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. Finding Volume

Volume of Solid Figures

The resources above cover the following skills:

Geometry (NCTM)

Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships.

Precisely describe, classify, and understand relationships among types of two- and three-dimensional objects using their defining properties.

Use visualization, spatial reasoning, and geometric modeling to solve problems.

Use geometric models to represent and explain numerical and algebraic relationships.

Measurement (NCTM)

Apply appropriate techniques, tools, and formulas to determine measurements.

Select and apply techniques and tools to accurately find length, area, volume, and angle measures to appropriate levels of precision.

Develop strategies to determine the surface area and volume of selected prisms, pyramids, and cylinders.