Free Integers Worksheets Grade 7

Are you a grade 7 student searching for free integers worksheets? Look no further! In this blog post, we will provide you with a selection of worksheets designed to help you practice and master the concept of integers. Each worksheet focuses on a specific aspect of integers, providing you with ample opportunities to develop your understanding and skills. So, if you're ready to dive into the world of integers, keep reading to find the perfect worksheets for you.

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What is an integer?

An integer is a whole number that can be positive, negative, or zero. It does not include fractions or decimals, only whole numbers without any fractional or decimal part.

What is the difference between positive and negative integers?

Positive integers are numbers greater than zero, while negative integers are numbers less than zero. Positive integers are denoted by a plus sign (+) or no sign at all, while negative integers are denoted by a minus sign (-). Essentially, positive integers represent quantities that are to the right of zero on the number line, while negative integers represent quantities that are to the left of zero.

How can integers be represented on a number line?

Integers can be represented on a number line by placing positive integers to the right of zero and negative integers to the left of zero. The distance between each integer point on the number line is the same, showing the magnitude and relative size of the integers. Zero is the reference point on the number line, separating positive and negative integers.

What does it mean for two integers to be equal?

Two integers are said to be equal when they have the same value and represent the same quantity on the number line, meaning they are the same numerical value regardless of their magnitude or position. In mathematical terms, two integers a and b are considered equal if a = b, showing that they have identical numerical values.

How can integers be added and subtracted?

Integers can be added by simply adding their numeric values together; positive integers are added as usual, while negative integers are subtracted (or added as negative numbers). Subtraction of integers can be done by changing the sign of the integer being subtracted and then adding it to the other integer. Adding and subtracting integers follow the rules where positive numbers added to positive numbers give a positive result, negative numbers added to negative numbers give a negative result, positive numbers added to negative numbers are subtracted, and negative numbers added to positive numbers are also subtracted.

How can integers be multiplied and divided?

Integers can be multiplied by simply multiplying the two numbers together. For example, when you multiply two integers, the result is another integer. When dividing integers, the same principle applies – you divide the first number by the second number. If the division is not exact, you may get a quotient and a remainder. Integer division always results in an integer answer, but the remainder may not be an integer.

What is the difference between the absolute value and opposite of an integer?

The absolute value of an integer is its distance from zero on the number line, always resulting in a non-negative value. In contrast, the opposite of an integer is obtained by changing the sign of the integer but keeping its magnitude the same, resulting in a value with the same distance from zero but on the opposite side of the number line.

How can integers be compared using the greater than and less than symbols?

Integers can be compared using the greater than symbol (>), where the number on the left is larger than the number on the right, and the less than symbol (<), where the number on the left is smaller than the number on the right. For example, if comparing 5 and 3, you would write 5 > 3 because 5 is greater than 3, and 3 < 5 because 3 is less than 5.

How can integers be used to represent real-life situations?

Integers can be used to represent real-life situations by quantifying objects or values that can be counted, such as representing the number of students in a class, temperature changes, money transactions, or even locations on a coordinate grid. Positive integers can denote gains or additions, while negative integers can represent losses or subtractions. By utilizing integers, we can effectively measure, analyze, and make predictions about various real-world scenarios.

What are some real-life examples of positive and negative integers?

A positive integer example could be a person's bank account balance of $500, or the temperature of 30 degrees Celsius. On the other hand, a negative integer example could be a person's debt of -$1000, or a temperature of -10 degrees Celsius. Positive integers are used to represent gains, quantities, or values above zero, while negative integers are used to represent losses, debts, or values below zero.