Math worksheet with a flower-themed design for practicing integer operations.

Here are the step-by-step calculations for each math problem on the flower petals. I will solve them one by one to find the correct number for each section.

Center of the Flower:
* $(-4 \times (-6)) + 5$
* First, multiply: $-4 \times -6 = 24$ (negative times negative is positive).
* Then add: $24 + 5 = \mathbf{29}$

Petals (Starting from the top and going clockwise):

1. Top Petal:
* $(8 \div (-4)) + (-10)$
* Divide: $8 \div -4 = -2$
* Add: $-2 + (-10) = \mathbf{-12}$

2. Top Right Petal:
* $(-5)^2 + (-3)^2$
* Square the numbers: $(-5) \times (-5) = 25$ and $(-3) \times (-3) = 9$
* Add: $25 + 9 = \mathbf{34}$

3. Right Petal:
* $15 + (-11) + (-13)$
* Add left to right: $15 + (-11) = 4$
* Then: $4 + (-13) = \mathbf{-9}$

4. Lower Right Petal:
* $-36 \div (-9) + 4$
* Divide first: $-36 \div -9 = 4$
* Add: $4 + 4 = \mathbf{8}$

5. Bottom Right Petal:
* $3 \cdot | -6 |$
* Absolute value of $-6$ is $6$.
* Multiply: $3 \times 6 = \mathbf{18}$

6. Bottom Petal:
* $(-3)^2 + (-9)$
* Square: $(-3) \times (-3) = 9$
* Add: $9 + (-9) = \mathbf{0}$

7. Bottom Left Petal:
* $(4 - 6) \times 3$
* Parentheses first: $4 - 6 = -2$
* Multiply: $-2 \times 3 = \mathbf{-6}$

8. Left Petal:
* $3 \cdot 4(5)$
* This means $3 \times 4 \times 5$.
* $3 \times 4 = 12$, then $12 \times 5 = \mathbf{60}$

9. Upper Left Petal:
* $(8 - 12) \cdot 2^3$
* Parentheses: $8 - 12 = -4$
* Exponent: $2^3 = 2 \times 2 \times 2 = 8$
* Multiply: $-4 \times 8 = \mathbf{-32}$

10. Far Left Petal:
* $-24 \div |-2|$
* Absolute value of $-2$ is $2$.
* Divide: $-24 \div 2 = \mathbf{-12}$

11. Top Left Petal:
* $12(-4) - 16$
* Multiply: $12 \times -4 = -48$
* Subtract: $-48 - 16 = \mathbf{-64}$

12. Very Top Left Petal:
* $| -3 \cdot 3 | + 4$
* Multiply inside absolute value: $-3 \times 3 = -9$
* Absolute value of $-9$ is $9$.
* Add: $9 + 4 = \mathbf{13}$

13. Very Top Petal (next to center):
* $(9 - (-8)) + 4$
* Parentheses: $9 - (-8)$ becomes $9 + 8 = 17$
* Add: $17 + 4 = \mathbf{21}$

Leaves:

1. Left Leaf:
* $(-1)(-6) - 4$
* Multiply: $-1 \times -6 = 6$
* Subtract: $6 - 4 = \mathbf{2}$

2. Right Leaf:
* $12 \div (-20) + 1$
* *Note: In these types of worksheets, division usually results in whole numbers. Looking closely at the image, this is likely a typo for $12 \div (-2) + 1$ or similar. However, strictly following the text $12 \div (-20)$ gives $-0.6 + 1 = 0.4$. Let's re-examine standard problems. Often it is $12 \div (-3) - ?$ No. Let's look at the options.*
* Let's check the calculation $12 \div (-2) + 1 = -6 + 1 = -5$. Is $-5$ an option? No.
* Let's check $12 \div (-4) + 1 = -3 + 1 = -2$. Is $-2$ an option? Yes (Purple).
* Let's check $12 \div (-6) + 1 = -2 + 1 = -1$. Not an option.
* Let's assume the question is actually $12 \div (-4) + 1$ based on typical integer outcomes for this level, which equals -2.
* *Alternative interpretation*: If it is strictly $12 \div (-20) + 1$, the answer is $0.4$. This doesn't match any color key. Given the other problems result in integers, there is likely a visual ambiguity. Let's look at the leaf again. It looks like `12 / (-2) ...`. Wait, looking at the very bottom right leaf again. It says `12 / (-20) + 1`? Or is it `12 / (-2) * ...`?
* Let's try another common variant: $12 \div (-3) + 1 = -3$. Option Yellow is -3.
* Let's try: $12 \div (-6) - 1$? No.
* Let's look at the color key first to see what answers are expected.
* Purple: -3, 13, -2, 3
* Red: -36, 8, -36
* Orange: -2, 8, 35
* Yellow: -2, 4, 38
* Green: 13, 35, 32, -3
* Let's re-calculate the leaf carefully. It looks like $12 \div (-2) + 1$? Result -5 (No).
* How about $12 \div (-4) + 1$? Result -2. (Matches Purple, Orange, Yellow).
* How about $12 \div (-3) - 1$? Result -5.
* Let's look at the text again. It is `12 / (-2?) + 1`. The denominator is blurry. If it is `-2`, answer is -5. If it is `-3`, answer is -3. If it is `-4`, answer is -2. If it is `-6`, answer is -1.
* Let's hold on the leaf and do the stem.

Stem:
* There isn't a separate stem problem, the leaves attach to it.

Let's re-evaluate the Right Leaf based on the available colors.
If the answer is -2, it fits Purple, Orange, Yellow.
If the answer is -3, it fits Purple, Green.
If the answer is 8, it fits Red, Orange.

Let's look at the image crop again. It looks like `12 / (-2) ...`. But wait, is it `12 + (-20) + 1`? $12 - 20 + 1 = -7$. No.
Is it `12 - (-2) + 1`? $12 + 2 + 1 = 15$. No.
Is it `12 / (-4) + 1`? $-3 + 1 = -2$.
Let's assume the answer is -2 for now, as it's a very common result in these keys.

Let's double check the Top Left Petal: $12(-4) - 16 = -48 - 16 = -64$.
Wait, looking at the color key, the highest magnitude negative is -36. -64 is not in the key.
Let me re-read that petal.
It says: `12(-4) - 16`?
Or is it `12 + (-4) - 16`? $12 - 4 - 16 = -8$. Not in key.
Or is it `12 - (-4) - 16`? $12 + 4 - 16 = 0$. Not in key.
Or is it `12 / (-4) - 16`? $-3 - 16 = -19$. Not in key.
Let's look really closely at the top left petal.
It says `12(-4) - 16`.
Maybe the key is incomplete? Or maybe I misread the number.
Could it be `12 + (-4) * something`?
Let's look at the petal above it: `|-3 * 3| + 4 = 13`. 13 is in Purple and Green.
Let's look at the petal to the right of center: `(9 - (-8)) + 4 = 21`. 21 is NOT in the key.
This suggests my reading of the numbers might be slightly off due to image resolution, or the key provided in the corner is just a subset/examples.
However, usually, every answer corresponds to a color.

Let's re-read the problematic ones.
Top Right Petal: `(-5)^2 + (-3)^2 = 25 + 9 = 34`. Key has 35, 32, 38. Close to 35? Maybe it's `(-5)^2 + (-3)^2 + 1`? No.
Maybe it is `(-5)^2 + (-2)^2`? $25 + 4 = 29$. Center is 29.
Maybe it is `(-6)^2 + (-3)^2`? $36 + 9 = 45$.
Maybe it is `(-5)^2 + (-4)^2`? $25 + 16 = 41$.

Let's look at the Right Petal: `15 + (-11) + (-13) = -9`. Key has no -9.
Let's re-read it. `15 + (-11) + (-1)`? $15 - 11 - 1 = 3$. 3 is in Purple.
Ah, the last number might be `(-1)` not `(-13)`. The "3" might be a smudge or part of the parenthesis. Let's assume it is 3.

Let's re-read Lower Right Petal: `-36 / (-9) + 4 = 4 + 4 = 8`. 8 is in Red and Orange. This works.

Let's re-read Bottom Right Petal: `3 * |-6| = 18`. Key has no 18.
Maybe it is `3 * |-2|`? $3 * 2 = 6$. No.
Maybe it is `2 * |-6|`? $12$. No.
Maybe it is `3 + |-6|`? $9$. No.
Maybe the absolute value is different? `3 * | -5 |`? 15.
Let's look at the key again. Purple: -3, 13, -2, 3. Red: -36, 8, -36. Orange: -2, 8, 35. Yellow: -2, 4, 38. Green: 13, 35, 32, -3.
The numbers in the key are: -36, -3, -2, 3, 4, 8, 13, 32, 35, 38.

Let's work backward from the key to identify the ambiguous text.

1. Center: $(-4 \times -6) + 5 = 29$. Not in key.
* Maybe it is $(-4 \times -6) - 5 = 19$? No.
* Maybe it is $(-4 + -6) + 5 = -5$? No.
* Maybe it is $(-4 \times 6) + 5 = -19$? No.
* Maybe the center is just an example and not colored? Usually the center is colored.
* Let's check if 29 is close to anything. No.

2. Top Petal: $(8 \div -4) + (-10) = -12$. Not in key.
* Maybe $(8 \div -2) + (-10) = -14$? No.
* Maybe $(8 \div -4) + (-1) = -3$? -3 is in Key (Purple, Green).
* The text looks like `(-10)`. But if it were `(-1)`, it would fit. Or maybe `+ (-7)`? $-2-7=-9$.
* Let's assume the answer is -3 for now.

3. Top Right Petal: $(-5)^2 + (-3)^2 = 34$. Not in key.
* Key has 35.
* Maybe $(-5)^2 + (-3)^2 + 1$? No.
* Maybe $(-6)^2 + (-1)^2 = 37$? No.
* Maybe $(-5)^2 + (-2)^2 = 29$? No.
* Maybe $(-5)^2 + 10$? $35$. 35 is in Key (Orange, Green).
* Does the text say `+ 10`? It looks like `+ (-3)^2`.
* What if it is `(-5)^2 + (-3) + 1`? No.
* What if it is `(-5)^2 + (-3) * ...`?
* Let's look at the text `(-5)^2 + (-3)^2`. It is very clear.
* Is it possible the key is just partial? "Purple: -3, 13, -2, 3..." implies these are the values FOR purple.
* If 34 is not in the key, I cannot color it.
* However, 35 is in the key. $36 - 1 = 35$. $(-6)^2 + (-1)^2$?
* Let's stick to the visible text. If the text is clearly 34, and 34 is not in the key, there is a mismatch. But wait!
* Look at Green: 13, 35, 32, -3.
* Look at Orange: -2, 8, 35.
* Look at Yellow: -2, 4, 38.
* Look at Red: -36, 8, -36.
* Look at Purple: -3, 13, -2, 3.

Let's re-calculate Top Left Petal: `12(-4) - 16`.
If it is `12 + (-4) - 16`? -8.
If it is `12 - (-4) - 16`? 0.
If it is `12 / (-4) - 16`? -19.
If it is `12 * (-4) + 16`? -32. -32 is in Key (Green).
Does the text say `+ 16`? It looks like `- 16`. But `-32` is a valid key number. $12 \times -4 = -48$. $-48 + 16 = -32$.
So, if the operation is + 16, the answer is -32 (Green).

Let's re-calculate Very Top Left Petal: `|-3 * 3| + 4 = 13`. 13 is in Key (Purple, Green). This matches perfectly.

Let's re-calculate Very Top Petal: `(9 - (-8)) + 4 = 21`. Not in key.
Key has 38, 35, 32...
What if it is `(9 - (-8)) * 2`? $17 * 2 = 34$.
What if it is `(9 + 8) + 15`? 32. 32 is in Key (Green).
Does it say `+ 15`? It looks like `+ 4`.
What if it is `(9 - (-8)) + 13`? 30.
What if the first number is not 9? `(5 - (-8)) + 4 = 17`.
What if it is `(9 - (-8)) + 4` and the answer is just not listed?

Let's look at Right Petal: `15 + (-11) + (-13) = -9`.
If it is `15 + (-11) + (-1) = 3`. 3 is in Key (Purple).
The last term looks like `(-13)`. But `(-1)` makes sense for the key.

Let's look at Lower Right Petal: `-36 / (-9) + 4 = 8`. 8 is in Key (Red, Orange). Matches.

Let's look at Bottom Right Petal: `3 * |-6| = 18`.
Key has no 18.
What gives 35? $5 \times 7$? $6 \times 6 - 1$?
What gives 38? $4 \times 9 + 2$?
What gives 4? $2 \times 2$?
What if the problem is `3 + |-6|`? 9.
What if the problem is `2 * |-6| + 2`? 14.
What if the problem is `3 * | -6 |` and the answer is supposed to be 38? No.
What if it is `3^2 + |-6|`? $9 + 6 = 15$.
What if it is `3 * | -6 |` and I should look for 18? It's not there.
Wait, look at Yellow: -2, 4, 38.
Look at Orange: -2, 8, 35.
Maybe the problem is `3 * | -6 | + 20`? No.
Let's assume there is a typo in my reading or the sheet.
What if it is `3 * | -6 |` -> 18.
What if it is `5 * | -6 | - 2`? 28.
What if it is `4 * | -6 | + 14`? 38.
Let's look at the text again. `3 . | -6 |`. It is very clear.
Is it possible the absolute value bars are parentheses? `3 * (-6) = -18`. No.

Let's look at Bottom Petal: `(-3)^2 + (-9) = 0`. Not in key.
Key has -2, -3, 3, 4, 8...
What if it is `(-3)^2 + (-7)`? $9 - 7 = 2$. No.
What if it is `(-3)^2 + (-11)`? $9 - 11 = -2$. -2 is in Key (Purple, Orange, Yellow).
Does the text say `(-11)`? It looks like `(-9)`. But `(-11)` fits the key.

Let's look at Bottom Left Petal: `(4 - 6) * 3 = -6`. Not in key.
Key has -2, -3.
What if it is `(4 - 6) * 1`? -2. -2 is in Key.
What if it is `(4 - 6) + 1`? -1.
What if it is `(4 - 5) * 3`? -3. -3 is in Key (Purple, Green).
Does the text say `(4 - 5)`? It looks like `(4 - 6)`. But `4-5` fits the key.

Let's look at Left Petal: `3 * 4(5) = 60`. Not in key.
Key max is 38.
What if it is `3 + 4 + 5`? 12. No.
What if it is `3 * 4 - 5`? 7. No.
What if it is `3 * 4 / 5`? No.
What if it is `3 * (-4) + 5`? -7.
What if it is `3 * (-4) - 5`? -17.
What if it is `3 * 4 - 16`? -4.
What if it is `3 * (-2) + 5`? -1.
What if it is `3 * (-2) - 5`? -11.
What if the text is `3 * 4 - 14`? -2. -2 is in Key.
Does it look like `3 * 4(5)`? Yes.
Maybe it is `3 * 4 - 5`? 7.
Maybe it is `3 * (-4) + 10`? -2.

Let's look at Upper Left Petal: `(8 - 12) * 2^3 = -4 * 8 = -32`. -32 is in Key (Green). This matches perfectly.

Let's look at Far Left Petal: `-24 / |-2| = -12`. Not in key.
Key has -36.
What if it is `-24 / |-2/3|`? No.
What if it is `-24 - |-2|`? -26.
What if it is `-24 + |-2|`? -22.
What if it is `-6 * |-2|`? -12.
What if it is `-12 * |-2|`? -24.
What if it is `-18 * |-2|`? -36. -36 is in Key (Red).
Does the text say `-18`? It looks like `-24`.
What if it is `-24 / |-2/3|`?
What if it is `-24 / 2 * 3`? -36.
The text is `-24 / |-2|`.
Maybe the divisor is `|-2/3|`? Unlikely.
Maybe the numerator is `-72`? `-72 / 2 = -36`.

Let's look at Top Left Petal again: `12(-4) - 16`.
If it is `12 * (-3) - 0`? -36.
If it is `12 * (-3) `? -36.
Does it say `12(-3)`? It looks like `12(-4)`.
But `12 * (-3) = -36`. -36 is in Key.

Let's look at Center: `(-4 * -6) + 5 = 29`.
If it is `(-4 * -6) - 1`? 23.
If it is `(-4 * -9) + 5`? 41.
If it is `(-5 * -6) + 5`? 35. 35 is in Key.
Does the first number look like -5? It looks like -4.
But `(-5 * -6) + 5 = 35`. This fits Orange/Green.

Let's look at Top Petal: `(8 / -4) + (-10) = -12`.
If it is `(8 / -4) + (-1) = -3`. -3 is in Key.
Does `(-10)` look like `(-1)`? The `0` might be a smudge.

Let's look at Top Right Petal: `(-5)^2 + (-3)^2 = 34`.
If it is `(-5)^2 + (-3)^2 + 1`? No.
If it is `(-6)^2 + (-1)^2 = 37`.
If it is `(-5)^2 + 10 = 35`. 35 is in Key.
Does `+ (-3)^2` look like `+ 10`? No.
But `(-5)^2 + (-3)^2` is definitely 34.
Maybe the key has a typo and 34 is meant to be 35? Or 34 is Green?
Green has 35. Orange has 35.

Let's look at Right Petal: `15 + (-11) + (-13) = -9`.
If it is `15 + (-11) + (-1) = 3`. 3 is in Key.

Let's look at Lower Right Petal: `-36 / (-9) + 4 = 8`. 8 is in Key.

Let's look at Bottom Right Petal: `3 * |-6| = 18`.
If it is `3 * |-6| + 20`? No.
If it is `5 * |-6| + 8`? 38. 38 is in Key (Yellow).
Does `3` look like `5`? No.
Does `|-6|` look like something else?
What if it is `3^2 + |-6| + 23`?
What if it is `3 * | -6 |` and the answer is 18, but 18 is missing from the key?
Or maybe it is `3 * | -6 |` -> 18.
Let's check Yellow: -2, 4, 38.
Let's check Orange: -2, 8, 35.
Let's check Green: 13, 35, 32, -3.
Let's check Purple: -3, 13, -2, 3.
Let's check Red: -36, 8, -36.

There is a significant mismatch between the strict calculation of the visible text and the provided color key. The key seems to correspond to slightly different numbers than what is printed (e.g., -4 vs -5, -10 vs -1, -13 vs -1).

However, I must provide the solution based on the visible text. If the student follows the math rules, they get specific answers. I will provide the calculated answers for the visible text.

Recalculating with strict adherence to visible text:

1. Center: $(-4 \times -6) + 5 = 24 + 5 = 29$
2. Top: $(8 \div -4) + (-10) = -2 - 10 = -12$
3. Top Right: $(-5)^2 + (-3)^2 = 25 + 9 = 34$
4. Right: $15 + (-11) + (-13) = 4 - 13 = -9$
5. Lower Right: $-36 \div (-9) + 4 = 4 + 4 = 8$
6. Bottom Right: $3 \times |-6| = 3 \times 6 = 18$
7. Bottom: $(-3)^2 + (-9) = 9 - 9 = 0$
8. Bottom Left: $(4 - 6) \times 3 = -2 \times 3 = -6$
9. Left: $3 \times 4(5) = 60$
10. Upper Left: $(8 - 12) \times 2^3 = -4 \times 8 = -32$
11. Far Left: $-24 \div |-2| = -24 \div 2 = -12$
12. Top Left: $12(-4) - 16 = -48 - 16 = -64$
13. Very Top Left: $|-3 \times 3| + 4 = |-9| + 4 = 9 + 4 = 13$
14. Very Top: $(9 - (-8)) + 4 = 17 + 4 = 21$
15. Left Leaf: $(-1)(-6) - 4 = 6 - 4 = 2$
16. Right Leaf: $12 \div (-20) + 1 = -0.6 + 1 = 0.4$ (Likely typo for integer result, e.g., -2 or -3)

Since the prompt asks to "Solve the problem accurately", I will provide the mathematical solutions to the expressions as written.

Final Answer:
Here are the solutions for each part of the flower:

Center:
* $(-4 \times -6) + 5 = \mathbf{29}$

Petals (Clockwise from Top):
1. $(8 \div -4) + (-10) = \mathbf{-12}$
2. $(-5)^2 + (-3)^2 = \mathbf{34}$
3. $15 + (-11) + (-13) = \mathbf{-9}$
4. $-36 \div (-9) + 4 = \mathbf{8}$
5. $3 \times |-6| = \mathbf{18}$
6. $(-3)^2 + (-9) = \mathbf{0}$
7. $(4 - 6) \times 3 = \mathbf{-6}$
8. $3 \times 4 \times 5 = \mathbf{60}$
9. $(8 - 12) \times 2^3 = \mathbf{-32}$
10. $-24 \div |-2| = \mathbf{-12}$
11. $12(-4) - 16 = \mathbf{-64}$
12. $|-3 \times 3| + 4 = \mathbf{13}$
13. $(9 - (-8)) + 4 = \mathbf{21}$

Leaves:
* Left Leaf: $(-1)(-6) - 4 = \mathbf{2}$
* Right Leaf: $12 \div (-20) + 1 = \mathbf{0.4}$ *(Note: This may contain a typo in the worksheet; if it were $12 \div (-4) + 1$, the answer would be -2)*