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Chapter 4: Problem 75

Distinguish among dividend, divisor, quotient, and remainder.

Short Answer

Expert verified
In division, the dividend is the number being divided, the divisor is the number by which the dividend is divided, the quotient is the result of the division, and if any amount is left from the dividend after division, it's called the remainder.

Step by step solution

01

Define Dividend

Dividend is the number that is being divided in a division operation. For example, in the division \(8 梅 2 = 4\), 8 is the dividend.
02

Define Divisor

Divisor is the number by which the dividend is divided. In the above example (\(8 梅 2 = 4\)), 2 is the divisor.
03

Define Quotient

Quotient is the result obtained from the division operation. In the provided example, 4 is the quotient as it is the result of \(8 梅 2\).
04

Define Remainder

Remainder is what is left over from the dividend after division. For instance, if we divide 10 by 3, we get a quotient of 3 and a remainder of 1, because 1 is what is left over from 10 after subtracting 9 (which is \(3 脳 3\)). In the example \(8 梅 2 = 4\), there is no remainder because 8 is exactly divisible by 2.

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Key Concepts

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

Understanding the Dividend
The dividend is the starting point of any division operation. It is the number you want to divide up. Think of it as a big cake you want to share among friends. Each "slice" of cake is determined by the divisor, which we'll discuss later. For example, in a division problem like \(8 \div 2 = 4\), the number 8 is our dividend. Whether you're dealing with big numbers or small, the concept of the dividend remains the same. It is always the number being split into parts.
Getting to Know the Divisor
The divisor is your helper in a division problem. It is the number by which the dividend is divided. In simpler terms, it's like the number of friends you're sharing a cake with. If you have a cake (the dividend) and you want to share it equally among 4 friends, 4 becomes your divisor. In our previous example of \(8 \div 2 = 4\), 2 is the divisor because it indicates how many groups the dividend will be divided into. Remember, the divisor helps determine how many pieces the dividend can be split into.
Introducing the Quotient
The quotient is the result or outcome of a division operation. It's what you get when you evenly divide a dividend by a divisor. Continuing with our cake analogy, the quotient represents the amount of cake each friend gets after the division. In the example \(8 \div 2 = 4\), 4 is the quotient, meaning each group or "friend" gets 4 parts of the dividend. So, whenever you perform division, the quotient tells you the size of each portion when the dividend is divided evenly by the divisor.
Exploring the Remainder
The remainder is what is left over after division when the dividend does not divide evenly by the divisor. Picture this scenario: you have 10 pieces of candy (the dividend) and 3 friends (the divisor). Each friend can receive 3 pieces, because \(3 \times 3 = 9\), but you will still have 1 piece left, which is the remainder. In cases where there's no leftover, like \(8 \div 2 = 4\), the remainder is zero since 8 divides evenly by 2. The remainder is crucial for understanding divisions that don't result in whole numbers.

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Most popular questions from this chapter

Divide and give the answer in quotient \(+\frac{\text { remainder }}{\text { divisor }}\) form. Assume no division by \(0 .\) $$1 9 \longdiv { 2 7 1 }$$

Perform each division. Assume no division by \(0 .\) $$\frac{8 a^{2}+2 a-3}{2 a-1}$$

Identify the base and the exponent in each expression. $$-3 y^{6}$$

Give the degree of each polynomial. $$-25$$

Find each product. $$(2 b-1)(3 b+4)$$
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