Understanding Negative Numbers

Which ancient text is known for the earliest use of negative numbers?

• Aristotle's Metaphysics

• Euclid's Elements

• Jiuzhang Suanshu

• Pythagorean Theorems

Answer explanation

The Jiuzhang Suanshu, an ancient Chinese mathematical text, is recognized for its early use of negative numbers, unlike the other texts listed, which do not address this concept.

What did Brahmagupta contribute to the understanding of negative numbers?

• He ignored negative numbers completely.

• He used them to represent solutions to quadratic equations.

• He considered them as non-numbers.

• He only used them for counting objects.

Answer explanation

Brahmagupta was one of the first to use negative numbers in a meaningful way, specifically to represent solutions to quadratic equations, which marked a significant advancement in mathematical understanding.

How do you move on a number line when adding a negative number?

• Move right

• Move left

• Stay in place

• Move up

Answer explanation

When adding a negative number, you move left on the number line. This is because adding a negative value decreases the total, which corresponds to moving in the left direction.

Why do we use parentheses around negative numbers in equations?

• To make the equation look longer

• To avoid mistakes

• To make it harder to solve

• To change the value of the number

Answer explanation

We use parentheses around negative numbers in equations to avoid mistakes in calculations. They clarify the order of operations and ensure that the negative sign is correctly applied, preventing errors in the final result.

What property of addition allows numbers to be added in any order?

• Associative property

• Identity property

• Distributive property

• Commutative property

Answer explanation

The commutative property of addition states that numbers can be added in any order, meaning a + b = b + a. This property allows flexibility in calculations, unlike the associative or distributive properties.

What is the result of subtracting a negative number?

• The number stays the same

• The number becomes zero

• The number decreases

• The number increases

Answer explanation

Subtracting a negative number is equivalent to adding its positive counterpart, which increases the value of the original number. Therefore, the correct answer is that the number increases.

What is the absolute value of the difference between -7 and -9?

• 3

• 1

• 2

• 4

Answer explanation

To find the absolute value of the difference between -7 and -9, calculate |-7 - (-9)| = |-7 + 9| = |2| = 2. Thus, the correct answer is 2.

What does the associative property allow us to do?

• Add numbers in any order

• Group numbers in any way

• Divide numbers in any way

• Multiply numbers in any order

Answer explanation

The associative property allows us to group numbers in any way when adding or multiplying. This means that the way numbers are grouped does not affect the sum or product, making 'Group numbers in any way' the correct choice.

What is the result of 5 - (-2)?

• 3

• 5

• 7

• 0

Answer explanation

To solve 5 - (-2), remember that subtracting a negative is the same as adding. Thus, 5 - (-2) becomes 5 + 2, which equals 7. Therefore, the correct answer is 7.

What is the main benefit of rewriting subtraction as addition of the opposite?

• It changes the value of the numbers

• It makes equations longer

• It allows the use of the commutative property

• It makes subtraction easier

Answer explanation

Rewriting subtraction as addition of the opposite allows us to use the commutative property, which states that the order of addition does not affect the sum. This simplifies calculations and helps in solving equations more easily.