Question

Divide. Divide 856 by 29

Short answer

856 ÷ 29 = 29 remainder 15

Step-by-step solution

Setup the Division

Firstly, write the division problem in long division format. This means placing 856 under the division symbol, and 29 outside of it. This setups up the division problem 856 ÷ 29.

Divide, multiply, subtract and bring down

Divide the leftmost number of the dividend, 8, by 29. Since 8 is smaller than 29, we have to consider the next digit, 5. We have now 85. Still, 85 is smaller than 29, so we consider the next digit, 6, getting 856. Now, divide 856 by 29. This equals to about 29. Multiply 29 by 29 and get 841. Write this below 856 and subtract to get 15, which is the remainder.

Write the Answer

So, 856 divided by 29 gives 29 remainder 15. In decimal form, you could continue the division to obtain a decimal.

Key concepts

Dividing Large Numbers

Long division is a method used to divide large numbers that can't be easily handled with simple mental arithmetic or short division. When dividing 856 by 29, the numbers are quite large, and a systematic approach is necessary to ensure accuracy.

In practice, you start by comparing the size of the number you're dividing (the dividend) with the number you're dividing by (the divisor). You must find how many times the divisor can fit into the dividend without exceeding it. This process can be challenging when dealing with large numbers like in our example, which is why long division is a valuable tool. It helps break down the complex problem into more manageable pieces.

Remember, correctly setting up the problem is vital. Writing the dividend and divisor in the right places will help prevent common mistakes. This step-by-step approach, employed in long division, ensures that large numbers are dealt with systematically and efficiently.

Division with Remainder

When dividing numbers, you'll often encounter a situation where the divisor does not perfectly divide the dividend. The division with remainder becomes a critical concept to understand this scenario. Taking our example, when you divide 856 by 29, after extracting as many full sets of 29 from 856, we're left with some amount that doesn't make a full set. This amount is called the 'remainder'.

In the problem presented, the long division process reveals that 29 goes into 856 a total of 29 times with a leftover, or remainder, of 15. This means that although 29 sets of 29 fit into 856, there are an extra 15 units that can't be divided by 29 to form another whole set. Remainders are an integral part of understanding division as they indicate the part of the dividend that is too small to be divided by the divisor.

Long Division Steps

Long division is a multi-step process that can be broken down into several key steps for clearer understanding and execution. Following the problem of dividing 856 by 29, let's review the critical long division steps.

The first step is setting up the division correctly with the dividend under the division bar and the divisor outside. Then you look at the dividend, starting from the left, to find the first number or combination of numbers that the divisor can divide. In our example, you combine the first and second digits to get 85, as 29 doesn't fit into 8.

Next, you divide, multiply, subtract, and finally, bring down the next digit of the dividend. Continue this cycle until you have brought down all digits of the dividend. If there's a remainder that can't be divided fully, as in our case, we're left with the number 15, that becomes the remainder of the division.

Key Takeaway

It's important to follow these steps methodically, ensuring each operation—dividing, multiplying, and subtracting—is performed accurately. By practicing these steps, students can gain confidence and precision in handling division problems with large numbers and remainders.