Solve multiplication equations and color the Easter egg and flower picture using the provided key.

Let’s solve this step by step.

We have a coloring page with multiplication problems inside different shapes. Each shape has a number (the product of the two numbers being multiplied). We need to calculate each product, then use the color key to decide what color to use for that section.

The color key is:

- yellow → products: 32, 49, 81
- orange → products > 84
- purple → products: 108, 144
- green → products: 54, 60, 132
- pink → products > 36, 64
- blue → products: 18, 56

Wait — let’s read the key again carefully from the image description:

Actually, looking at the original problem statement in the image text:

> yellow → 32, 49, 81
> orange → >84
> purple → 108, 144
> green → 54, 60, 132
> pink → >36, 64 ← This seems ambiguous. Let me re-read.

Actually, the way it's written in the image:

“pink → >36, 64” — that might mean “products greater than 36 AND equal to 64”? That doesn’t make sense. Or maybe it’s “>36 or =64”? But that would overlap with other categories.

Wait — perhaps it’s a typo or misformatting. Looking again:

In the original user input, it says:

> pink → >36, 64

But in standard coloring keys like this, usually each category is mutually exclusive. Let me check the actual values we’ll get and see which makes sense.

Alternatively, maybe it’s meant to be:

- pink → products that are >36 AND also include 64? No.

Another possibility: maybe it’s “pink → 36 < product ≤ 64” or something? But that’s not what’s written.

Wait — let’s look at the exact wording from the image as given in the prompt:

“pink → >36, 64”

This is confusing. Perhaps it’s a list: pink includes any product that is greater than 36 OR equals 64? But then orange is >84, so there’s overlap.

Actually, let’s think logically. In these worksheets, usually the ranges don’t overlap. So likely, the key is:

- yellow: exactly 32, 49, 81
- orange: anything greater than 84
- purple: exactly 108, 144
- green: exactly 54, 60, 132
- pink: anything greater than 36 up to 84? But it says “>36, 64” — maybe it’s “>36 and ≤64”? Or perhaps “64” is a separate value?

Wait — another idea: maybe “pink → >36, 64” means “products greater than 36, and also 64 is included in pink”? But 64 is greater than 36, so redundant.

Perhaps it’s a mistake, and it should be “pink → 37 to 64” or something.

But let’s look at the blue: “blue → 18, 56”

And green: “54, 60, 132”

Purple: “108, 144”

Orange: “>84” — so 85 and above, except those specified elsewhere? But 108 and 144 are listed under purple, so probably orange is >84 excluding 108 and 144? But that’s messy.

Actually, in such worksheets, the categories are usually designed so that every possible product falls into exactly one category. So let’s list all the multiplication problems in the image and compute their products, then assign colors based on the key, resolving ambiguities as we go.

First, let’s list all the equations visible in the image (from the description):

From the egg parts and flower and leaves:

Egg left side:
- 8 x 6 = ?
- 3 x 9 = ?
- 5 x 8 = ?
- 4 x 8 = ?
- 9 x 6 = ?
- 5 x 12 = ?

Egg right side:
- 7 x 6 = ?
- 8 x 3 = ?
- 9 x 4 = ?
- 7 x 7 = ?
- 12 x 3 = ?
- 12 x 11 = ?

Flower:
- 11 x 8 = ?

Leaves:
- 9 x 2 = ?
- 5 x 7 = ?
- 6 x 9 = ?
- 12 x 5 = ?
- 12 x 7 = ?
- 12 x 9 = ?
- 9 x 9 = ?
- 7 x 7 = ? (already have?)
- 12 x 10 = ?
- 12 x 8 = ?
- 12 x 11 = ? (duplicate?)
- 9 x 6 = ? (duplicate?)

Wait, some may be repeated, but in the image, each section is separate, so we treat each occurrence separately, even if same equation.

But for solving, we can compute unique ones first.

Let me list all unique equations and compute:

1. 8 x 6 = 48
2. 3 x 9 = 27
3. 5 x 8 = 40
4. 4 x 8 = 32
5. 9 x 6 = 54
6. 5 x 12 = 60
7. 7 x 6 = 42
8. 8 x 3 = 24
9. 9 x 4 = 36
10. 7 x 7 = 49
11. 12 x 3 = 36
12. 12 x 11 = 132
13. 11 x 8 = 88
14. 9 x 2 = 18
15. 5 x 7 = 35
16. 6 x 9 = 54 (same as #9)
17. 12 x 5 = 60 (same as #6)
18. 12 x 7 = 84
19. 12 x 9 = 108
20. 9 x 9 = 81
21. 7 x 7 = 49 (same as #10)
22. 12 x 10 = 120
23. 12 x 8 = 96
24. 12 x 11 = 132 (same as #12)
25. 9 x 6 = 54 (same)

Also, in the top right corner, there’s "6 x 12" which is 72, and "3 x 2"=6, but wait, in the image description, it says "6-12" in a box, but that might be the grade level or something. Ignore that.

Now, let’s list all computed products:

From above:

- 48 (8x6)
- 27 (3x9)
- 40 (5x8)
- 32 (4x8)
- 54 (9x6)
- 60 (5x12)
- 42 (7x6)
- 24 (8x3)
- 36 (9x4)
- 49 (7x7)
- 36 (12x3)
- 132 (12x11)
- 88 (11x8)
- 18 (9x2)
- 35 (5x7)
- 54 (6x9) — duplicate
- 60 (12x5) — duplicate
- 84 (12x7)
- 108 (12x9)
- 81 (9x9)
- 49 (7x7) — duplicate
- 120 (12x10)
- 96 (12x8)
- 132 (12x11) — duplicate
- 54 (9x6) — duplicate

Also, I think I missed some. In the initial list, there was "6 x 9" already, but let's ensure we have all sections.

From the image description, the sections are:

Left egg half: 6 sections: 8x6, 3x9, 5x8, 4x8, 9x6, 5x12 → products: 48,27,40,32,54,60

Right egg half: 6 sections: 7x6, 8x3, 9x4, 7x7, 12x3, 12x11 → 42,24,36,49,36,132

Flower: 1 section: 11x8=88

Leaves: multiple. From description: 9x2, 5x7, 6x9, 12x5, 12x7, 12x9, 9x9, 7x7, 12x10, 12x8, 12x11, 9x6 — but some duplicates in value, but different sections.

Specifically, leaves have:

- Top leaf: 9x2=18, 5x7=35, 6x9=54

- Middle leaf: 12x5=60, 12x7=84, 12x9=108

- Bottom leaf: 9x9=81, 7x7=49, 12x10=120, 12x8=96, 12x11=132, 9x6=54 — wait, that's too many. Probably each leaf has a few sections.

To avoid confusion, let's list all distinct products that appear, and then map to colors.

Unique products from all equations:

List all calculated values:

From left egg: 48,27,40,32,54,60

From right egg: 42,24,36,49,36,132 → so 24,36,42,49,132

From flower: 88

From leaves: let's say from the descriptions: 18 (9x2), 35 (5x7), 54 (6x9), 60 (12x5), 84 (12x7), 108 (12x9), 81 (9x9), 49 (7x7), 120 (12x10), 96 (12x8), 132 (12x11), 54 (9x6) — so additional: 18,35,84,108,81,120,96

So overall unique products: 18,24,27,32,35,36,40,42,48,49,54,60,81,84,88,96,108,120,132

Now, apply the color key:

Key:

- yellow: 32,49,81 → so 32,49,81 are yellow

- orange: >84 → so products greater than 84: 88,96,108,120,132

But wait, purple is 108,144 — so 108 and 144 are purple, not orange. Similarly, green has 132, so 132 is green, not orange.

Ah, here's the issue: the key has specific values for some colors, and ranges for others, but they might overlap. We need to prioritize the specific values over the ranges.

Typically in such keys, if a number is listed specifically, it takes precedence over a range.

So let's interpret the key as:

- If product is in {32,49,81} → yellow

- Else if product is in {108,144} → purple

- Else if product is in {54,60,132} → green

- Else if product is in {18,56} → blue

- Else if product >84 → orange (but since 108,144,132 are already taken, this would be 85-83? Wait no, >84 means 85 and above, but 108 etc are excluded because they have their own color)

Actually, better to define:

The key likely means:

- yellow: only 32,49,81

- purple: only 108,144

- green: only 54,60,132

- blue: only 18,56

- orange: any product >84 that is not already assigned to purple or green (since 108,144 are purple, 132 is green, so orange would be >84 except those)

- pink: >36,64 — this is still ambiguous.

For pink, it says ">36,64". Perhaps it's "products greater than 36 and less than or equal to 64", or "greater than 36 including 64".

But 64 is not in our product list yet. Do we have 64? Let's see: is there an equation that gives 64? 8x8=64, but I don't see 8x8 in the list. 4x16 no. So 64 may not appear.

In our list, we have products like 40,42,48, etc.

Perhaps "pink → >36, 64" means "products greater than 36, and 64 is an example" or something. But that doesn't help.

Another possibility: maybe it's "pink → 37 to 64 inclusive", and "64" is listed separately by mistake.

Or perhaps "pink → >36 and ≤64", and "64" is part of it.

Let's assume that "pink → >36, 64" means products greater than 36 up to and including 64. Since 64 is mentioned, and it's a common number.

In our product list, we have: 40,42,48,35,36, etc.

36 is not greater than 36, so if pink is >36, then 36 is not included.

But what about 36? Where does 36 go?

From key, blue is 18,56 — 36 not there.

Green is 54,60,132 — not 36.

Yellow is 32,49,81 — not 36.

Purple is 108,144 — no.

Orange is >84 — 36<84, no.

So 36 must be in pink or blue, but blue is only 18,56.

Perhaps pink includes 36.

Maybe "pink → >36, 64" is a typo, and it's "pink → 36, 64" or "pink → ≥36 and ≤64".

Let's look at the values we have and see what makes sense.

List all products and try to assign:

Products: 18,24,27,32,35,36,40,42,48,49,54,60,81,84,88,96,108,120,132

Assign based on key:

- 18: blue (since blue is 18,56)

- 24: ? not in any specific list. >36? No, 24<36. So perhaps not pink. What color? Maybe I missed something.

This is problematic.

Perhaps the key is:

- yellow: 32,49,81

- orange: >84 (and not otherwise specified)

- purple: 108,144

- green: 54,60,132

- pink: >36 and ≤84, but excluding those in other categories? But then 49,81 are in yellow, so pink would be >36 and ≤84 except 49,81,54,60, etc.

But 54 and 60 are in green, so they are not pink.

Similarly, 49 and 81 are yellow.

So for pink: products >36 and ≤84, not in yellow, green, purple, blue, orange.

But orange is >84, so for ≤84, orange doesn't apply.

So pink could be: >36 and ≤84, and not in {32,49,81,54,60,132,108,144,18,56}

But 132>84, so not in this range.

So for products between 37 and 84 inclusive, not in the specific lists.

Specific lists for this range: yellow has 49,81; green has 54,60; blue has 56? 56 is in blue, but 56 is between 37 and 84.

Blue is 18,56, so 56 is blue.

So pink would be: >36 and ≤84, and not in {49,81,54,60,56} (since those are assigned to other colors)

Also, 32 is yellow, but 32<36, so not in pink range.

So let's list products in 37 to 84: from our list: 40,42,48,84

40,42,48,84

Are any of these in specific colors? 49,81,54,60,56 are not among them, so they should be pink.

What about 36? 36 is not >36, so if pink is >36, then 36 is not included.

Where does 36 go? Not in any specific list. Blue is 18,56 — not 36. Green no, etc.

Perhaps 36 is also pink, or maybe the key has a mistake.

Another idea: perhaps "pink → >36, 64" means "products greater than 36 or equal to 64", but 64 not in list.

Or perhaps "64" is a separate value for pink, but since it's not in our calculations, ignore.

Let's check if 64 appears. Is there an equation like 8x8? In the image, I don't see it. 4x16 no. So probably not.

Perhaps "pink → >36" and "64" is a typo or for another purpose.

Let's look back at the user's input: "pink → >36, 64"

In some formats, it might mean "pink for products >36 and also for 64", but since 64>36, it's redundant.

Perhaps it's "pink → 36 < product ≤ 64" , so from 37 to 64 inclusive.

Then 64 is included.

In our list, products in 37 to 64: 40,42,48,54,60

But 54 and 60 are in green, so they are not pink.

So pink would be 40,42,48

Then what about 36? Still unassigned.

36 is 9x4 and 12x3.

Perhaps 36 is blue? But blue is 18,56.

Or maybe the key has "blue → 18,56" but 36 is close to 32, but 32 is yellow.

Another thought: perhaps "pink → >36, 64" means "products greater than 36, and 64 is an example of a pink product", but since 64 not present, we can ignore.

But then 36 is still unassigned.

Let's calculate all products again to make sure we have them all.

From the image description, the sections are:

- Left egg: 6 sections: 8x6=48, 3x9=27, 5x8=40, 4x8=32, 9x6=54, 5x12=60

- Right egg: 6 sections: 7x6=42, 8x3=24, 9x4=36, 7x7=49, 12x3=36, 12x11=132

- Flower: 1 section: 11x8=88

- Leaves: let's say from the drawing, there are several parts. Typically, for such images, the leaves have:

- One leaf with 9x2=18, 5x7=35, 6x9=54

- Another leaf with 12x5=60, 12x7=84, 12x9=108

- Another leaf with 9x9=81, 7x7=49, 12x10=120, 12x8=96, 12x11=132, 9x6=54 — but that's 6 sections for one leaf? Unlikely.

Perhaps the leaves are divided into fewer sections.

To resolve, let's assume that all equations are as listed in the initial extraction, and we have the products.

Perhaps for 36, it is intended to be pink, or blue.

Let's look at the key again: "blue → 18,56" — 56 is 7x8, but is 7x8 in the image? I don't see it. 8x7=56, but not listed. In our list, we have 5x7=35, not 56.

So 56 may not appear, similarly 64 may not appear.

So perhaps the key is:

- yellow: 32,49,81

- orange: >84 (and not purple or green)

- purple: 108,144

- green: 54,60,132

- blue: 18,56

- pink: all other products that are >36

But then 24,27,35,36 are ≤36, so not pink.

What color for 24,27,35,36?

Not specified.

Perhaps "pink → >36" means products greater than 36 are pink, unless specified otherwise, and products ≤36 are blue or something, but blue is only 18,56.

This is messy.

Another idea: perhaps "pink → >36, 64" is "pink for products >36 and for 64", but since 64>36, it's the same, and for products ≤36, they are blue if 18 or 56, else perhaps no color, but that can't be.

Let's calculate the product for 9x4=36, and 12x3=36.

In many such worksheets, 36 might be intended for a specific color.

Perhaps the key has a mistake, and "pink → 36, 64" or "pink → ≥36 and ≤64".

Let's assume that "pink → >36, 64" means products from 37 to 64 inclusive, and 64 is emphasized.

Then for our products:

- 36: not >36, so not pink. What color? Perhaps it is blue, but blue is 18,56.

Or maybe 36 is yellow? But yellow is 32,49,81 — 36 not there.

Perhaps 36 is green? No.

Let's list all products and assign based on priority:

Priority to specific values first.

So:

- If product in {32,49,81} -> yellow

- Else if in {108,144} -> purple

- Else if in {54,60,132} -> green

- Else if in {18,56} -> blue

- Else if >84 -> orange (since 108,144,132 are already taken, this would be 85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,109, etc, but in our case 88,96,120)

- Else if >36 -> pink (so 37 to 84, but excluding those already assigned)

- Else -> ? for ≤36 and not in blue

For ≤36 and not in {18,56}, we have 24,27,35,36

56 is not in our product list, as we saw.

So for 24,27,35,36, no color assigned.

Perhaps they are also pink, or blue.

Maybe "pink → >36, 64" includes 36, or perhaps the ">" is a typo.

Another possibility: in some keys, ">36, 64" might mean "greater than 36 or equal to 64", but again, 64 not present.

Perhaps "64" is for a different purpose.

Let's notice that in the top right, there is "6-12" which might be the grade, but also "6 x 12" is 72, and "3 x 2"=6, but in the image, it might be part of the design.

In the user's input, it says "6-12" in a box, but that's likely the grade level, not an equation.

So ignore.

Perhaps for 36, it is intended to be pink, and " >36" is a mistake, or "≥36".

Let's assume that "pink → >36, 64" means products greater than or equal to 36, and 64 is an example.

Then pink includes 36,40,42,48, etc.

Then for our products:

- 36: pink

- 40: pink

- 42: pink

- 48: pink

- 54: green (specific)

- 60: green

- 84: ? 84 is not >84, so not orange. Is it in other? 84 not in yellow, purple, green, blue. So if pink is ≥36, then 84 is pink.

But 84 is 12x7, and in the key, orange is >84, so 84 is not orange.

So if pink is ≥36, then 84 is pink.

Then orange is >84, so 88,96,108,120,132, but 108,132 are purple and green, so orange would be 88,96,120

108 is purple, 132 is green, so yes.

Now, what about 35? 5x7=35, which is <36, so not pink. Not in other categories. Blue is 18,56 — 35 not there.

So 35 is unassigned.

Similarly, 24,27 are unassigned.

Perhaps they are blue, but blue is only 18,56.

Or maybe the key has "blue → 18,56" but 56 is not present, so perhaps blue is for small numbers.

Another idea: perhaps "pink → >36, 64" is "pink for products >36, and blue for 18,56, and for other small numbers, they are also blue or something.

But let's calculate 5x7=35, and 3x9=27, 8x3=24.

In the context, perhaps 35,27,24 are to be colored with a default, but the key doesn't specify.

Perhaps I missed that "blue → 18,56" but 56 is 7x8, and if 7x8 is in the image, but in our list, we have 5x7=35, not 7x8.

Unless "5x7" is a typo, but unlikely.

Perhaps "64" is for 8x8, but not present.

Let's count the number of sections.

From the image description, there are:

- Egg: 12 sections (6+6)

- Flower: 1 section

- Leaves: let's say 6 sections or so.

Total around 19 sections.

Our product list has duplicates in value, but each section is separate.

For example, 54 appears multiple times, but each is a different section, so we color each based on its product.

So for assignment, we can do per section.

But for the key, we need to know what color for each product value.

Perhaps for products not in the key, they are not to be colored, but that can't be.

Let's look for a standard interpretation.

Upon second thought, in many such worksheets, the key is:

- yellow: 32,49,81

- orange: >84

- purple: 108,144

- green: 54,60,132

- pink: 36,64 (perhaps " >36, 64" is a miswrite, and it's "36,64")

- blue: 18,56

Then for 36, it is pink.

For 64, if it appears, pink, but it doesn't.

For 56, if it appears, blue, but in our list, we have 35, not 56.

So for 35, it is not in any, so perhaps it is pink or blue.

Assume that "pink → 36,64" and "blue → 18,56", and for other values, they fall into the ranges.

But then for 40, it is >36, so if pink is only 36,64, then 40 is not pink.

This is not working.

Perhaps "pink → >36" means all products >36 are pink, unless specified otherwise, and for ≤36, they are blue if 18 or 56, else perhaps no color, but that can't be.

Let's calculate the product for 9x4=36, and see what color it should be.

Perhaps in the key, "pink → >36, 64" and "blue → 18,56", and for 36, it is considered >36? No, 36 is not >36.

Unless the ">" is inclusive, but usually ">" means strictly greater.

Another idea: perhaps " >36, 64" means "greater than 36 or equal to 64", but 64>36, so same as >36.

I think the most reasonable assumption is that "pink → >36" means products greater than 36 are pink, and for products ≤36, they are to be colored with blue if 18 or 56, but since 56 may not appear, and for 24,27,35,36, they might be intended to be blue or pink.

Perhaps 36 is included in pink by convention.

Let's check online or standard practice, but since I can't, let's assume that for this worksheet, the key is:

- yellow: 32,49,81

- orange: >84 (and not purple or green)

- purple: 108,144

- green: 54,60,132

- blue: 18,56

- pink: all other products (i.e., not in the above)

Then for our products:

- 18: blue

- 24: pink (since not in other)

- 27: pink

- 32: yellow

- 35: pink

- 36: pink

- 40: pink

- 42: pink

- 48: pink

- 49: yellow

- 54: green

- 60: green

- 81: yellow

- 84: pink (since not >84, and not in other)

- 88: orange (>84, not purple or green)

- 96: orange

- 108: purple

- 120: orange

- 132: green

This seems consistent, and 56 and 64 are not in our list, so no problem.

For 84, it is not >84, so not orange, and not in other specific, so pink.

For 36, pink.

For 35,24,27, pink.

So let's go with that.

So summary of color assignment:

- yellow: 32,49,81

- orange: 88,96,120 (since >84 and not 108,132,144)

- purple: 108

- green: 54,60,132

- blue: 18

- pink: 24,27,35,36,40,42,48,84

Now, let's list each section with its product and color.

From left egg:
- 8x6=48 -> pink
- 3x9=27 -> pink
- 5x8=40 -> pink
- 4x8=32 -> yellow
- 9x6=54 -> green
- 5x12=60 -> green

From right egg:
- 7x6=42 -> pink
- 8x3=24 -> pink
- 9x4=36 -> pink
- 7x7=49 -> yellow
- 12x3=36 -> pink
- 12x11=132 -> green

From flower:
- 11x8=88 -> orange

From leaves:
Assume the leaves have:
- 9x2=18 -> blue
- 5x7=35 -> pink
- 6x9=54 -> green
- 12x5=60 -> green
- 12x7=84 -> pink
- 12x9=108 -> purple
- 9x9=81 -> yellow
- 7x7=49 -> yellow (another section)
- 12x10=120 -> orange
- 12x8=96 -> orange
- 12x11=132 -> green (another section)
- 9x6=54 -> green (another section)

In the image, there might be more or less, but based on common design, this should cover.

So to answer the user, since the task is to solve the equations and color using the key, and the user may want the color for each section, but since it's a coloring page, perhaps they want the final colored image, but as text, we can list the color for each equation.

But the user said "solve the problem accurately", and "provide the final answer", so perhaps list the color for each unique equation or something.

Since it's a homework, likely they need to know what color to use for each part.

But for the final answer, perhaps we can state the color mapping.

Since the instruction is to provide the final answer after reasoning, and for this type, the final answer might be the completed coloring, but in text, we can summarize.

Perhaps the "final answer" is the list of colors for the sections, but that's long.

Another way: perhaps the user wants the solution to the multiplications and the corresponding colors.

But to keep it simple, since the task is to color based on the key, and we have resolved the key, we can box the color assignments.

But for the response, since the options are false, we only need Final Answer.

So let's provide the color for each product value as per our resolution.

Final Answer:

Based on the color key and calculations:

- Products 32, 49, 81: yellow
- Products >84 and not 108,132,144: orange (e.g., 88,96,120)
- Products 108, 144: purple
- Products 54, 60, 132: green
- Product 18: blue (56 not present)
- All other products (24,27,35,36,40,42,48,84): pink

For the specific sections in the image, apply this mapping.

To be precise, here is the color for each equation mentioned:

- 8×6=48: pink
- 3×9=27: pink
- 5×8=40: pink
- 4×8=32: yellow
- 9×6=54: green
- 5×12=60: green
- 7×6=42: pink
- 8×3=24: pink
- 9×4=36: pink
- 7×7=49: yellow
- 12×3=36: pink
- 12×11=132: green
- 11×8=88: orange
- 9×2=18: blue
- 5×7=35: pink
- 6×9=54: green
- 12×5=60: green
- 12×7=84: pink
- 12×9=108: purple
- 9×9=81: yellow
- 12×10=120: orange
- 12×8=96: orange
- 9×6=54: green (if present)

Note: Some equations repeat, but each section is colored based on its product.

This should allow the student to color the page correctly.

For the Final Answer, since it's a coloring task, perhaps there is no single answer, but the mapping is the solution.

Given the constraints, I'll box the color mapping as the final answer.

Final Answer:
The color for each product is determined as follows:
- Yellow: 32, 49, 81
- Orange: products greater than 84 except 108, 132, 144 (e.g., 88, 96, 120)
- Purple: 108, 144
- Green: 54, 60, 132
- Blue: 18, 56 (though 56 may not appear)
- Pink: all other products (24, 27, 35, 36, 40, 42, 48, 84)

Apply this to each section's product to color the page.