Writing integers in descending order

Oct 13, 2025 by recoveryshake.com 4 views

Introduction

In mathematics, simplifying expressions and understanding integer properties are essential skills for solving various problems. In this article, we will focus on simplifying two given expressions and exploring the properties of integers.

Simplifying Expressions

a) $698 \times 32$

To simplify the expression $698 \times 32$ , we can use the distributive property of multiplication over addition. This property states that for any numbers $a$ , $b$ , and $c$ , $a(b + c) = ab + ac$ . We can apply this property to simplify the expression.

# Simplifying the expression 698 * 32
result = 698 * 32
print(result)

Using this method, we can simplify the expression $698 \times 32$ as follows:

$698 \times 32 = (700 - 2) \times 32$

Using the distributive property, we can expand this expression as:

$698 \times 32 = (700 \times 32) - (2 \times 32)$

$698 \times 32 = 22400 - 64$

$698 \times 32 = 22336$

Therefore, the simplified expression is $698 \times 32 = 22336$ .

b) $984 \div 24$

To simplify the expression $984 \div 24$ , we can use the division property of integers. This property states that for any integers $a$ and $b$ , if $b \neq 0$ , then $a \div b = \frac{a}{b}$ . We can apply this property to simplify the expression.

# Simplifying the expression 984 / 24
result = 984 / 24
print(result)

Using this method, we can simplify the expression $984 \div 24$ as follows:

$984 \div 24 = \frac{984}{24}$

$984 \div 24 = 41$

Therefore, the simplified expression is $984 \div 24 = 41$ .

Integer Properties

Is it possible for an integer to be neither positive nor negative?

In mathematics, integers are defined as whole numbers, either positive, negative, or zero. Therefore, it is not possible for an integer to be neither positive nor negative.

The reason for this is that integers are defined as a set of numbers that includes all whole numbers, both positive and negative. Since zero is a whole number, it is also an integer. Therefore, the only integer that is neither positive nor negative is zero.

Writing integers in descending order

To write the given integers in descending order, we need to compare each integer with the others. The integers in descending order are:

$527, 498, 489, 112, -39, -31$

Therefore, the integers in descending order are $527, 498, 489, 112, -39, -31$ .

Conclusion

Introduction

In our previous article, we explored the concept of simplifying expressions and understanding integer properties. In this article, we will provide a Q&A guide to help you better understand these concepts.

Q&A Guide

Q: What is the difference between a positive integer and a negative integer?

A: A positive integer is a whole number greater than zero, while a negative integer is a whole number less than zero. For example, 5 is a positive integer, while -3 is a negative integer.

Q: Can an integer be zero?

A: Yes, an integer can be zero. Zero is a whole number and is considered an integer.

Q: How do you simplify an expression like $698 \times 32$ ?

A: To simplify an expression like $698 \times 32$ , you can use the distributive property of multiplication over addition. This property states that for any numbers $a$ , $b$ , and $c$ , $a(b + c) = ab + ac$ . You can apply this property to simplify the expression.

Q: How do you simplify an expression like $984 \div 24$ ?

A: To simplify an expression like $984 \div 24$ , you can use the division property of integers. This property states that for any integers $a$ and $b$ , if $b \neq 0$ , then $a \div b = \frac{a}{b}$ . You can apply this property to simplify the expression.

Q: Can an integer be neither positive nor negative?

A: No, an integer cannot be neither positive nor negative. The only integer that is neither positive nor negative is zero.

Q: How do you write integers in descending order?

A: To write integers in descending order, you need to compare each integer with the others. The integers in descending order are the ones with the largest value first.

Q: What is the difference between an integer and a whole number?

A: An integer is a whole number, either positive, negative, or zero. A whole number is a number without a fractional part, but it can be a decimal number. For example, 5 is a whole number, while 3.5 is not an integer but a whole number.

Q: Can an integer be a decimal number?

A: No, an integer cannot be a decimal number. An integer is a whole number, either positive, negative, or zero.

Q: How do you simplify an expression like $-3 \times 4$ ?

A: To simplify an expression like $-3 \times 4$ , you can use the distributive property of multiplication over addition. This property states that for any numbers $a$ , $b$ , and $c$ , $a(b + c) = ab + ac$ . You can apply this property to simplify the expression.

Q: How do you simplify an expression like $-6 \div 2$ ?

A: To simplify an expression like $-6 \div 2$ , you can use the division property of integers. This property states that for any integers $a$ and $b$ , if $b \neq 0$ , then $a \div b = \frac{a}{b}$ . You can apply this property to simplify the expression.

Conclusion

In conclusion, simplifying expressions and understanding integer properties are essential skills for solving various problems in mathematics. By using the distributive property of multiplication over addition and the division property of integers, we can simplify expressions and explore the properties of integers. Additionally, we can write integers in descending order by comparing each integer with the others.

Practice Problems

Simplify the expression $-5 \times 3$ .
Simplify the expression $-8 \div 2$ .
Write the integers $-2, 0, 4, -6, 8$ in descending order.
Simplify the expression $-9 \times 2$ .
Simplify the expression $-12 \div 3$ .

Answer Key

$-15$
$-4$
$8, 4, 0, -2, -6$
$-18$
$-4$