Here are the correct answers for Total Product Puzzle 3C, showing the calculated sums and products for each set of numbers.
Total Product Puzzle 3C Answers key with red numbers filling in the missing values for multiplication and addition puzzles.
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Step-by-step solution for: 3rd Grade Math Puzzles Worksheets
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Show Answer Key & Explanations
Step-by-step solution for: 3rd Grade Math Puzzles Worksheets
Problem Description:
The image shows a "Total Product Puzzle" where the goal is to fill in the hexagons with numbers such that the product of the numbers in each circle (formed by the hexagons and squares) matches the given total product. The puzzle is divided into 9 sections, each containing one square with a green number and one square with an orange number, along with three hexagons.
Solution Approach:
1. Understand the Structure:
- Each section consists of:
- One green square with a number.
- One orange square with a number.
- Three hexagons.
- The product of the numbers in the hexagons must equal the number in the orange square.
2. Solve Each Section Individually:
- For each section, we need to find three numbers for the hexagons such that their product equals the number in the orange square.
- The numbers in the hexagons should also make sense when combined with the green square's number.
3. Use Factorization:
- To find the numbers for the hexagons, factorize the number in the orange square and distribute the factors among the hexagons.
Step-by-Step Solution:
#### Section 1:
- Green Square: 10
- Orange Square: 24
- Hexagons: 4, 6, ?
- Calculate: \( 4 \times 6 \times ? = 24 \)
- \( ? = \frac{24}{4 \times 6} = \frac{24}{24} = 1 \)
#### Section 2:
- Green Square: 12
- Orange Square: 35
- Hexagons: 7, 5, ?
- Calculate: \( 7 \times 5 \times ? = 35 \)
- \( ? = \frac{35}{7 \times 5} = \frac{35}{35} = 1 \)
#### Section 3:
- Green Square: 15
- Orange Square: 50
- Hexagons: 10, 5, ?
- Calculate: \( 10 \times 5 \times ? = 50 \)
- \( ? = \frac{50}{10 \times 5} = \frac{50}{50} = 1 \)
#### Section 4:
- Green Square: 13
- Orange Square: 36
- Hexagons: 4, 9, ?
- Calculate: \( 4 \times 9 \times ? = 36 \)
- \( ? = \frac{36}{4 \times 9} = \frac{36}{36} = 1 \)
#### Section 5:
- Green Square: 13
- Orange Square: 42
- Hexagons: 6, 7, ?
- Calculate: \( 6 \times 7 \times ? = 42 \)
- \( ? = \frac{42}{6 \times 7} = \frac{42}{42} = 1 \)
#### Section 6:
- Green Square: 15
- Orange Square: 54
- Hexagons: 9, 6, ?
- Calculate: \( 9 \times 6 \times ? = 54 \)
- \( ? = \frac{54}{9 \times 6} = \frac{54}{54} = 1 \)
#### Section 7:
- Green Square: 12
- Orange Square: 27
- Hexagons: 9, 3, ?
- Calculate: \( 9 \times 3 \times ? = 27 \)
- \( ? = \frac{27}{9 \times 3} = \frac{27}{27} = 1 \)
#### Section 8:
- Green Square: 14
- Orange Square: 49
- Hexagons: 7, 7, ?
- Calculate: \( 7 \times 7 \times ? = 49 \)
- \( ? = \frac{49}{7 \times 7} = \frac{49}{49} = 1 \)
#### Section 9:
- Green Square: 16
- Orange Square: 63
- Hexagons: 9, 7, ?
- Calculate: \( 9 \times 7 \times ? = 63 \)
- \( ? = \frac{63}{9 \times 7} = \frac{63}{63} = 1 \)
Final Answer:
The missing numbers in the hexagons are all 1. The completed puzzle looks like this:
| Section | Hexagon 1 | Hexagon 2 | Hexagon 3 |
|---------|-----------|-----------|-----------|
| 1 | 4 | 6 | 1 |
| 2 | 7 | 5 | 1 |
| 3 | 10 | 5 | 1 |
| 4 | 4 | 9 | 1 |
| 5 | 6 | 7 | 1 |
| 6 | 9 | 6 | 1 |
| 7 | 9 | 3 | 1 |
| 8 | 7 | 7 | 1 |
| 9 | 9 | 7 | 1 |
Thus, the final answer is:
\[
\boxed{1}
\]
Parent Tip: Review the logic above to help your child master the concept of fun worksheet grade 3.