Now, since we all have a deeper insight into Percentage,allow me to explain it in greater detail.
To change a fraction to a percentage, simply multiply the denominator and numerator by 100 divided by the denominator, such that it becomes 100. Then, just take the numerator and add a percentage sign behind it for good measure.
For example, take a typical fraction, like 3/4. 100 divided by 4 is 25, thus, we must multiply 3 and 4 by 25, which would give us 75/100. Take the numerator and throw a percentage sign and bingo! 75%.
For the reverse, simply swap the percentage sign for a /100 and simply the fraction.
One example is: 80%. We switch the percentage sign for a /100--->80/100. Finally, we simplify it--->80/100=4/5.
Otherwise, if you wish to change a percentage to a decimal, just take away the percentage sign and place the decimal point two places forward.
Like such, 63%, we take away the "%" sign, get 63, move the decimal point 2 places forward, and achieve our answer---> 0.63.
Again, if you wish to do the opposite, just move the decimal point 2 places backwards and give it a percentage sign in return.
As such: 0.57, move the "." two places back, get 57, present it with a "%", and get your answer--->57%.
Percentage is usually used to express the quantity of something compared to another. For example, a typical percentage question would be: "Jim has 15 apples. Tom has 20 apples. What is the percentage of Jim's apples over Tim's apples?How about Tim's over Jim's?
A)We convert 15/20 to a percentage, as we have learned earlier, and get 75%, which is our answer.
B)Again, we convert 20/15 to a percentage, and get 120%, which is our answer.
However, if the question is phrased like this: "Jim has 20 apples.Tom has 25 apples. How much more percent is Tim's apples than John's apples?
(Notice I have bold-ed and italic-ed "than". )
In any percentage question, this is probably the most crucial word to look out for, something that could change the entire meaning of the question. WHY? Very simple.
In any percentage question, the person who's name is after "than", is the 100% guy, which means that he/she is the one whose quantity or number of something should be converted to 100%, that is, be the denominator. I cannot stress too much how important this is.
For example, in the question above, John is the 100% guy. Thus, we must convert 25 /20 to 125/100= 125%/100% Lastly, we deduct 100% from 125% to get 25%, which is our answer.
Here is the same question phrased differently again:
"Jim has 20 apples.Tom has 25 apples. How much less is the percentage pf John's apples than Tim's?"
Here, Tim is the 100% guy. Thus, we must convert 20/25 to 80/100=80%/100%. Finally, we take away 80% from 100% and get 20%, which is our answer. If we didn't know about the "than", we might have gotten 25%, like our previous answer.
This is a very common mistake that is very costly.
Uses of Percentage
Percentage is often used by merchants, businessman, shop owners and companies that involve services and products to find out the amount of tax or duty they must pay. In Singapore, there is the Goods and Services Tax, also known as the GST. This is the tax that must be paid to the government. It comprises of 7.5% of the product or service.
For example, if a television set costs $800, its GST would be 7.5%X$800, which is $(7.5X8), equals $60. Thus, $60 must be paid to the government. This is essential knowledge as many shops and companies pass on the GST to their consumers, thus, whenver we buy something, its price is actually 107.5% of the original cost. However, there are duty-free shops which absorb this GST and thus you will only pay for only the original cost of the product or service.
Additionally, percentage is utilized to show the discount on a certain product or service. For example, in shopping malls, we often spot large signs saying "All shirts 50% off!" or "Up to 70% discount on jeans!" This signs signifies that the products the shops sell are half its original price and 30% its original price respectively. The price of the shirts is the percentage infront of the word "discount" is subtracted from 100%, then mulitplied by the original cost of the shirt.
Like so: A shirt costs $50. The shop advertises that "All shirts 50% off!".
Thus, Price of Shirt= (100%-50%)X$50= 50%X$50= $25.
Percentage is also used in the stock market and Forex( Foreign Exchange) to determine profit and loss, or increase and decrease. To determine profit or increase in value, take the percentage of the later value minus 100%, then mulitply it by the amount invested. For example, I buy a share in Microsoft for 1 million dollars. Fortunately, Microsoft's shares' value all increase by 12%. Thus, the new value of my share is 112% of my original 1 million.
Hence, my profit is 112% of $1,000,000-100% of $1,000,000=12% of $1,000,000= $120,000.
So, I have earned $120,000. :)
To determine loss or decrease in value, take the 100% minus the later percentage, then mulitply it by the amount invested. Another example is as such: I invest $50,000 of my profit, $120,000, in American Insurance Group(AIG). However, this time my luck runs out; AIG files for bankruptcy days after I complete my investment. Luckily, I had a tip-off that it would flop, thus I quickly sold my share before it collapsed. At that point of time, it was 70% of its original value.
Thus, my loss/decrease in value is 100% of $50,000-70% of $50,000= 30% of $50,000= $7500
Hence, I have lost $7500. :(
To determine loss or decrease in value, take the 100% minus the later percentage, then mulitply it by the amount invested.
Maths Joke:
Q^A Joke:
Q: Why do you rarely find mathematicians spending time at the beach?
A: Because they have sine and cosine to get a tan and don't need the sun!
For example, if a television set costs $800, its GST would be 7.5%X$800, which is $(7.5X8), equals $60. Thus, $60 must be paid to the government. This is essential knowledge as many shops and companies pass on the GST to their consumers, thus, whenver we buy something, its price is actually 107.5% of the original cost. However, there are duty-free shops which absorb this GST and thus you will only pay for only the original cost of the product or service.
Additionally, percentage is utilized to show the discount on a certain product or service. For example, in shopping malls, we often spot large signs saying "All shirts 50% off!" or "Up to 70% discount on jeans!" This signs signifies that the products the shops sell are half its original price and 30% its original price respectively. The price of the shirts is the percentage infront of the word "discount" is subtracted from 100%, then mulitplied by the original cost of the shirt.
Like so: A shirt costs $50. The shop advertises that "All shirts 50% off!".
Thus, Price of Shirt= (100%-50%)X$50= 50%X$50= $25.
Percentage is also used in the stock market and Forex( Foreign Exchange) to determine profit and loss, or increase and decrease. To determine profit or increase in value, take the percentage of the later value minus 100%, then mulitply it by the amount invested. For example, I buy a share in Microsoft for 1 million dollars. Fortunately, Microsoft's shares' value all increase by 12%. Thus, the new value of my share is 112% of my original 1 million.
Hence, my profit is 112% of $1,000,000-100% of $1,000,000=12% of $1,000,000= $120,000.
So, I have earned $120,000. :)
To determine loss or decrease in value, take the 100% minus the later percentage, then mulitply it by the amount invested. Another example is as such: I invest $50,000 of my profit, $120,000, in American Insurance Group(AIG). However, this time my luck runs out; AIG files for bankruptcy days after I complete my investment. Luckily, I had a tip-off that it would flop, thus I quickly sold my share before it collapsed. At that point of time, it was 70% of its original value.
Thus, my loss/decrease in value is 100% of $50,000-70% of $50,000= 30% of $50,000= $7500
Hence, I have lost $7500. :(
To determine loss or decrease in value, take the 100% minus the later percentage, then mulitply it by the amount invested.
Maths Joke:
Q^A Joke:
Q: Why do you rarely find mathematicians spending time at the beach?
A: Because they have sine and cosine to get a tan and don't need the sun!
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