Divisibility

Divisibility is the ability of one number to be divided by another number without leaving a remainder. This concept is important in understanding the properties of numbers and is used extensively in arithmetic and algebra.

Divisibility Rules

There are specific rules that can help determine if a number is divisible by another number. Here are the most commonly used divisibility rules:

Divisibility by 2: A number is divisible by 2 if its last digit is even (0, 2, 4, 6, 8).
Divisibility by 3: A number is divisible by 3 if the sum of its digits is divisible by 3.
Divisibility by 4: A number is divisible by 4 if the number formed by its last two digits is divisible by 4.
Divisibility by 5: A number is divisible by 5 if its last digit is 0 or 5.
Divisibility by 6: A number is divisible by 6 if it is divisible by both 2 and 3.
Divisibility by 9: A number is divisible by 9 if the sum of its digits is divisible by 9.
Divisibility by 10: A number is divisible by 10 if its last digit is 0.

Practice Problems

Now that you understand the divisibility rules, let's practice with some problems:

Is 648 divisible by 3?
What is the smallest 3-digit number that is divisible by 9?
Which of the following numbers is divisible by 4: 362, 448, 521, 706?

Answers

Is 648 divisible by 3? Yes, because the sum of its digits (6 + 4 + 8) is 18, which is divisible by 3.
What is the smallest 3-digit number that is divisible by 9? The smallest 3-digit number divisible by 9 is 108.
Which of the following numbers is divisible by 4: 362, 448, 521, 706? The number 448 is divisible by 4 because the number formed by its last two digits (48) is divisible by 4.

Practice using these divisibility rules with various numbers to strengthen your understanding of this concept!

◂Math Worksheets and Study Guides Seventh Grade. Fraction Operations

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The resources above cover the following skills:

Number and Operations (NCTM)

Compute fluently and make reasonable estimates.

Develop and analyze algorithms for computing with fractions, decimals, and integers and develop fluency in their use.

Grade 7 Curriculum Focal Points (NCTM)

Number and Operations and Algebra: Developing an understanding of operations on all rational numbers and solving linear equations

Students extend understandings of addition, subtraction, multiplication, and division, together with their properties, to all rational numbers, including negative integers. By applying properties of arithmetic and considering negative numbers in everyday contexts (e.g., situations of owing money or measuring elevations above and below sea level), students explain why the rules for adding, subtracting, multiplying, and dividing with negative numbers make sense. They use the arithmetic of rational numbers as they formulate and solve linear equations in one variable and use these equations to solve problems. Students make strategic choices of procedures to solve linear equations in one variable and implement them efficiently, understanding that when they use the properties of equality to express an equation in a new way, solutions that they obtain for the new equation also solve the original equation.