Grade 7 Math Worksheets Integers

Integers can be a challenging concept for grade 7 students to grasp, but with the right resources, like well-designed worksheets, they can become confident in their understanding. Our grade 7 math worksheets on integers are designed to help students practice and master this essential mathematical concept.

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What is an integer?

An integer is a whole number that can be positive, negative, or zero, and does not have any fractional or decimal parts. Examples of integers include -3, 0, 5, and 100.

How do you represent integers on a number line?

Integers are represented on a number line by plotting each integer at an equal distance from its neighboring integers. Positive integers are plotted to the right of zero, while negative integers are plotted to the left of zero. The further the integer is from zero, the greater its numerical value. The number line extends infinitely in both directions to accommodate all integers.

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 represented by the numerals 1, 2, 3, and so on, while negative integers are represented by numerals like -1, -2, -3, and so forth. In essence, positive integers denote quantities that can be counted in a forward direction, while negative integers denote quantities that count in a backward direction on a number line.

How do you order integers from greatest to least and vice versa?

To order integers from greatest to least, you arrange them in descending order starting from the largest integer to the smallest. To order integers from least to greatest, you arrange them in ascending order starting from the smallest integer to the largest. This can be done by comparing the values of the integers and placing them in the desired order accordingly.

How do you add and subtract integers?

To add integers, simply add the numbers together. For subtracting integers, you can either add the opposite of the number you want to subtract or subtract the numbers directly. To subtract a negative integer, it is the same as adding the positive value of that number. Remember to pay attention to the signs (+ and -) and keep track of the rules for adding and subtracting integers to ensure accuracy in your calculations.

What are the rules for multiplying and dividing integers?

When multiplying integers, you simply multiply the two numbers together. If the integers have different signs, the result will be negative. When dividing integers, similarly divide the numbers. If the signs are different, the result will be negative. Remember, division by zero is undefined.

How do you find the absolute value of an integer?

To find the absolute value of an integer, you simply drop the negative sign (if the integer is negative) and keep the number as it is (if the integer is positive or zero). In other words, the absolute value of an integer is the numerical value without considering its sign.

How do you solve integer word problems?

To solve integer word problems, carefully read the problem to identify the key information such as the quantities being compared or operated on. Translate the words into mathematical expressions and equations, applying the rules of integers for addition, subtraction, multiplication, and division. Make sure to pay attention to the signs of the numbers and perform the operations accordingly. Finally, check your answer against the given conditions in the problem to ensure accuracy.

What is the significance of zero in relation to integers?

Zero is significant in relation to integers as it serves as the additive identity, meaning any integer plus zero equals that integer. It also acts as the starting point on the number line, separating positive integers from negative integers. Additionally, zero allows for the concept of opposites to exist in the realm of integers, with each integer having a corresponding negative version.

How do you compare and evaluate integer expressions?

To compare and evaluate integer expressions, you must follow the order of operations (parentheses, exponents, multiplication and division from left to right, addition and subtraction from left to right). Start by simplifying any expressions inside parentheses, then evaluate any exponents, followed by multiplication and division, and finish with addition and subtraction. Remember to evaluate each operation within the expression before moving on to the next one. Once all operations are completed, compare the final values using comparison symbols (<, >, =) to determine the relationship between the expressions.