Welcome to our lesson on division. Division is one of the four basic arithmetic operations, and it's the inverse of multiplication. When we divide, we're splitting a number, called the dividend, into equal parts based on another number, called the divisor. The result is called the quotient, and sometimes there's a leftover amount called the remainder. In this example, we have twenty divided by four equals five. We can visualize this as twenty squares arranged in four columns, with five squares in each column.
Now, let's look at division with a remainder. When the divisor doesn't divide the dividend evenly, we have a leftover amount called the remainder. The relationship can be expressed as: Dividend equals Divisor times Quotient plus Remainder. For example, seventeen divided by four equals four with a remainder of one. We can visualize this as sixteen squares arranged in four equal groups of four, plus one extra square representing the remainder. This can be written as seventeen equals four times four plus one.
Now, let's learn about the long division method, which is a standard algorithm for dividing large numbers. Let's work through an example of dividing 128 by 3. First, we divide the first digits, 12, by 3, which gives us 4. We write 4 above the division symbol. Next, we multiply 4 by 3, which equals 12, and write this below the 12 in our dividend. Then we subtract 12 from 12, giving us 0. We bring down the next digit, 8, to get 8. We divide 8 by 3, which gives us 2 with a remainder of 2. So our final answer is 42 with a remainder of 2.
Now, let's look at division with decimals. When the divisor is a decimal, we can simplify the calculation by multiplying both the dividend and divisor by the same power of 10 to make the divisor a whole number. For example, to divide 24.6 by 0.3, we multiply both numbers by 10, converting the problem to 246 divided by 3. Then we perform the division as usual. First, 24 divided by 3 is 8. We multiply 8 by 3 to get 24, subtract from 24, and get 0. Next, we bring down the 6, divide 6 by 3 to get 2, multiply 2 by 3 to get 6, subtract from 6, and get 0. So our answer is 82.
To summarize what we've learned about division: Division is the process of splitting a number, called the dividend, into equal parts based on another number, called the divisor. The result is called the quotient, and any leftover amount is called the remainder. The relationship can be expressed as: Dividend equals Divisor times Quotient plus Remainder. We've also learned about the long division method for dividing large numbers, and how to handle division with decimals by converting the divisor to a whole number. These division skills are fundamental in mathematics and are used in many real-world applications.