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Quizzes > High School Quizzes > Mathematics

Rule of 9s Burns Practice Quiz

Enhance your burn calculation skills for success

Difficulty: Moderate
Grade: Grade 11
Study OutcomesCheat Sheet
Paper art promoting the fast-paced 9s Burn Challenge, a 9th-grade math quiz.

Which of the following numbers is divisible by 9?
52
45
47
34
45 is divisible by 9 because the sum of its digits is 4 + 5 = 9, which meets the rule of 9s. The other numbers do not yield a digit sum that is divisible by 9.
Which statement correctly shows that 729 is divisible by 9?
7 + 2 + 9 = 18, and 18 is divisible by 9
7 + 2 + 9 = 17, and 17 is not divisible by 9
7 + 2 + 9 = 19, and 19 is a prime number
7 + 2 + 9 = 16, which is not divisible by 9
The sum of the digits in 729 is 7 + 2 + 9 = 18, and since 18 is divisible by 9, 729 is divisible by 9. The alternative options contain incorrect calculations.
According to the rule of 9s, if a number's digits add up to 9, is the number divisible by 9?
True
False
Only if it is even
Only if it ends in 9
If a number's digits sum to 9, the number is divisible by 9 as per the rule. This property holds no matter what the individual digits are.
Which of the following best describes the rule of 9s?
A rule for converting numbers to base 9
A rule for multiplying numbers by 9
A process to calculate the square of a number
A method to determine divisibility by 9 using the sum of digits
The rule of 9s relies on adding the digits of a number to determine divisibility by 9. This succinct method distinguishes it from the other, unrelated descriptions.
What is the digit sum of 324?
9
10
8
7
The digit sum of 324 is computed as 3 + 2 + 4, which equals 9. Since 9 is divisible by 9, the rule of 9s confirms the number's divisibility.
Determine if 561 is divisible by 9.
No, because 5 + 6 + 1 = 12 is only divisible by 3
Yes, because it has three digits
No, because 5 + 6 + 1 = 12 is not divisible by 9
Yes, because 5 × 6 × 1 = 30
The sum of the digits in 561 is 5 + 6 + 1 = 12, which is not a multiple of 9, so 561 is not divisible by 9. This directly applies the rule of 9s.
Find the missing digit in 8?4 such that the number is divisible by 9.
6
8
7
5
Adding the known digits yields 8 + 4 = 12, and to reach the next multiple of 9 (which is 18), the missing digit must be 6. Other alternatives would not make the total sum divisible by 9.
Which property does the rule of 9s rely on?
A number's parity is determined by its digits
A number's square is equal to the sum of its digits repeated
A number is congruent to the sum of its digits modulo 9
The prime factors of a number equal the sum of its digits
The rule of 9s is based on the concept that any number is congruent to the sum of its digits modulo 9. This modular arithmetic principle is crucial, unlike the other options which are incorrect.
Identify which of the following numbers is divisible by 9: 738, 847, 592, or 157.
738
157
847
592
738 has a digit sum of 7 + 3 + 8 = 18, and since 18 is divisible by 9, 738 is divisible by 9. The remaining numbers do not meet the divisibility condition.
A number 932? is known to be divisible by 9. What digit should replace the '?'?
7
5
4
3
The sum of the known digits is 9 + 3 + 2 = 14, and to reach the next multiple of 9 (18), the missing digit must be 4. The other options would not yield a sum divisible by 9.
If a number is divisible by 9, what is always true about its digital root?
Its digital root equals the number of digits
Its digital root is equal to the sum of its digits, which is never 9
Its digital root is 9
Its digital root is always 1
For any non-zero number divisible by 9, summing its digits repeatedly always results in a digital root of 9. This is an inherent property of numbers divisible by 9.
Which of the following statements is FALSE regarding the rule of 9s?
Adding or subtracting 9 does not change a number's divisibility by 9
A number is divisible by 9 if the sum of its digits is divisible by 9
Using the sum of digits is a quick test for divisibility by 9
Multiplying a number by 9 always results in a number that is not divisible by 9
The false statement claims that multiplying a number by 9 makes it not divisible by 9, which is incorrect. In fact, any product involving 9 will be divisible by 9, making the other statements true.
How many numbers between 1 and 100 are divisible by 9?
9
12
10
11
The numbers divisible by 9 between 1 and 100 are 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, and 99, totaling 11. This count is determined by listing or mathematically calculating the frequency.
Which of the following numbers is not divisible by 9?
594
825
738
432
825 has a digit sum of 8 + 2 + 5 = 15, which is not divisible by 9. The other numbers yield sums that are multiples of 9, affirming their divisibility by 9.
What is the result of applying the rule of 9s to the product of two numbers if one of them is divisible by 9?
The product always has a digital root of 1
The product is never divisible by 9
The product is always divisible by 9
The product's digit sum equals that of the non-multiple factor
If one factor is divisible by 9, then the product will contain 9 as a factor and thus be divisible by 9 as well. This follows directly from the multiplication properties of divisibility.
If a number has a missing digit in its hundreds place represented by 'x' in the four-digit number x247 and is known to be divisible by 9, what is the value of x?
6
3
5
7
Here, the digit sum is x + 2 + 4 + 7 = x + 13. For the number to be divisible by 9, the sum must equal a multiple of 9; setting x + 13 = 18 gives x = 5. Other values would not yield a valid digit sum.
A large number is formed by repeating '123' consecutively 4 times (i.e., 123123123123). Determine its divisibility by 9.
Divisible by 9
Divisible by 9 only when rearranged
Not divisible by 9
Divisible by 9 if truncated
The block '123' has a digit sum of 1 + 2 + 3 = 6, and repeating it four times gives a total sum of 6 × 4 = 24. Since 24 is not a multiple of 9, the entire number is not divisible by 9.
When multiplying two numbers, neither of which is divisible by 9, what can be said about the product's divisibility by 9?
The product is never divisible by 9
The product is always divisible by 9
The product is divisible by 9 only if both numbers are prime
The product can be divisible by 9 under certain conditions
Even if neither number is individually divisible by 9, their product can be divisible by 9 if the factors combine appropriately to include a full factor of 9. This situation depends on their remainders modulo 9, unlike the absolute claims in the other options.
Consider the number 7?842 such that it is divisible by 9; find the missing digit '?'
6
8
5
7
The sum of the known digits is 7 + 8 + 4 + 2 = 21, and to make the total sum divisible by 9, it must reach 27. Hence, the missing digit is 6, as 21 + 6 = 27.
A number N has digits that add up to 45. What can you conclude about N using the rule of 9s?
N is divisible by 5
N is a prime number
N's digits form a palindrome
N is divisible by 9
Since the digit sum is 45 and 45 is divisible by 9, the rule of 9s tells us that N is divisible by 9. This conclusion is independent of the number's other properties.
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Study Outcomes

  1. Understand the rule of 9s and its relevance to divisibility and arithmetic operations.
  2. Apply mental math techniques to quickly solve challenging numerical problems.
  3. Analyze mathematical problems to identify patterns and efficient solving methods.
  4. Evaluate personal performance to pinpoint areas requiring further practice.
  5. Develop quick reasoning skills that enhance overall mathematical fluency.

Rule of 9s Burns Cheat Sheet

  1. Master the Pythagorean Theorem - Think of it as the OG rule for right triangles: the square of the longest side (hypotenuse) equals the sum of the squares of the other two sides. It's your go‑to trick for finding missing lengths and acing those geometry quizzes. Embrace your inner Euclid and watch your confidence skyrocket! Toppers Bulletin
  2. Understand the Distance Formula - This formula is just Pythagoras in disguise: compute the straight‑line distance between two points \((x₝, y₝)\) and \((x₂, y₂)\) with a quick square, subtract, sum and root routine. Perfect for coordinate geometry and plotting points like a pro. Soon you'll be racing through graphing assignments! Toppers Bulletin
  3. Learn the Slope Formula - Slope measures the steepness of a line: calculate rise over run between two points and you're golden. It's like giving your line a personality - positive, negative, zero or undefined! Master this to sketch lines effortlessly and solve algebra puzzles in no time. Toppers Bulletin
  4. Apply the Quadratic Formula - When you've got \(ax² + bx + c = 0\), plug into \(x = \frac{-b \pm \sqrt{b² - 4ac}}\) to find the magic roots. This formula takes the guesswork out of quadratic equations and guarantees you'll find all real solutions. It's like having a mathematical Swiss Army knife! Toppers Bulletin
  5. Explore the Law of Sines - For any triangle, the ratio of a side to the sine of its opposite angle stays constant: \(a/\sin A = b/\sin B = c/\sin C\). Ideal for finding missing sides or angles in non‑right triangles without breaking a sweat. Turn every triangle problem into a piece of cake. Toppers Bulletin
  6. Understand the Law of Cosines - Think of this as the Pythagorean Theorem's more flexible cousin: \(a² = b² + c² - 2bc\cos A\). It helps you solve triangles when you know two sides and the included angle, or all three sides. Geometry just got a whole lot cooler! Toppers Bulletin
  7. Grasp Exponential Growth and Decay - Model those skyrocketing populations or radioactive breakdowns with \(A = A₀e^\). Here, \(A₀\) is your starting point, \(k\) is the growth/decay rate, and \(t\) is time. Whether you're studying biology or finance, this formula makes change over time a breeze. Toppers Bulletin
  8. Memorize Key Algebraic Identities - Speed up your algebra by knowing \((a + b)² = a² + 2ab + b²\) and \((a - b)² = a² - 2ab + b²\) off by heart. These shortcuts turn long expansions into quick mental math. Once these identities are locked in, simplifying expressions feels like a fun puzzle! BYJU'S
  9. Calculate Areas and Perimeters - Don't get tripped up on shapes: rectangles use \(A = l \times w\) and \(P = 2(l + w)\), while circles roll with \(A = \pi r²\) and \(C = 2\pi r\). These basics power everything from design projects to real‑world problem solving. Soon, you'll see geometry everywhere you look! BYJU'S
  10. Apply Heron's Formula - When you know all three sides \(a\), \(b\), \(c\), find the semi‑perimeter \(s = \frac{a+b+c}\) and then \(A = \sqrt{s(s-a)(s-b)(s-c)}\). It's like magic - no need to drop a height! Perfect for tricky triangle area problems that stump your classmates. BYJU'S
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