Math is a very interesting and innovative subject, we start learning it from a very young age and use it all our lives. The secret to metal math can be understood when you want to solve questions much faster and efficiently. This can be applied for both the students and tutors. Often we wonder why the same question is solved by different people in different ways. This is the beauty of math, there are many ways and approaches to get to the same answer. One method can take more time and many steps whereas another method can take less time and fewer steps to reach the final answer. The thing to realize here is all the different approaches are right and you can follow which ever method best suits your ability to understand the given question.
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Let us now take a look at some mental math tricks which will help you while solving different math homework help questions.
While changing the percentages to fractions, divide by 100 and for changing a given fraction to percentage multiply by 100. Here are some examples:
Betty went to trekking with her friends. She drank 75% of the protein shake she brought with her after trekking for 3 hours. What fraction of the protein shake does she have left?
For the above question we are given that 75% of the protein shake is finished. This implies the remaining amount is equal to 100% – 75% = 25%.
Therefore, the amount of protein shake Betty has = 25%. For converting the given percentage into a fraction divide by 100. Hence Betty still has 1/4 of the protein shake remaining during her trekking.
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Did you find the example quite interesting? Now let us look at another example for changing fractions to percentages.
Samuel finished 1/5 of his homework. What percentage of his homework is still to be completed?
Here you are given that 1/5 of the homework is completed. This implies the amount of homework to be completed is 1 – 1/5 = 4/5.
Now for converting the fraction into a percentage multiply by 100. Follow the diagram given below and try to visualize the calculations mentally:
This method mentioned above is very useful because percentage are used almost in every branch of mathematics. Let us look at some quick applications of what we have just learned:
Percentage to fraction:
The above examples are for percent to fractions which can be quickly solved in your mind. Practice similar questions to realize how you will become much faster and efficient in your calculations.
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Fractions to percent: Below examples are for quick conversion from fractions to percentages. After the percentages, let us take a look at how the fractions can be changed to decimals. Do you feel you already know them? Well remember, we are trying to learn the metal math. Here is how you can convert them in your mind. Take a look at the following questions:
Fractions to decimals: Change the fraction 2/5 into a decimal number. Here the given fraction is 2/5. The mental math trick is, for changing any given fraction to decimal number try to have 10 or multiples of 10 in the denominator. Multiply the numerator and denominator if the fraction 2/5 by 2. Follow the diagram below: Did you follow the method? This trick has limitation though it can only be applied to the numbers which get 10 or multiples of 10 in the denominator via multiplication. Let us look at more examples to perfect this method.
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Convert 7/25 into a decimal number.
Look at the denominator here its 25, which can be changed to 100 on multiplication by 4. Hence multiplying and diving the given fraction by 4. Follow the diagram below, this needs to be visualized mentally.
Therefore the fraction 7/25 can be written as 0.28 in the decimal form.
Let me share another branch of math, Algebra where mental math tricks can be applied.
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Adding the exponents: Combine the expression 3x4 (x5) Here for the given expression we have multiplication between the same variable x which needs to be combined. Since the base variable is the same for the given exponents add the powers. Here is the rule: Subtracting the exponents: Combine the expression 2x11/ x9. Here for the given expression we have division between the same variable x which needs to be combined. Since the base variable is the same for the given expressions subtract the exponents of x. Here is the rule: Multiplying the exponents: Combine the expression (x3)5? Here for the given expression we can combine exponents of the variable x by multiplying since they are raised to the same base. Follow the diagram below:
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Therefore, today we looked through different methods and examples for solving math mentally. Use these methods to solve different questions whenever and wherever applicable. For more info you can chat with live math tutor online and get your math assignment help from amazing math tutors.