Questions and Answers
Which number is divisible by both 2 and 3?
What is the divisibility rule for 4?
Which of the following numbers is not divisible by 5?
If a baker has 48 cookies, how many boxes of 4 can he fill?
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To simplify an expression, which rule can be applied to quickly identify factors?
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Which of the following numbers is divisible by 2?
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How can the number 90 be described in terms of divisibility by 10?
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Which statement regarding divisibility by 6 is correct?
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Which of the following problems demonstrates the application of divisibility?
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Using the divisibility rules, which number is divisible by 3?
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Study Notes
Rules For Divisibility
- 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 10: A number is divisible by 10 if its last digit is 0.
Applications In Problem Solving
- Determine whether a number can be evenly divided by another to solve fraction problems or simplify calculations.
- Use divisibility rules to identify factors quickly when simplifying expressions or solving equations.
- Apply in real-life scenarios, such as grouping items (e.g., packaging or scheduling) where equal distribution is needed.
Divisibility Tests
- Practice testing numbers using the above rules:
- Example: Is 154 divisible by 2? Check last digit (4 → yes).
- Example: Is 123 divisible by 3? Sum of digits (1+2+3=6 → yes).
- Example: Is 100 divisible by 4? Last two digits (00 → yes).
- Develop speed and accuracy in recognizing divisibility to improve mathematical efficiency.
Word Problems Involving Divisibility
- Common forms:
- "If a number is divisible by X, find the smallest such number greater than Y."
- "How many items can be evenly distributed among a group without remainder?"
- Strategy:
- Identify which divisibility rule applies.
- Break down the problem into manageable parts.
- Use algebraic expressions to represent quantities and apply divisibility principles.
- Example Problem: "A baker has 36 cookies. How can he package them in boxes of 6?" (36 ÷ 6 = 6 boxes, confirming divisibility).
Rules For Divisibility
- A number ends with an even digit (0, 2, 4, 6, 8) is divisible by 2.
- The sum of a number's digits must be divisible by 3 for the number itself to be divisible by 3.
- For a number to be divisible by 4, the last two digits of that number must form a value that is divisible by 4.
- A last digit of either 0 or 5 indicates that a number is divisible by 5.
- A number is divisible by 6 if it meets the criteria for both divisibility by 2 and by 3.
- A last digit of 0 confirms that a number is divisible by 10.
Applications In Problem Solving
- Divisibility rules are essential for simplifying fractions and calculations.
- Quickly identifying factors simplifies expressions and aids in solving equations.
- These concepts are applicable in practical situations like packing items or arranging schedules where even distribution is required.
Divisibility Tests
- Practice recognizing divisibility through examples:
- For 154, the last digit is 4, thus it is divisible by 2.
- For 123, the sum of digits equals 6, making it divisible by 3.
- For 100, the last two digits are 00, confirming divisibility by 4.
- Develop quick recognition of divisibility to enhance mathematical efficiency.
Word Problems Involving Divisibility
- Common word problem formats include determining the smallest number divisible by a given value greater than another number, or calculating how many items can be evenly shared among a group.
- To solve, identify the applicable divisibility rule, break down the problem, and utilize algebraic expressions for calculations.
- Example: A baker has 36 cookies and can package them into boxes of 6, resulting in 6 boxes, thus confirming the divisibility of 36 by 6.
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Description
Test your knowledge of the rules for divisibility by 2, 3, 4, 5, 6, and 10. This quiz will help you learn how to determine whether a number can be evenly divided by another, which is useful in solving fraction problems and simplifying equations. Perfect for practicing quick calculation skills.
