Let's work first with your particular numbers. Suppose that an item is originally priced at 100 (dollars). Imagine that you inrease the price by $x$ percent. Then the new price is $100+x$. You want to make sure that if you apply a 20 percent discount to this new price $100+x$, you end up with a price of exactly $100$ dollars. A $20$ percent discount on a price of $100+x$ means that the price will be $80$ percent of $100+x$. So the new price is $$(100+x)\frac{80}{100}, \qquad\text{or equivalently,} \qquad \frac{(100+x)(80)}{100}$$ It so happens that you want this new price to be $100$ dollars. This gives you the equation $$\frac{(100+x)(80)}{100}=100.$$ You would like to "extract" $x$ from this equation. First multiply both sides by $100$. On the left, you get simply $(100+x)(80)$. On the right, you get $(100)(100)$, which is $10000$. So our new equation is $$(100+x)(80)=10000.$$ So something, namely $100+x$, multiplied by $80$, is $10000$. What is the something? The idea is to divide both sides by $80$. On the left, you get $100+x$. On the right, you get $10000/80$. By calculator or by hand division, you get that $10000/80=125$. So our new equation is $$100+x=125.$$ Now subtract $100$ from both sides. We get $$x=25.$$ This tells you that you must apply a $25$ percent markup so that a $20$ percent discount will leave the price unchanged. This may look long, but that is only because I have done the calculations in great detail. Note Since we are dealing with percentages, the answer is independent of the actual initial price, which for simplicity we took to be $100$. Let's use the same reasoning to solve a different and harder problem. You want the final discount to be say $17$ percent. Let us ask what percent markup there should be so that at the end, after the discount, you end up selling the originally $100$ dollar item for $105$ dollars. The process will be almost exactly the same, except that the numbers will be a lot uglier, so you will have to use a calculator. Let the desired markup be $x$ percent. Then the price is $100+x$. You want to apply a $17$ percent discount to that. So the new price would be $83$ percent of $100+x$. You want this new price to be $105$. So $83$ percent of $100+x$ is $105$. That gives you the equation $$\frac{(100+x)(83)}{100}=105.$$ You want to extract $x$ from this equation. The procedure is in outline much the same as before. First multiply both sides by $100$. So our new equation is $$(100+x)(83)=10500.$$ Now divide both sides by $83$. We will not get a simple integer on the right, so I will round off, and sloppily still write "$=$" when I mean almost equal. If you are following this with a calculator, you should get something like $$100+x=126.506.$$ Now, like before, subtract $100$ from both sides. We get $$x=26.506.$$ Of course this is absurd precision. For all practical purposes, the markup should be $26.5$ percent. I hope there is enough detail in the above calculations to enable you to solve problems of the same general kind with not much difficulty.
 Welcome to the our Reverse Percentages Calculator. Here you will our reverse percentage calculator which will help you to find the original number before a percentage increase or decrease. Our calculators will not only find the original numbers, but also show you all the working out along the way! Reverse Percentages Calculator 2
Read on below if you want to find out how to solve reverse percentage questions without the calculators. Reverse percentages are used when the percentage and the final number are given, and the original number needs to be found.
Step 1) Get the percentage of the original number. If the percentage is an increase then add it to 100, if it is a decrease then subtract it from 100. Step 2) Find 1% of the missing number by dividing the final number by the percentage from Step 1) Step 3) Find 100% of the missing number by multiplying the result from Step 2) by 100.
Step 1) The percentage of the original number is 35% Our percentage equation is 35% of ? = 320 Step 2) So 1% of ? = 320 ÷ 35 = 9.1429 (to 4dp). Steo 3) 100% of ? = 9.1429 x 100 = 914.29 (to 2dp) Answer: the original number was 914.29 to 2dp. You can use calculator 1 to solve this problem. Example 2) A car is reduced by 20% in price to $40,000. What was the original price?Step 1) The percentage of the original number is 100% - 20% = 80% Our percentage equation is 80% of ? = $40,000 Step 2) So 1% of ? = $40,000 ÷ 80 = $500 Step 3) 100% of ? = $500 x 100 = $50,000 Answer: the original car cost $50,000 You can use calculator 2 to solve this problem. Example 3) Sally invests money in some shares. Five years later, she sells them for $7200 at a profit of 25% of their original value. How much did she spend on the shares?Step 1) The percentage of the original number is 100% + 25% = 125% Our percentage equation is 125% of ? = $7200 Step 2) So 1% of ? = $7200 ÷ 125 = $57.60 Step 3) 100% of ? = $57.60 x 100 = $5760 Answer: the amount she spent on shares was $5760. You can use calculator 2 to solve this problem. Example 4) Tyger buys a mountain bike. Three years later, he sells it for $675 which is 45% of its original value. How much did he pay for the bike originally?Step 1) The percentage of the original number is 45% Our percentage equation is 45% of ? = $675 Step 2) So 1% of ? = $675 ÷ 45 = $15 Step 3) 100% of ? = $15 x 100 = $1500 Answer: the amount he paid for the bike was $1500. You can use calculator 1 to solve this problem. Take a look at some more of our resources similar to these.
Our online percentage practice zone gives you a chance to practice finding percentages of a range of numbers. You can choose your level of difficulty and test yourself with immediate feedback!
This is the calculator to use if you want to find a percentage of a number. Simple choose your number and the percentage and the calculator will do the rest.
If you need to find the percentage increase/decrease between 2 numbers, then this calculator is the one you need. Simple input the original number, then the new number and the calculator will tell you the percentage increase or decrease.
If you need to convert a percentage to a fraction - either a decimal fraction or a fraction in its simplest form, then use this calculator. You can also use the fraction to percentage calculator for converting any fraction into a percentage. This calculator takes a percentage and converts it at the click of a button.
We have a wide range of free math calculators to help you. Most of our calculators show you their working out so that you can see exactly what they have done to get the answer. Our calculator hub page contains links to all of our calculators!
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The Math Salamanders hope you enjoy using these free printable Math worksheets and all our other Math games and resources. We welcome any comments about our site or worksheets on the Facebook comments box at the bottom of every page. Page 2
Welcome to our 2 Digit Multiplication Worksheets page. We have plenty of worksheets on this page to help you practice the skills of multiplying 2-digit numbers by 1 or 2 digits.
We have split the worksheets on this page into two sections:
Each section ends with some trickier challenge sheets for more able students. Within each section, the sheets are carefully graded with the easiest sheets first.
These sheets are aimed at 3rd graders. Sheets 1 to 4 consists of 15 problems; sheets 5 and 6 consist of 20 problems. Sheets 1 and 2 involve multiplying 2-digit numbers by 2, 3, 4 or 5. Sheets 3 to 6 involve multiplying a 2-digit number by single digit numbers and finding increasing trickier products.
These 2-digit multiplication worksheets have been designed for more able students who need that extra challenge!
These sheets are aimed at 4th graders. Sheet 1 involves 2-digit by 2-digit multiplication with smaller numbers and answers up to 1000. Sheets 2 to 4 have harder 2-digit numbers to multiply and answers that are generally larger than 1000.
These 2-digit multiplication worksheets have been designed for more able students who need that extra challenge!
We have more 2-digit multiplication worksheets, including 2-digit x 3-digit multiplication problems on this page.
Take a look at some more of our worksheets similar to these.
Need to create your own long or short multiplication worksheets quickly and easily? Our Multiplication worksheet generator will allow you to create your own custom worksheets to print out, complete with answers.
Here you will find a range of Multiplication Worksheets to help you become more fluent and accurate with your tables. Using these sheets will help your child to:
All the free 3rd Grade Math Worksheets in this section are informed by the Elementary Math Benchmarks for 3rd Grade.
Here you will find a range of Free Printable Multiplication Games to help kids learn their multiplication facts. Using these games will help your child to learn their multiplication facts to 5x5 or 10x10, and also to develop their memory and strategic thinking skills.
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The Math Salamanders hope you enjoy using these free printable Math worksheets and all our other Math games and resources. We welcome any comments about our site or worksheets on the Facebook comments box at the bottom of every page. |
When a value is increased by 20% by what percent should it be reduced to get the actual value?
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