Starting with the ones digit of the bottom number, the multiplier, multiply it by the last digit in the top number Long multiplication with decimals using the standard algorithm has a few simple additional rules to follow. Long multiplication means you're doing multiplication by hand. The traditional method, or Standard Algorithm, involves multiplying numbers and lining up results according to place value. These are the steps to do long multiplication by hand: Use long addition to add your number columns from right to left, carrying as you normally do for long addition. The first multiple they all share is 12, so this is the least common multiple. To complete an addition (or subtraction) problem, multiply the numerators and denominators of each fraction in the problem by whatever value will make the denominators 12, then add the numerators. EX:

Change in percentage points (pp): The difference between two percentage values. If one value is 10 % and the other is 30 %, the change is 20 percentage points (20 pp). Let's go the other way around and try to find the numerator. Say we know that 70 percent of fruits in the basket are apples, and there are 30 fruits altogether. It could be worse — they could be lemons. So how many apples do we have? Let's get our percentage formula: 100 × numerator / denominator = percentage. We want to find out the numerator. Let's move all the other parts of the equation to the other side. Divide both sides by 100 (to get rid of 100 on the left) and then multiply both sides by the denominator. This is what we get: numerator = percentage × denominator / 100. Let's substitute percentage and denominator with our values: numerator = 70 × 30 / 100. Now it's easy: numerator = 2100 / 100 = 21, we have 21 apples. Should be enough for lunch or a rather violent food fight. Insert a decimal point in the product so it has the same number of decimal places equal to the total from step 1.An alternative method for finding a common denominator is to determine the least common multiple (LCM) for the denominators, then add or subtract the numerators as one would an integer. Using the least common multiple can be more efficient and is more likely to result in a fraction in simplified form. In the example above, the denominators were 4, 6, and 2. The least common multiple is the first shared multiple of these three numbers. Multiples of 2: 2, 4, 6, 8 10, 12 The term percent is often attributed to Latin per centum, which means by a hundred. Actually, it is wrong. We got the term from Italian per cento — for a hundred. The percent sign % evolved by the gradual contraction of those words over centuries. Eventually, cento has taken the shape of two circles separated by a horizontal line, from which the modern % symbol is derived. The history of mathematical symbols is sometimes astonishing. We encourage you to take a look at the origin of the square root symbol! As a unit of area, it has a magnitude equivalent to the area of a square with sides of 1 foot. This size makes it helpful to talk about the area of everyday objects such as a house (typically 500-1000 sq ft), a room (~100 sq ft) and even an A4 piece of paper (0.65 sq ft) without having to use either very big or very small numbers. There exist, obviously, other units of area that can express the same magnitude as the sq ft and might even be more suitable for very small objects (like the square inch), very big objects (like the acre), or to simply to communicate with the rest of the world by using the standardized SI/Metric units (whose default unit of area is the square meter).

Proceed right to left. Multiply the ones digit of the bottom number to the next digit to the left in the top number. If you carried a digit, add it to the result and write the answer below the equals line. If you need to carry again, do so. Change in percentage: The relative change between two percentage values. If one value is 10 % and the other is 30 %, the change is 200 % of the original 10 %. Similarly, fractions with denominators that are powers of 10 (or can be converted to powers of 10) can be translated to decimal form using the same principles. Take the fraction 1 Converting from decimals to fractions is straightforward. It does, however, require the understanding that each decimal place to the right of the decimal point represents a power of 10; the first decimal place being 10 1, the second 10 2, the third 10 3, and so on. Simply determine what power of 10 the decimal extends to, use that power of 10 as the denominator, enter each number to the right of the decimal point as the numerator, and simplify. For example, looking at the number 0.1234, the number 4 is in the fourth decimal place, which constitutes 10 4, or 10,000. This would make the fraction 1234 The percentage tells you how number A relates to number B. A real-world example could be: there are two girls in a group of five children. What's the percentage of girls? In other words, we want to know what's the ratio of girls to all children. It's 2 out of 5, or 2/5. We call the first number (2) a numerator and the second number (5) a denominator because this is a fraction. To calculate the percentage, multiply this fraction by 100 and add a percent sign. 100 × numerator / denominator = percentage. In our example, it's 100 × 2/5 = 100 × 0.4 = 40. Forty percent of the group are girls. That's the entire procedure of converting between decimal fractions and percentages.A percentage is also a way to express the relation between two numbers as a fraction of 100. In other words, the percentage tells us how one number relates to another. If we know that number A is 25% of number B, we know that A to B is like 25 is to 100, or, after one more transformation, like 1 to 4, i.e., A is four times smaller than B. This is what the percentage calculator teaches; what is a percentage and how to find a percentage of two numbers. This process can be used for any number of fractions. Just multiply the numerators and denominators of each fraction in the problem by the product of the denominators of all the other fractions (not including its own respective denominator) in the problem. EX: When a is a fraction, this essentially involves exchanging the position of the numerator and the denominator. The reciprocal of the fraction 3 the decimal would then be 0.05, and so on. Beyond this, converting fractions into decimals requires the operation of long division.