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# 30 Simple Algebra Tricks for Students

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### 30 Simple Algebra Tricks for Students

1. 1. 30 Simple Algebra Tricks for Students Algebra is one of the most important topics in mathematics and without algebra, perhaps our understanding of mathematics wouldn’t at the present state. But, on the other hand, algebra is also a tough topic and many students can find it impossibly difficult to master. But the truth is algebra can actually be practiced vary easily, of course with few tricks at hand. Here are some algebra tricks for students who want to master algebra without any fuss. Basic rules of algebra: For solving problems in algebra easily, first you need to know and remember some rules of algebra. These rules are the most important rules and it can be very hard to learn algebra without the knowledge of these rules. Addition across the equal sign: In an equation with + symbol, when you transfer the number to the other side of the equation the + becomes -. For ex: if x+9 = 7, finding x would be send 9 to the other side of the equation. Now, 9 here is positive with x, but when it is transferred to 7 the sign changes from plus to minus. In other words, x = 7-9 which is -2. And the answer is x= -2. Subtraction across the equal sign: Now, in the same way + symbol once transferred becomes -, when a number with – sign is transferred to the other side of the equation, it becomes + or positive. Taking the above example, if x-9 = 7, then in order to find x, you need to send -9 to the other side. As soon as you do that -9 gets converted to +9 and it changes the whole equation. This time, it is 7+9 = 16 and x = 16. Multiplying across the equal sign: Just as in the above rule of addition and subtraction, even multiplication has its own rule. In an equation with multiplication, when you send the number to the other side, then multiplication would become division sign. For ex: if 3x = 9, find x. So, you simply send the 3 in 3x to the other side, ie., x = 9/3 = 3. Hence, x = 3. Dividing across the equal sign: In the same way, when multiplication is changed to division sign, division sign when transferred also changes to multiplication sign. Using the same example, if x/3 = 9, find x, we can see that x/3 = 9, hence x = 9 × 3 = 27. Substituting negative signs: In an equation, if there is a negative number, then immediately it gives a shocker to many and the confusion starts. To avoid this, all you need to do is to turn all the negative signs into positive signs for easy calculation. This change will not affect the answer because, negative and negative is positive anyways. For example: If you find an equation like -3x +4 -12x2 - 10x3 = -15. All you need to do is to multiply the whole equation with -1. Now, the equation would be 3x -4 + 12x2 + 10x3 = 15. This equation would be easier to solve.
2. 2. Changing signs: In algebra, one of the very fundamental things to remember while solving equations is that when numbers are moved back and forth between the equation, the signs of the numbers will also change. For example, if you want to solve 3x-10 = 8 and find x. Now, most people, get 10 to the other side of the equation but get little confused about -10. First thing, you don’t need to worry because, when change the position of the number from one side to the other side of the equation, the sign should automatically change. So here, 3x = 10+8 = 18, x = 18/3 or 6. Note: The sign changing is only when there is any addition or subtraction involved in the step. For multiplication or division, the signs wouldn’t change. Cross-multiplication: Cross-multiplication is another trick that is easier to master and it can reduce the time taken to solve the problem in just few seconds. For ex, if you have a fractional equation like 12x/6 = 20/2x. Normally, you would solve this equation as 6 × 12x/6 = 6 × 20/2x 12x = 120/2x 12x ×2x = 120 24x2 = 120 These steps are long process, but cross-multiplication is an easy and accurate way out. Here’s how. 12 6 = 20 2 . Imagine that you have a big multiplication symbol in place of the equal sign. And now multiply the numerator of one fraction by the denominator of the other fraction. Here’s what you’ll get. 6 × 20 = 120 and 12x × 2x = 24x2 Or 24x2 = 120. By, using this step, you can save around 2 minutes to solve each equation. Easy squares: You can easily find the square of a number with a simple calculation and thus avoid the long process which is very time consuming. For this trick, you need to know where the number lies in terms of nearest multiple of 10. For ex: to find the square of 63, you need to know that 63 is 7 less than 70. So, (63+7) (63-7) + (7× 7) = 70 × 56 + 49 = 3920 + 49 = 3969. Now, while calculating 70×56, you can eliminate the 0 in 70 and add the 0 later on. This makes it easier to calculate. Squaring a 2 digit number ending with 5: Here’s another trick which can save your time while finding the square of a two digit number ending with 5. Here’s how. For square of 25, you need to take 2, add 1 to it, which is 3. Now, multiply 2 and 3 ie 6 and just write 25 beside it. Try 552 . 5×(5+1)and 25 = 5×6 and 25 which is 3025, the answer.