP – Three Things you should absolutely know to Solve Math Problems Faster!

These three letters simple means:

Practice – It could be that you are pretty smart at learning formulas, but just relying on cramming formulas in math won’t help you score better in the long run. Instead, you should memorize them and then practice. Try practicing that formula on differential equations. From easy, difficult to complex, keep practicing until you are confident.

Preparation – You must be lucky enough to score well without any preparation in math. Not all are skilled like a magician when it comes to math. Honestly, it is always better to appear prepared in the exam and avoid falling into the blank trap.

One tip for preparation is, start with solving the easiest equation and pump your conscious nerves. Eventually, you will become more confident, and that’s when you should start hopping on to the difficult ones. We are sure that once you start moving from simple to challenging questions, you will feel less troubled with the complexities of math.

Perseverance – Before getting into the technicalities, having the right amount of patience would help. Students often give up so quickly if their answers don’t match. But this is where you need to push yourself harder. Instead of escaping math at that stage, see what you are doing wrong and where you need help.

Now that you have learned these, we should talk about the real business – what are those tricks, tips, and methods that will help you learn math faster!

Quick Math Tricks for Solving Math Problems – QMT

Project questions of Mathematics for Blog

General instruction for Multiply:-

• Depending upon the numbers closer to the power of 10, we select that power of 10 as our Base.
• Subtract the digits from the Base. Those numbers if positive will be called excesses and negative will be called deficiencies.
• Multiply those deficiencies or excesses.
• Do cross addition of numbers with deficiencies or excesses.
• Always needs to have the same number of digits as the zeroes of the selected base. If less than prepend zeros. If more, carry forward initial digits to 1st compartment.

(1). Multiply 94 x 96

Solution:

Explanation:

1. Both the numbers are closer to 10 power(base 100)
2. 94 is 6 less than 100 and 96 is 4 less than 100
3. (-6)(-4)=24  (Since the base is 100 use 24)
4. 96 – 6 or 94 – 4 =90

(2).  Multiply 103 x 108

Solution

Explanation:

1. Both the numbers are closer to 10 power (base 100)
2. 103 is 3  more than 100 and 108 is 8 more than 100
3. (+3)(+8)=24 (Since the base is 100 use 24)
4. 103 +8 or 108 +3 =111

(3). Multiply 962 x 998

Solution:

Explanation:

1. Both the numbers are closer to 10 power ( base 1000)
2. 962 is less than 1000 and 998 is 2 less than 1000.
3. (-38) (-2)=76 (Since the base is 1000 use 076)
4. 962 -2= 998 – 38 =960

(4). Multiply 110 x 112

Solution:

Explanation:

1. Both the numbers are closer to 10 power ( base 1000)
2. 110 is 10 more than 1000 and 112 is 12 more than 1000.
3. (110) (12)=120 (Since the base is 100 carry forward 1  use 20)
4. 110 +12= 112+10 =122
5. Add 1(carry forward 1) to 122=123

Multiply and divide

Let’s understand this with an example and then have a look at its explanation.

(5) 33 x 48 as an example,

66 x 24

132 x 12

264 x 6

528 x 3

Now, did you understand what happened? When a student has to multiply two integers, he or she can work on speeding up with the process when one number is an even number. All that a student is supposed to do is halve the even number given and double the other number.

When should a student stop?

There will come a point during the calculations when the equation will no longer be solved. Or it will look impossible to move further. There is when you have to stop, and that’s what your answer is.

Tip – You should know the table 2 times and everything else will be sorted.

(6) 58 x 32

Multiply 58 by 2 and divide 32 by 2 = 116 x 16

Multiply 116 by 2 and divide 16 by 2 = 232 x 8

Multiply 232 by 2 and divide 8 by 2 = 464 x 4

Multiply 464 by 2 and divide 4 by 2 = 928 x 2

(7) 41 x 16

Multiply 41 by 2 and divide 16 by 2 = 82 x 8

Multiply 82 by 2 and divide 8 by 2 = 232 x 8

Multiply 164by 2 and divide 4 by 2 = 464 x 4

Multiply 328 by 2 and divide 2 by 2 = 928 x 2

Multiplying by Powers of 2

So, you just doubled and halved above right? It is again something similar but with a twist.

Simplify the multiplication if a number in the equation is a power of 2. In simple words, 2, 4, 8, 16, 32, and so on.

(8) For example: 8 x 16 => 8 (2 x 2 x 2 x 2) or 8 x 2^4

You will now double 8 three times to get the right answers.

8 x 2^4

16 x 2^3

32 x 2^2

64 x 2

(9) 12 x 2^3

12 doubled 2^3 halved = 24 x 2^2

24 doubled 2^2 halved = 48 x 2

(10) 5 x 2^5

5 doubled 2^5 halved = 10 x 2^4

10 doubled 2^4 halved = 20 x 2^3

20 doubled 2^3 halved = 40 x 2^2

40 doubled 2^2 halved = 80 x 2

Multiplying even numbers by 5

Are you good at basic division skills? You should know that this is where you have to understand that there are two steps, for example, 5 x 8.

Now, first, divide the number being multiplied by 5. That is 8. 8 divided in half and second, also add 0 to the right of the number.

The result is 40! This is the right answer!

It is the ideal technique to know and practice only if you have mastered the 5 times table properly!

(11) 5 x 22

First, divide the number being multiplied by 5. That is 22. 22 divided in half and second, also add 0 to the right of the number.

(12) 5 x 46

First, divide the number being multiplied by 5. That is 46. 46 divided in half and second, also add 0 to the right of the number.

Multiplying odd numbers by 5

So, let’s add up more to your tricks! Let us tell you that 5 numbers are so helpful that you can’t imagine how many questions can be solved easily with them!

(13)This equation has three steps which are 5 x 9

We know how to do it for even numbers. So what we can do is represent the odd number as a sum of even numbers and 1.

5 x 9 = (8+1) x 5

(5 x 8) + 5

Divide 8 by 2 and put zero in the end.

40 + 5

(14) 17 x  5

We know how to do it for even numbers. So what we can do is represent the odd number as a sum of even numbers and 1.

5 x 17 = (16+1) x 5

(5 x 16) + 5

Divide 16 by 2 and put zero in the end.

80 + 5

(15) 25 x 5

We know how to do it for even numbers. So what we can do is represent the odd number as a sum of even numbers and 1.

5 x 25 = (24+1) x 5

(5 x 24) + 5

Divide 24 by 2 and put zero in the end.

120 + 5

MULTIPLICATION

(16)  Multiply 94× 96

The sum of unit digits is 6+4 = 10. When, sum of unit digits are 10, and then multiply

both the digits  6×4 = 24 and both tens are same then, multiply tens digit to more

than one of itself.

Means 9× (9+1) = 9×10 = 90

Hence, we can put together both the values and we get the multiplication of 54 and 56.

That means, 94×96 = 9024

(17)  Multiply 58× 52

The sum of unit digits is 8+2= 10. When, sum of unit digits are 10, and then multiply

both the digits  8×2 = 16 and both tens are same then, multiply tens digit to more

than one of itself.

Means 5× (5+1) = 5×6 = 30

Hence, we can put together both the values and we get the multiplication of 54 and 56.

That means, 58× 52 = 3016

(18)  Multiply 124×126:- In 121 and 129, the sum of unit digits are 4+6 = 10 and other digits are the same, which are 12.

So, 12× (12+1) = 12×13 = 156 and 4×6 = 24

Hence, we can put together both the values and we get the multiplication of 121 and 129.

121×129 = 15624

Multiplying even numbers by 5

(19) 5× 88

First, divide the number being multiplied by 5. That is 88. 88 divided in half and second, also add 0 to the right of the number.

= 440

(20) 5× 76

First, divide the number being multiplied by 5. That is 76. 76 divided in half and second, also add 0 to the right of the number.

= 380

(21) 5 × 110

First multiply 11 by 5 i.e.- 11×5= 55 and add 0 to the right of the number.

Means

5 ×110= 550

(22) 5× 220

First multiply 22 by 5 i.e.- 22×5= 110 and add 0 to the right of the number.

Means  5×220= 1100

MULTIPLICATION AND DIVISION:-

When digits get higher most of the students are afraid of multiplication and division, It can be generated some tricks to make multiplication and division easy.

We can use these tricks:-

(23) Multiply 54 by 56:- In 54 and 56, the sum of unit digits are 6+4 = 10 and both tens are the same, which are 5. So, here is a simple trick to multiply 54 and 56.

When, sum of unit digits are 10, and then multiply both the digits-

6×4 = 24 and both tens are same then, multiply tens digit to more than one of itself.

Means 5× (5+1) = 5×6 = 30

Hence, we can put together both the values and we get the multiplication of 54 and 56.

That means, 54×56 = 3024

Note :- This trick is only useful when the sum of unit digits are 10 and the other digits are the same.

(24) Multiply 67 by 63:- In 67 and 63, the sum of unit digits are 7+3 = 10 and both tens are the same, which are 6.

So, 6× (6+1) =6×7=42 and 7×3=21

Hence, we can put together both the values and we get the multiplication of 67 and 63.

67×63 = 4221

(25) Multiply 121 by 129:- In 121 and 129, the sum of unit digits are 1+9 = 10 and other digits are the same, which are 12.

So, 12× (12+1) = 12×13 = 156 and 1×9 = 09

Hence, we can put together both the values and we get the multiplication of 121 and 129.

121×129 = 15609

Note:- We put 09 instead of 9, because the multiplications are of three digits and the answer will be in five digits.

Multiplication:

Most of the students face the issue of multiplication. Every time the teacher uses the traditional method to learn the calculation. And this is the reason why students move towards the calculator which blunt the brain and make students handicapped.

Here are some tricks for the student who knows the table up to 9. There is no need to remind the table up to 30 or 40 or 50. Math is not a dinosaur to be horrible for children. This is the duty of the teacher to simplify the method of multiplication.

Start from basic, the multiplication of single digits is given in the table form as follows,

It is considered that the student knows addition and he/she can add the digits very easily.

26) Two digits multiplication:

To simplify the multiplication, here are some examples of two digit multiplication.

28 × 38

= 1064

Here it can be seen that the multiplication of 28 and 38 requires high calculation if done with the help of a traditional method. But here we learn the shortcut methods to solve this problem.

To understand this multiplication, start from unit position, the unit digit of both numbers is 8. The digit at the position of Tenth is 2 and 3 respectively.

The first step to calculate this multiplication is to multiply 8 with 8,

8×8=64

Put the digit 4 at unit position and then carry forward the 6 for the next step.

Now for tenth position, multiply and add the digits as follows,

8×2+3×8=16+24=40

Now add the carry forward amount in 40

40+6=46

Put the digit 6 at tenth position. And carry forward the 4 for the next step.

Now for hundred position, multiply and add the digits as follows,

3×2=6

Now add the carry forward amount in 6

6+4=10

Put the digit 10 at tenth position.

To understand the method, the image given below may help to understand the position.

This is a simple trick and this trick may apply to any kind of number whether it has 2 digit or 3 digit or 5 digit.

27) Three digit multiplication:

Now the digits are 204 and 390. To solve these digits, the above method will be used as follows,

204

×390

= 79560

For unit position, the digit will be calculated as,

4×0=0

For tenth position, the digit will be calculated as,

0×0+9×4=36

Put the 6 in tenth position and carry forward the 3 for next step,

For hundredth position, the digit will be calculated as,

0×2+9×0+3×4=12

Add the 3 in 12 as 3 was a carry forwarded amount,

12+3=15

Put the 5 in hundredth position and carry forward 1 to next step,

For thousandth position, the digit will be calculated as,

9×2+3×0=18

Add the 1 in 18 as 1 was a carry forwarded amount,

18+1=19

Put the 9 in thousandth position and carry forward 1 to next step,

For ten thousandth position, the digit will be calculated as,

3×2=6

Add the 1 in 6 as 1 was a carry forwarded amount,

6+1=7

Keep the 7 in ten thousandth position.

Now the result comes out is,

204×390=79560

The pattern need to be followed is given below,

28) Four digit multiplications:

Now the digits are 2060 and 4890. To solve these digits, the above method will be used as follows,

2060

× 4890

= 10073400

For unit position, the digit will be calculated as,

0×0=0

For tenth position, the digit will be calculated as,

0×6+9×0=0

For hundredth position, the digit will be calculated as,

0×0+9×6+8×0=54

Put the value of 4 at hundredth position and carry forward the 5,

For thousandth position, the digit will be calculated as,

0×2+9×0+8×6+4×0=48

Add the 5 in 48 as 5 was a carry forwarded amount,

48+5=53

Put the 3 in thousandth position and carry forward 5 to next step,

For ten thousandth position, the digit will be calculated as,

9×2+8×0+4×6=42

Add the 5 in 42 as 5 was a carry forwarded amount,

42+5=47

Keep the 7 in ten thousandth position and carry forward 4 to next step,

For hundred thousandth position, the digit will be calculated as,

2×8+4×0=16

Add the 4 in 16 as 4 was a carry forwarded amount,

16+4=20

Keep the 0 in hundred thousandth position and carry forward 2 to next step,

For millionth position, the digit will be calculated as,

2×4=8

Add 2 in 8 as 2 is a carry forward amount.

8+2=10

Keep the 10 at the millionth position.

Now the result comes out is,

2060×4890=10073400

The pattern need to be followed is given below,

DIVISION

(29) Divide 798 by 10:-It looks difficult to divide 798 by 10. But when we divide any number by, we have to put a point prior to the unit digit.

That means, 798 by 10 = 798 ÷ 10 = 79.8

Note:- Similarly, when we divide any number by 100,1000,10000…. and so on. We can put a point prior to digits as much as the zeros are in the divisor.

(30) Divide 4782367 by 100000:- As we know the short trick for these types of division. So, there are 5 zeros in the divisor (100000).

Hence, 4782367 ÷ 100000 = 47.82367

(31) Divide 238 by 0.01:- It looks difficult to divide any digit by a point digit. But we can make it easy by converting a point digit into a simple digit. If we convert the divisor (0.01) into 1. Then, we have to multiply the dividend by 100. Because there are 2 digits after a point in the divisor.

Hence, 238 ÷ 0.01 = (238 × 100) ÷1 = 23800 ÷ 1 = 23800

Similarly, (a) 324 ÷ 0.02 = (324 × 100) ÷ 2 = 32400 ÷ 2 =16200

(b) 678 ÷ 0.03 = (678 × 100) ÷3 = 67800 ÷ 3 = 22600

Rules:

•  A number will be divisible by 2 if and only if the unit digit of any number is 0, 2, 4, 6, 8.
•  A number will be divisible by 3 if and only if the sum of the all digits of a given number is divisible by 3.
• A number will be divisible by 4 if and only if its last two digits, that is digit placed at unit and tenth stage, are divisible by 4.
• A number will be divisible by 5 if and only if the last digit or unit digit will be 0, 5.
• A number will be divisible by 6 if and only if the number is divisible by both 2 and 3.
•  A number will be divisible by 7 only and only if the last digit multiplied by 2 and the difference between the remaining number and the number obtained by multiplying 2 is divisible by 7.
•  A number will be divisible by 8 if the last three digits of the number are divisible by 8.

(32) Divide 456 by 2:

To divide the above number with respect to 2 first check the condition, whether it is divisible or not. The unit digit of the number 456 is 6 and 6 is divisible by 6 so the number will be divisible by 6.

456/2=228

(33) Divide 2022 by 3:

To initiate the division, first add all digits and check whether the sum of all digits is divisible by 3 or not. The sum of the digits are 2+0+2+2 = 6. And 6 is divisible by 3 so the 2022 is divisible by 3,

2022/3=674

(34) Divide 1996 by 4:

To check whether the given number is divisible by 4 or not, check whether the last two digits are divisible by 4 or not. The 96 is divisible by 4 so the whole number will be divisible by 4 as shown,

1996/4=499

These are some ways with which division can become short and easier.

Above all method explains the shortest way to find out the solution of big digits sum subtraction multiplication and division.

Square

How to find the square of any number ending with 5?

To find out square of any number we can use these tricks:-

(35)   (35)^2

Square of unit digit 5 is 25 and multiply tens to itself by adding one i.e.

3×(3+1) = 12

Hence, we can put together both the values and we get square of 35

Means- (35)^2= 1225

(36)    (125)^2

Square of unit digit 5 is 25 and multiply tens to itself by adding one i.e.

12×(12+1) = 156

Hence, we can put together both the values and we get square of 125

Means- (125)^2= 15625

(37)   (95)^2

Square of unit digit 5 is 25 and multiply tens to itself by adding one i.e.

9×(9+1) = 90

Hence, we can put together both the values and we get square of 95

Means- (95)^2= 9025

Square Root Estimation by using different trick

The quantity x is called the square root of any numberx. And, it is the number, which when multiplied by itself will give us x. Let us see an example, the square root of 16, which is written as √16 will be 4, because 4×4=16.

As the square root of most numbers is not a whole number, we will be using the following method to estimate the square root of any number.

(38) Square Root Estimation by Divide and Average:

Let us understand this by estimating the square root of 11. The first step would be thinking about a number which when multiplied by itself will be closer to the given number, in this case, 12. We know 3×3=9 and 4×4=16. It looks like 16 is a larger value, so the answer would be something close to 3.

Now, our next step is to divide 11 by 3.

11/3=3.67

Now, we need to take the average of this value with the number which we selected initially as the closest possible value.

(3+3.67)/2=3.33

And, the square root of 11 rounded to two decimal places is 3.32. So our estimation is pretty close!

Now, let us look at a little harder problem.

(39) Estimate the square root of 72.

The first step would be thinking about a number which when multiplied by itself will be closer to the given number, in this case, 72. We know 88=64 and 99=81. So, your answer will be somewhat between 8 and 9. It looks like 64 is closer to 72, so the answer would be close to 8.

Now, our next step is to divide 72 by 8.

72/8=9

Now, let us take the average of this value with the number which we selected initially as the closest possible value.

(8+9)2=8.5

And, the square root of 72 rounded to two decimal places is 8.49. So our estimation is pretty close!

SQUARE QUESTIONS BY USING DIFFERENT TRICKS.

(40). (14)2

Solution:

(14+4)42= 1816 = 196

Explanation:

Here 14 is 4 more than 10(Base 10), so Excess=4

Increase it still further to that extent, so (14+4)=18

Square its excessive , so 42=16

(40). 972

Solution:

(97-3)32

=94/09

=9409

Explanation:

Here 97 is 3 less than100(Base 100), So deficiency=3

Reduce it still further to the extent, (97-3)=94

Square its deficiency, So 32=09 (As base is 100, we need exactly two digits hence           09)Final Answer =9409

(42).  252( if the last digit is 5)

Solution:

252

=2 x 3=6

=52=25

=625

Explanation:

1. Check if the last digit is 5, square of 5=25
2. Add 1 to previous number and then multiply each other (2 x 3)=6
3. 3 Step 1 and 2 together gives the final answer

(43). (195)2

Solution:

19 x 20=380

52=25

=38025

Explanation:

1. Check if the last digit is 5, square of 5=25
2. Add 1 to previous number and then multiply each other (19 x 20)=380
3. 3 Step 1 and 2 together gives the final answer.

Two-step subtraction

If your teacher asks you to solve a question using the subtraction method, what would you do? Simply calculate or maybe use this trick:

(44) The difference between 767 and 253. 767 is minuend and 253 is the subtrahend. So, students will see that 700 is an easy number and they will now remove 67 from it.

Now, here is the process:

767 – 253

(767 – 67) – (253 – 67)

700 – 186

(45) 568 – 244

The difference between 568 and 244. 568 is minuend and 244 is the subtrahend. So, students will see that 500 is an easy number and they will now remove 68 from it.

568 – 244

(568 – 68) – (244 – 68)

500 – 176

(46) 962 – 421

The difference between 962 and 421. 962 is minuend and 421 is the subtrahend. So, students will see that 900 is an easy number and they will now remove 62 from it.

962 – 421

(962 – 62) – (421 – 62)

900 – 359

SUBTRACTION BY TRICK

If your math teacher asks you to subtract two complex digits in a few moments. What will you do?

Simply calculate or may be use these tricks-

(47)   Subtract 243 from 586:- 586 is minuend and 243 is subtrahend. 586 and 243 are looking too complex to subtract.

So, students see 200 and 500 as easy numbers.

Then, we can write 586= (500+86) and 243= (200+43)

Now, subtract 243 from 586=586-243

To make it a subtraction, we have to put 586 and 243 in the upper form

Hence, 586-243= (500+86)-(200+43)

When we open the brackets, then it becomes

500+86-200-43 = 500-200+86-43 = (500-200) + (86-43)

• Now subtraction of 500 and 200 looks easy to subtract.
• 86 and 43 are small digits, easy to subtract.

So, (500-200) = 300 and (86-43) = 43

Hence, 586-243 = 300+43 = 343

(48)   Subtract 479 from 679:- 679 is minuend and 479 is subtrahend. 679 and 479 are looking somehow difficult to subtract.

So, we will try to make it easy.

We can write 679 = (600+79) and 479 = (400+79)

Then, 679-479 = (600+79) – (400+79) = (600-400) + (79-79)

Hence, 679 – 479 = 200

That means, when we have the same unit digits or unit and tens digits, then we can easily remove these digits and put the zeros in the final answer as much as the digits are removed. For example;

(a) 547 – 347 = 200 (4 and 7 are same in the minuend and subtrahend, so we get two zeros in the answer.)

(b) 312 – 212 = 100

(c) 321 – 211 = 110 (only unit digits are the same, so we get only one zero in the final answer.)

Two step subtraction:

If a math teacher asks you to subtract some of the numbers in a few hours. What will you do? Are you thinking about using a calculator? Please keep that aside. Here we will learn some small math tricks to add some sum.

First I would like to ask you to practice the simple calculation or sum of one digit numbers. That is,

(49) Subtract 54 and 76.

The subtraction of two numbers 54 and 76 can be done very easily if we split this into two different numbers.

At first it look so hard to solve this kind of subtraction, but splitting the same to the nearest 10th of each number, that is,

50

70

Now we have left 4 and 6 from 54 and 76 respectively. So, first the major number get subtracted,

70-50=20

Here it can be seen that the combination of the subtraction of 7-5 = 2 is used from above with some subtraction. And the zero at the place of the unit is kept as it was before.

Now the subtraction of remaining digit is,

6 – 4 = 2

20 + 2 = 22

(50) Subtract 125 from 369.

The subtraction of two numbers 125 and 369 can be done in the very easiest way. To make it easier it is required to split the digit to nearby hundred.

The nearby hundred of 125 is 100, and nearby lesser hundreds of 369 is 300. The splitting will be,

125 = 100 + 25

369 = 300 + 69

Subtract 125 from 369 as follows,

369 – 125 = (300 + 69) – (100 + 25)

369 – 125 = (300 – 100) – (69 – 25)

Now split the 69 and 25 as it was done in the previous example

369-125=200-{(60+9)-(20+5)

369-125=200-{60-20+9-5}

369-125=200-{40+4}

369-125=200-40-4

369-125=160-4

369-125=156

Here, we did the splitting method with which we simplify the subtraction and convert them into the form of general subtraction which is easier and used in day to day life. It is necessary to practice the basic subtraction which is mentioned in the first paragraph and the examples of the simple subtractions are enlisted there.

Fractions

(51) Multiplying Fractions: If we want to multiply two fractions, we simply need to multiply the numerators (top numbers) and then multiply the denominators (bottom numbers). Let us see an example,

(2/5) x (3/7)

First, we multiplied the top numbers, and we got 2×3=6. Now, we need to multiply the bottom numbers, which will give us 5×7=35.

(2/5) x (3/7) = 6/35

Isn’t it simpler!

(52) Dividing Fractions: Dividing fractions is similar to multiplying fractions, we just need an extra step. We need to flip the second fraction, which is referred to as reciprocal, and multiply with the first fraction. For example,

(1/2) ÷  (5/9)

Reciprocal of 5/9 will be 9/5. Now, let us multiply them.

(1/2) x (9/5) = 9/10

(53) Simplifying Fractions: If we multiply the numerator and denominator of a fraction by the same number, we will get a fraction that will be equivalent to the first fraction. The same is true for division, that if we divide the numerator and denominator by the same number, we will get a fraction that will be equal to the first fraction. Let us analyze an example,

2/7=(2/7) x (6/6)=12/42

We know that when we multiply any number by 1, the number remains unchanged. We also know that 6/6=1. So, if we replace 1 with 6/6, we get 12/42. Which is equivalent to 2/7.

4/10=(4/10) x (2/2)=2/5

Similarly, if we divide the top and bottom numbers of a fraction with the same value, we will get a fraction that will be equivalent to the starting fraction.

This is called simplifying the fractions!

(54) Combining Like Fractions: Combining fractions with equal denominators is easy, these fractions are also called the like fractions. To combine these fractions, keep the denominator the same and combine the numerator. For example,

2/5+1/5=(2+1)/5=3/5

7/8-3/8=(7-3)/8=4/8

In the above examples, we had fractions with the same denominator, and to solve them we just needed to combine the numerator. Sometimes, we can also simplify the answer, for instance,

4/8=4/8 ÷ 4/4=1/2

(55) Combining Unlike Fractions: Combining fractions with unequal denominators is a little tricky. Here, we need to replace the fraction with the unlike denominator with the fraction where the denominator is the same. Let us understand this with a few examples,

2/5+7/15

We can see these fractions have unlike denominators. Let us simplify them such that they have a common denominator.

2/5 x 3/3=6/15

Now, we can combine them.

6/15+7/15=13/15

Let us see another example:

-3/7+5/14

We notice that

-3/7 x 2/2=-6/14

Now, we can combine them.

-6/14+5/14=-1/14

Addition of numbers by using different tricks.

If a math teacher asks you to subtract some of the numbers in a few hours. What will you do? Are you thinking of using a calculator? This will not sharpen your brain. Here we will learn how to add major numbers in a few seconds.

First I would like to ask you to practice the simple calculation or sum of one digit numbers. That is,

To use the simple method that you do not need to go over 10. Let see some examples,

Keep in mind that the sum should not exceed 10.

Here dot means the 1 carry forwarded. Now start from the right hand, the sum of 9 and 9 will be 18 so 1 will be forwarded to the next number and a dot will be formed as shown in figure. The remaining amount is 8 and then 1 will be added to the remaining. The sum of 8 and 1 will be, 8+1 = 9 then add 9+3=12. Here again the count exceeds 10. So a point will be marked at the head of 1 as shown in figure. The 2 will be written at unit position.

Now process the tenth position sum. 8+6 = 14 and also the dot represents 1 so the total will be 8+6+1 = 15, here again the limit exceeds 10 so a dot will be replaced before 6 as shown in figure. Keep the 5 in hand and then add 7 into 5, that is 5+7 = 12, a dot will be placed before 7 and 2 will get added with 1 and dot, that is, 2+1+1 = 4.

Now for the hundredth position, we have 2 dots, which means 1+ 1 = 2. Place the 2 at hundredth position.

(57) Addition of 5 digits number:

Take two numbers of five digits 25045 and 97854. Now we are adding these digits as we did it before and the addition is as follows,

Here a sum can be seen easily, we are going to discuss the sum of the position of the thousandth place. Here the sum of 7 and 5 is 12 and it exceeds 10 so a dot will be placed at the head of 9. Now add the number 9+2+1(dot) = 12 here the sum again exceeds 10 so the dot will be placed before 9 and at the head of zero as shown in figure above. And 2 will be placed at ten thousandth position.

At the position of hundred thousandth there is only one dot so the sum will be 1 at the place of hundred thousandth place.

(58) Addition of 10 numbers of 7 digits:

This example will be toughest if added with the help of a traditional way. But it will be easier if it is tried with the above method.

Here the sum and the dot pattern can be seen as it was explained before. With the help of this method the major sum can be completed in a few seconds and the necessity of a calculator can be reduced.

What else do you think you should do to improve at math?

Sometimes, tricks and tips work great, but several times, you can be in urgent need of help! That’s when you need assistance from those who are pretty expert at handling your on-the-spot questions.

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