Intergers Worksheets 7th Grade Common Core

Integers are an essential concept in middle school mathematics, particularly for 7th-grade students working with the Common Core curriculum. These worksheets are designed to provide targeted practice on integers, allowing students to strengthen their understanding and gain confidence in working with positive and negative whole numbers.

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  7th Grade Common Core Worksheets

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What is an integer?

An integer is a whole number that can be positive, negative, or zero, and does not include fractions or decimals. It represents a value on the number line that is not a fraction or a decimal point.

How is an integer represented on a number line?

An integer is represented on a number line by a point or dot at a specific location on the line. The position of the point corresponds to the value of the integer, with positive integers to the right of zero and negative integers to the left. The distance of the point from zero indicates the magnitude of the integer, with larger values placed farther from zero.

Explain the concept of opposites in integers.

In integers, opposites are numbers that have the same absolute value but differ in sign. For example, 3 and -3 are opposites because they are the same distance from zero on the number line but have different signs. When you add an integer to its opposite, the result is always zero. This concept is important in arithmetic operations such as addition and subtraction involving integers.

How does addition work with integers?

When adding integers, you simply combine the values together. If you are adding two positive integers, the result will be a positive integer. If you are adding two negative integers, the result will be a negative integer. If you are adding a positive integer and a negative integer, you subtract the absolute value of the two numbers and the result will have the sign of the number with the greater absolute value.

How does subtraction work with integers?

Subtraction with integers works by taking away a value from another value. When subtracting integers, you need to consider the sign of the numbers. If you are subtracting a positive integer, it is like adding a negative integer. Similarly, when subtracting a negative integer, it is like adding a positive integer. The rules for subtracting integers are that the signs must be taken into account, and the subtraction operation can be carried out as usual.

Describe the rules for multiplying integers.

To multiply integers, you simply multiply the numbers together and apply the rules of positive and negative numbers. If the two numbers have the same sign (both positive or both negative), the product is positive. If the two numbers have different signs, the product is negative. In summary, when multiplying integers, remember to multiply the numbers and apply the rule for the signs based on whether the integers have the same or different signs.

Describe the rules for dividing integers.

When dividing integers, if both integers share the same sign (positive or negative), the result is positive. If the integers have different signs, the result is negative. Additionally, when dividing integers, the quotient is usually rounded towards zero (truncated towards zero) - ignoring any remainder.

How are integers compared using the greater than and less than symbols?

Integers are compared using the greater than symbol (>), which indicates that the number on the left is larger than the number on the right, and the less than symbol (<), which indicates that the number on the left is smaller than the number on the right.

Explain the concept of absolute value and how it is calculated.

The absolute value of a number is its distance from zero on the number line, regardless of direction. It is always positive or zero. To calculate the absolute value of a number, if the number is positive or zero, the absolute value is the same as the number itself. If the number is negative, the absolute value is the number multiplied by -1 to make it positive. For example, the absolute value of -5 is |-5| = 5, and the absolute value of 3 is |3| = 3.

How are integers used in real-life situations, such as temperatures or bank balances?

Integers are used in real-life situations like temperatures and bank balances as they represent whole numbers without fractions or decimals. Temperatures are often represented as integers on thermometers, where positive numbers indicate above freezing temperatures and negative numbers indicate below freezing temperatures. Bank balances are also represented as integers to show the exact amount of money in an account, where positive numbers represent money deposited and negative numbers represent money owed or withdrawn. Integers provide a clear and precise way to quantify specific values in these real-life scenarios.