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Chapter 5: Problem 33

Divide. $$71 \div 33$$

Short Answer

Expert verified
2 with a remainder of 5, or approximately 2.15

Step by step solution

01

- Understand the Division

Division involves finding out how many times one number is contained within another number. Here, we need to determine how many times 33 can fit into 71.
02

- Perform the Division

Divide 71 by 33 using long division and note down the quotient and the remainder. 1. 71 divided by 33 is 2 since 33 * 2 = 66.2. The remainder is 71 - 66 = 5.
03

- Express the Solution

Write the answer in the form of quotient with the remainder. The solution will be expressed as a mixed number or a decimal. 2 with a remainder of 5 can be written as \(2 + \frac{5}{33}\) or as a decimal: 2.1515 (where 5 is repeating)

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

What is Division?
Division helps us find out how many times one number can fit into another.
It's like distributing items evenly. The number being divided is called the 'dividend'. The number you divide by is called the 'divisor'.
In our example, 71 is the dividend and 33 is the divisor.
The goal is to see how many times 33 fits into 71 without exceeding it.
Understanding Quotient
The quotient is the result you get when you divide one number by another.
It represents the number of times the divisor fits into the dividend without going over.
In the problem 71 divided by 33, the quotient is 2 since 33 * 2 = 66, which is less than 71.
The leftover part, which we will find next, is the remainder.
The Concept of Remainder
After dividing, sometimes there is a leftover part that doesn't fit evenly.
This leftover part is called the remainder.
To find the remainder, you subtract the product of the divisor and quotient from the dividend.
For example, in 71 divided by 33, the remainder is found as follows: 71 - (33 * 2) = 71 - 66 = 5.
So, the remainder is 5.
Mixed Number Representation
A mixed number combines a whole number and a fraction.
You can use this representation for division results with a remainder.
For 71 梅 33, we got the quotient 2 and the remainder 5, which is written as: 2 + \(\frac{5}{33}\).
In this format, the quotient is the whole number part and the remainder over the divisor forms the fractional part.
Decimal Representation
To convert the division result into a decimal, you continue the division to get a decimal number.
This is done by adding zeros to the remainder and continuing the division.
For 71 梅 33, after finding that the quotient is 2 and the remainder is 5, you can continue:
Bring down zeros to make it 50, so 50 梅 33 is approximately 1.515, repeating.
Hence, the decimal representation is 2.1515 (with 5 repeating).

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