Multiplication is the third basic math operation. When you multiply two numbers, this is the same as adding the number to itself as many times as the value of the other number is. Think of it like this: You have 5 groups of apples and each group has 3 apples. One of the ways you can find out how many apples you have is this one:. You can see that it is way too much work especially if you have larger numbers , so you can use multiplication to solve this problem:.
In the other words, the expression of multiplication signifies the number of times one number is multiplied by another number. Division is the fourth basic math operation. Basically, you can say that dividing means splitting objects into equal parts or groups.
For example, you have 12 apples that need to be shared equally between 4 people. So, how many apples will each person get? The division is the opposite of multiplication:. The basic math operations are addition, subtraction, multiplication, and division. Depending on the directions for the math problem, you may see different words:. In mathematics when you perform computational actions, you must have in mind that there is a sequence that need to be respected in order to do calculations properly.
Addition and subtraction are first degree mathematical operations. They are part of the same step, however, they can only be done after items in parentheses, exponents, and any multiplication and division. Video Source mins Transcript. Remember to take it one step at a time and rewrite your equation after completing an operation. As you are beginning to see, we are using multiplication a lot in these lessons and they will be easier if you know your multiplication.
There are various steps in the order of operations. Use only the steps required to solve this problem. There are various steps in the Order of Operations. Use only the steps required to solve this particular problem. Replace the previous exponents in the problem with the answers 16 and 8 respectively. Now, solve any multiplication or division from left to right. Subtraction is the opposite of addition. Instead of adding two quantities numbers , we are removing one quantity from another.
Thus, if we have nine squares and take away subtract five, we are left with four squares. Using just the numbers, where the minus sign — represents the subtraction operation,. Here, 9 and 5 are the terms of the operation, and 4 is the difference. Unlike addition, subtraction is not commutative. That is to say, 9 — 5 and 5 — 9 are not the same-in fact, they yield quite different results!
The symbol? Negative Numbers. Addition and any other of the basic operations can involve the counting numbers 1, 2, 3, 4, 5, and so on , the number zero 0 , and any number in between fractional values such as a half, for instance. Also, we may encounter negative numbers, which are quantities that are less than zero. If we think of positive numbers as quantities of something that we possess say, for instance, that we have 10 oranges , then a negative number would be a quantity of something that we owe if we owed someone 10 oranges, then we might say that we have negative 10 oranges.
Negative numbers are typically expressed using a minus sign — ; thus, negative 10 can be written as The use of the minus sign is no coincidence-in fact, subtraction is nothing more than addition involving a negative number!
Imagine you have in your possession nine apples positive nine , but you owe a friend four apples negative four. Thus, you take four apples out of the nine that you have, leaving five. Let's say we want to add a particular number, such as six, to itself many times. For instance, a worker at a factory may wish to count the number of parts delivered in several boxes. Each box contains six parts, and there are a total of five boxes.
To find out how many parts he has, the worker must add the number six to itself five times. We can find the sum simply by performing the addition several times over. A shortcut, however, is multiplication.
Imagine the parts in each of the five boxes laid out in rows, as shown below we use a square to represent a part. Each row above represents a box; in each row is six parts. The idea here is that losing a debt is the same thing as gaining a credit. When multiplying positive and negative numbers, the sign of the product is determined by the following rules:. The idea again here is that losing a debt is the same thing as gaining a credit. In this case, losing two debts of three each is the same as gaining a credit of six:.
If the dividend and the divisor have the same sign, that is to say, the result is always positive. The basic properties of addition commutative, associative, and distributive also apply to negative numbers. For example, the following equation demonstrates the distributive property:. A fraction represents a part of a whole and consists of an integer numerator and a non-zero integer denominator. A fraction represents a part of a whole.
The numerator represents a certain number of equal parts of the whole, and the denominator indicates how many of those parts are needed to make up one whole.
An example can be seen in the following figure, in which a cake is divided into quarters:. Quarters of a cake: A cake with one-fourth removed. The remaining three-fourths are shown. Dotted lines indicate where the cake can be cut to divide it into equal parts.
The first rule of adding fractions is to start by adding fractions that contain like denominators—for example, multiple fourths, or quarters. Imagine one pocket containing two quarters, and another pocket containing three quarters.
In total, there are five quarters. Since four quarters is equivalent to one dollar , this can be represented as follows:. To add fractions that contain unlike denominators e.
One easy way to to find a denominator that will give you like quantities is simply to multiply together the two denominators of the fractions. It is important to remember that each numerator must also be multiplied by the same value its denominator is being multiplied by in order for the fraction to represent the same ratio. This method always works. However, sometimes there is a faster way—a smaller denominator, or a least common denominator—that can be used.
What if a fraction is being added to a whole number? The process for subtracting fractions is, in essence, the same as that for adding them. Find a common denominator, and change each fraction to an equivalent fraction using that common denominator.
Then, subtract the numerators. For instance:. To subtract a fraction from a whole number or to subtract a whole number from a fraction, rewrite the whole number as a fraction and then follow the above process for subtracting fractions.
Unlike with addition and subtraction, with multiplication the denominators are not required to be the same. To multiply fractions, simply multiply the numerators by each other and the denominators by each other.
If any numerator and denominator shares a common factor, the fractions can be reduced to lowest terms before or after multiplying. Alternatively, the fractions in the initial equation could have been reduced, as shown below, because 2 and 4 share a common factor of 2 and 3 and 3 share a common factor of To multiply a fraction by a whole number, simply multiply that number by the numerator of the fraction:.
A common situation where multiplying fractions comes in handy is during cooking.
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