Welcome to our explanation of long division. Long division is a step-by-step method for dividing large numbers into smaller parts. It breaks down complex division problems into a series of simpler steps. For example, when dividing 735 by 24, we can use long division to find the answer of 30.625. The long division format helps us organize our work and solve the problem systematically.
Let's go through the steps of long division using our example of 735 divided by 24. First, we divide the first digit or digits of the dividend by the divisor. Since 7 is less than 24, we take the first two digits, 73, and divide by 24. 73 divided by 24 is 3, so we write 3 above. Next, we multiply this quotient by the divisor: 3 times 24 equals 72. Then we subtract 72 from 73, giving us 1. We bring down the next digit, 5, to get 15. We repeat the process: 15 divided by 24 is 0 with a remainder of 15, so we write 0 in the quotient. To continue, we add a decimal point and bring down a 0. Now 150 divided by 24 is 6 with a remainder of 6.
Let's examine our division example in more detail. In step 1, we look at the first digits of 735. Since 7 is less than 24, we consider 73. Dividing 73 by 24 gives us 3 as the quotient. In step 2, we multiply this quotient by our divisor: 3 times 24 equals 72. For step 3, we subtract 72 from 73, giving us 1, and then bring down the next digit, 5, to form 15. In step 4, we divide 15 by 24. Since 15 is less than 24, our quotient is 0 with a remainder of 15. To continue the division, we add a decimal point and bring down a 0, making 150. Dividing 150 by 24 gives us 6 with a remainder of 6. The final answer is 30.625.
Let's look at another example: 1247 divided by 16. First, we divide 12 by 16. Since 12 is less than 16, we need to use the first two digits, 12. But 12 is still less than 16, so we use 124. 124 divided by 16 is 7 with a remainder. We multiply 7 by 16 to get 112, and subtract from 124 to get 12. We bring down the next digit, 7, to get 127. Dividing 127 by 16 gives us 7 with a remainder of 15. To continue, we add a decimal point and bring down a 0. 150 divided by 16 is 9 with a remainder of 6. So our answer is 77.9 with a remainder of 6, or 77.9375. Remember these tips: estimate your quotient before dividing, check your work by multiplying, and adjust your quotient if your subtraction gives a number larger than the divisor or a negative number.
To summarize what we've learned about long division: Long division is a systematic method that breaks complex division problems into simpler steps. The process follows a clear approach: divide, multiply, subtract, bring down, and repeat until complete. This technique works for any division problem, including those with decimals and remainders. With practice, long division becomes an essential mathematical skill that helps solve a wide range of problems. Remember that estimation and checking your work are important parts of the process to ensure accuracy.