Likewise, three fifths minus two fifths is one fifth. For instance, adding one third and one third obviously gives us two thirds. In cases that involve simple numbers, addition and subtraction of fractions is easy enough. Now that we have developed a solid foundation regarding what fractions are as well as some different types of fractions, we can now turn to application of the basic arithmetic operations (addition, subtraction, multiplication, and division) to fractions. O Recognize and simplify complex fractions O Understand how to interpret fractions that involve negative numbers Before your proceed though, make sure you fully understand the four basic mathematical operations: adding, subtracting, multiplying and dividing. We'll also introduce complex fractions along with methods for simplifying them. In this article, we will review how to add, subtract, multiply, and divide two fractions as well as a fraction and an integer. In our example, we have 15 parts, with each whole circle being split into quarters.Before you can go on to master more advanced concepts in algebra and geometry, you need to first master all mathematical functions relating to fractions. Remember, we need to find out how many whole circles we have when we split them into quarters, and also determine if there are any fractions left over. Perhaps the easiest way to do this is with circles because they act as a great visual aid. So, now we just need to work out how many wholes and fractions we have in their simplest form. The numerator is telling us that we have 15 parts altogether, or 15 quarters. In our example, the denominator is telling us that the whole is split into 4 equal parts, known as quarters. However, in the real world, we tend to use mixed numbers more often, so it’s helpful to know how to convert it. In fact, many mathematicians prefer to use them over mixed numbers (a whole number and a fraction). There is nothing wrong with improper fractions. Now, this is an improper fraction because the numerator is larger than the denominator. So, basically, our denominator stays the same. We have already changed our whole number into a fraction, so we know that our calculation for the denominators is 1 x 4, which equals 4. Then, you can multiply your numerators together, just as we did above. This can easily be achieved by using your number as the numerator and adding 1 as the denominator (the denominator in any whole number is always 1). The first step is to turn your whole number into a fraction. This still looks a bit complicated, doesn’t it? Luckily, we can make the calculation simpler. Here, we need to group the fractions 5 times, which would look like this: Let’s say you have an equation that has both a whole number and a fraction. Multiply the numerator with the whole number Now, let’s find out how to multiply a fraction by a whole number.ġ. So, now we know the answer to our original equation in its simplest form: Simplify the product in the lowest formĢ/12 still looks like a complicated fraction, doesn’t it? Luckily, we can simplify it! All you have to do is divide the numerator and the denominator by the greatest common factor (number) that can divide into both numbers exactly. Then, we can put both of our answers together as their own fraction. In the example above, this would work out as: Now, you need to multiply the bottom numbers together, known as denominators. The first step to multiplying these fractions is to multiply both numerators. So, in this example, they would be 1 and 2. The numerators are the numbers at the top. Say you have a simple fraction calculation to work out. Mixed fractions - The combination of a whole number and a fraction.Improper fractions - Where the numerator is larger than the denominator.For example, ½ would be a proper fraction. Proper fractions - Where the numerator of a fraction (top number) is lower than the denominator (bottom number).Product - The answer to a multiplication problemįurthermore, there are three main types of fractions that you need to be aware of:.For example, you would multiply two factors to get the answer. Factor - A number that’s being multiplied in the calculation.Denominator - The bottom number in a fraction.Numerator - The top number in a fraction.The trick is to separate the bottom numbers and the top numbers of fractions into two different equations.īefore we dig into the steps involved in solving a fraction multiplication problem, it’s helpful to understand some of the terminology that’s commonly used: The calculations are slightly different between problems that multiply fractions by whole numbers and those that multiply fractions together. The result can either be a whole number or another fraction. Similarly, when you multiply fractions, you are grouping fractions. When multiplying whole numbers, we are adding groups of the same number.ģ×4 works out as 3+3+3+3 which equals 12.
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