Arithmogon Triangle Puzzle 5A – A math worksheet featuring nine triangular puzzles with decimal numbers and blank spaces to solve.
Educational worksheet: Addition Math Puzzles #5 Worksheets | 99Worksheets. Download and print for classroom or home learning activities.
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Show Answer Key & Explanations
Step-by-step solution for: Addition Math Puzzles #5 Worksheets | 99Worksheets
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Show Answer Key & Explanations
Step-by-step solution for: Addition Math Puzzles #5 Worksheets | 99Worksheets
To solve these puzzles, we need to understand the rule: The number in each rectangle is the sum of the two numbers in the circles connected to it.
Let's break down each triangle one by one. I will label the positions as Top Circle, Bottom-Left Circle, and Bottom-Right Circle. The rectangles are Left (connecting Top and Bottom-Left), Right (connecting Top and Bottom-Right), and Bottom (connecting Bottom-Left and Bottom-Right).
Triangle 1 (Top Left)
* Given: Top = 1.3, Bottom-Left = 0.7, Bottom-Right = 0.4, Left Rectangle = 2.
* Find Right Rectangle: Connects Top (1.3) and Bottom-Right (0.4).
* Calculation: $1.3 + 0.4 = 1.7$
* Find Bottom Rectangle: Connects Bottom-Left (0.7) and Bottom-Right (0.4).
* Calculation: $0.7 + 0.4 = 1.1$
* *Check:* Does Left Rectangle match? Top (1.3) + Bottom-Left (0.7) = 2. Yes.
Triangle 2 (Top Middle)
* Given: Top = 0.9, Bottom-Left = 1.2, Bottom-Right = 1.6.
* Find Left Rectangle: Connects Top (0.9) and Bottom-Left (1.2).
* Calculation: $0.9 + 1.2 = 2.1$
* Find Right Rectangle: Connects Top (0.9) and Bottom-Right (1.6).
* Calculation: $0.9 + 1.6 = 2.5$
* Find Bottom Rectangle: Connects Bottom-Left (1.2) and Bottom-Right (1.6).
* Calculation: $1.2 + 1.6 = 2.8$
Triangle 3 (Top Right)
* Given: Top = 2.3, Bottom-Left = 1.2, Bottom-Right = 0.8.
* Find Left Rectangle: Connects Top (2.3) and Bottom-Left (1.2).
* Calculation: $2.3 + 1.2 = 3.5$
* Find Right Rectangle: Connects Top (2.3) and Bottom-Right (0.8).
* Calculation: $2.3 + 0.8 = 3.1$
* Find Bottom Rectangle: Connects Bottom-Left (1.2) and Bottom-Right (0.8).
* Calculation: $1.2 + 0.8 = 2.0$ (or just 2)
Triangle 4 (Middle Left)
* Given: Top = 1.7, Bottom-Left = -0.3, Bottom-Right = 1.
* Find Left Rectangle: Connects Top (1.7) and Bottom-Left (-0.3).
* Calculation: $1.7 + (-0.3) = 1.4$
* Find Right Rectangle: Connects Top (1.7) and Bottom-Right (1).
* Calculation: $1.7 + 1 = 2.7$
* Find Bottom Rectangle: Connects Bottom-Left (-0.3) and Bottom-Right (1).
* Calculation: $-0.3 + 1 = 0.7$
Triangle 5 (Middle Center)
* Given: Bottom-Left = 0.7, Bottom-Right = 2.1, Left Rectangle = 2.
* Find Top Circle: We know Left Rectangle (2) = Top + Bottom-Left (0.7).
* Calculation: $2 - 0.7 = 1.3$. So, Top = 1.3.
* Find Right Rectangle: Connects Top (1.3) and Bottom-Right (2.1).
* Calculation: $1.3 + 2.1 = 3.4$
* Find Bottom Rectangle: Connects Bottom-Left (0.7) and Bottom-Right (2.1).
* Calculation: $0.7 + 2.1 = 2.8$
Triangle 6 (Middle Right)
* Given: Top = 3.5, Bottom-Right = -0.2, Left Rectangle = 4.3.
* Find Bottom-Left Circle: We know Left Rectangle (4.3) = Top (3.5) + Bottom-Left.
* Calculation: $4.3 - 3.5 = 0.8$. So, Bottom-Left = 0.8.
* Find Right Rectangle: Connects Top (3.5) and Bottom-Right (-0.2).
* Calculation: $3.5 + (-0.2) = 3.3$
* Find Bottom Rectangle: Connects Bottom-Left (0.8) and Bottom-Right (-0.2).
* Calculation: $0.8 + (-0.2) = 0.6$
Triangle 7 (Bottom Left)
* Given: Top = 4, Bottom-Left = -0.6, Bottom-Right = -0.3.
* Find Left Rectangle: Connects Top (4) and Bottom-Left (-0.6).
* Calculation: $4 + (-0.6) = 3.4$
* Find Right Rectangle: Connects Top (4) and Bottom-Right (-0.3).
* Calculation: $4 + (-0.3) = 3.7$
* Find Bottom Rectangle: Connects Bottom-Left (-0.6) and Bottom-Right (-0.3).
* Calculation: $-0.6 + (-0.3) = -0.9$
Triangle 8 (Bottom Middle)
* Given: Top = 1.5, Bottom-Left = 1.7, Bottom Rectangle = 2.3.
* Find Bottom-Right Circle: We know Bottom Rectangle (2.3) = Bottom-Left (1.7) + Bottom-Right.
* Calculation: $2.3 - 1.7 = 0.6$. So, Bottom-Right = 0.6.
* Find Left Rectangle: Connects Top (1.5) and Bottom-Left (1.7).
* Calculation: $1.5 + 1.7 = 3.2$
* Find Right Rectangle: Connects Top (1.5) and Bottom-Right (0.6).
* Calculation: $1.5 + 0.6 = 2.1$
Triangle 9 (Bottom Right)
* Given: Top = 1.7, Bottom-Right = 0.9, Bottom Rectangle = 1.7.
* Find Bottom-Left Circle: We know Bottom Rectangle (1.7) = Bottom-Left + Bottom-Right (0.9).
* Calculation: $1.7 - 0.9 = 0.8$. So, Bottom-Left = 0.8.
* Find Left Rectangle: Connects Top (1.7) and Bottom-Left (0.8).
* Calculation: $1.7 + 0.8 = 2.5$
* Find Right Rectangle: Connects Top (1.7) and Bottom-Right (0.9).
* Calculation: $1.7 + 0.9 = 2.6$
Final Answer:
Here are the missing numbers for each puzzle, listed from left to right, top to bottom:
Row 1:
1. Right Rectangle: 1.7, Bottom Rectangle: 1.1
2. Left Rectangle: 2.1, Right Rectangle: 2.5, Bottom Rectangle: 2.8
3. Left Rectangle: 3.5, Right Rectangle: 3.1, Bottom Rectangle: 2
Row 2:
4. Left Rectangle: 1.4, Right Rectangle: 2.7, Bottom Rectangle: 0.7
5. Top Circle: 1.3, Right Rectangle: 3.4, Bottom Rectangle: 2.8
6. Bottom-Left Circle: 0.8, Right Rectangle: 3.3, Bottom Rectangle: 0.6
Row 3:
7. Left Rectangle: 3.4, Right Rectangle: 3.7, Bottom Rectangle: -0.9
8. Left Rectangle: 3.2, Right Rectangle: 2.1, Bottom-Right Circle: 0.6
9. Bottom-Left Circle: 0.8, Left Rectangle: 2.5, Right Rectangle: 2.6
Let's break down each triangle one by one. I will label the positions as Top Circle, Bottom-Left Circle, and Bottom-Right Circle. The rectangles are Left (connecting Top and Bottom-Left), Right (connecting Top and Bottom-Right), and Bottom (connecting Bottom-Left and Bottom-Right).
Triangle 1 (Top Left)
* Given: Top = 1.3, Bottom-Left = 0.7, Bottom-Right = 0.4, Left Rectangle = 2.
* Find Right Rectangle: Connects Top (1.3) and Bottom-Right (0.4).
* Calculation: $1.3 + 0.4 = 1.7$
* Find Bottom Rectangle: Connects Bottom-Left (0.7) and Bottom-Right (0.4).
* Calculation: $0.7 + 0.4 = 1.1$
* *Check:* Does Left Rectangle match? Top (1.3) + Bottom-Left (0.7) = 2. Yes.
Triangle 2 (Top Middle)
* Given: Top = 0.9, Bottom-Left = 1.2, Bottom-Right = 1.6.
* Find Left Rectangle: Connects Top (0.9) and Bottom-Left (1.2).
* Calculation: $0.9 + 1.2 = 2.1$
* Find Right Rectangle: Connects Top (0.9) and Bottom-Right (1.6).
* Calculation: $0.9 + 1.6 = 2.5$
* Find Bottom Rectangle: Connects Bottom-Left (1.2) and Bottom-Right (1.6).
* Calculation: $1.2 + 1.6 = 2.8$
Triangle 3 (Top Right)
* Given: Top = 2.3, Bottom-Left = 1.2, Bottom-Right = 0.8.
* Find Left Rectangle: Connects Top (2.3) and Bottom-Left (1.2).
* Calculation: $2.3 + 1.2 = 3.5$
* Find Right Rectangle: Connects Top (2.3) and Bottom-Right (0.8).
* Calculation: $2.3 + 0.8 = 3.1$
* Find Bottom Rectangle: Connects Bottom-Left (1.2) and Bottom-Right (0.8).
* Calculation: $1.2 + 0.8 = 2.0$ (or just 2)
Triangle 4 (Middle Left)
* Given: Top = 1.7, Bottom-Left = -0.3, Bottom-Right = 1.
* Find Left Rectangle: Connects Top (1.7) and Bottom-Left (-0.3).
* Calculation: $1.7 + (-0.3) = 1.4$
* Find Right Rectangle: Connects Top (1.7) and Bottom-Right (1).
* Calculation: $1.7 + 1 = 2.7$
* Find Bottom Rectangle: Connects Bottom-Left (-0.3) and Bottom-Right (1).
* Calculation: $-0.3 + 1 = 0.7$
Triangle 5 (Middle Center)
* Given: Bottom-Left = 0.7, Bottom-Right = 2.1, Left Rectangle = 2.
* Find Top Circle: We know Left Rectangle (2) = Top + Bottom-Left (0.7).
* Calculation: $2 - 0.7 = 1.3$. So, Top = 1.3.
* Find Right Rectangle: Connects Top (1.3) and Bottom-Right (2.1).
* Calculation: $1.3 + 2.1 = 3.4$
* Find Bottom Rectangle: Connects Bottom-Left (0.7) and Bottom-Right (2.1).
* Calculation: $0.7 + 2.1 = 2.8$
Triangle 6 (Middle Right)
* Given: Top = 3.5, Bottom-Right = -0.2, Left Rectangle = 4.3.
* Find Bottom-Left Circle: We know Left Rectangle (4.3) = Top (3.5) + Bottom-Left.
* Calculation: $4.3 - 3.5 = 0.8$. So, Bottom-Left = 0.8.
* Find Right Rectangle: Connects Top (3.5) and Bottom-Right (-0.2).
* Calculation: $3.5 + (-0.2) = 3.3$
* Find Bottom Rectangle: Connects Bottom-Left (0.8) and Bottom-Right (-0.2).
* Calculation: $0.8 + (-0.2) = 0.6$
Triangle 7 (Bottom Left)
* Given: Top = 4, Bottom-Left = -0.6, Bottom-Right = -0.3.
* Find Left Rectangle: Connects Top (4) and Bottom-Left (-0.6).
* Calculation: $4 + (-0.6) = 3.4$
* Find Right Rectangle: Connects Top (4) and Bottom-Right (-0.3).
* Calculation: $4 + (-0.3) = 3.7$
* Find Bottom Rectangle: Connects Bottom-Left (-0.6) and Bottom-Right (-0.3).
* Calculation: $-0.6 + (-0.3) = -0.9$
Triangle 8 (Bottom Middle)
* Given: Top = 1.5, Bottom-Left = 1.7, Bottom Rectangle = 2.3.
* Find Bottom-Right Circle: We know Bottom Rectangle (2.3) = Bottom-Left (1.7) + Bottom-Right.
* Calculation: $2.3 - 1.7 = 0.6$. So, Bottom-Right = 0.6.
* Find Left Rectangle: Connects Top (1.5) and Bottom-Left (1.7).
* Calculation: $1.5 + 1.7 = 3.2$
* Find Right Rectangle: Connects Top (1.5) and Bottom-Right (0.6).
* Calculation: $1.5 + 0.6 = 2.1$
Triangle 9 (Bottom Right)
* Given: Top = 1.7, Bottom-Right = 0.9, Bottom Rectangle = 1.7.
* Find Bottom-Left Circle: We know Bottom Rectangle (1.7) = Bottom-Left + Bottom-Right (0.9).
* Calculation: $1.7 - 0.9 = 0.8$. So, Bottom-Left = 0.8.
* Find Left Rectangle: Connects Top (1.7) and Bottom-Left (0.8).
* Calculation: $1.7 + 0.8 = 2.5$
* Find Right Rectangle: Connects Top (1.7) and Bottom-Right (0.9).
* Calculation: $1.7 + 0.9 = 2.6$
Final Answer:
Here are the missing numbers for each puzzle, listed from left to right, top to bottom:
Row 1:
1. Right Rectangle: 1.7, Bottom Rectangle: 1.1
2. Left Rectangle: 2.1, Right Rectangle: 2.5, Bottom Rectangle: 2.8
3. Left Rectangle: 3.5, Right Rectangle: 3.1, Bottom Rectangle: 2
Row 2:
4. Left Rectangle: 1.4, Right Rectangle: 2.7, Bottom Rectangle: 0.7
5. Top Circle: 1.3, Right Rectangle: 3.4, Bottom Rectangle: 2.8
6. Bottom-Left Circle: 0.8, Right Rectangle: 3.3, Bottom Rectangle: 0.6
Row 3:
7. Left Rectangle: 3.4, Right Rectangle: 3.7, Bottom Rectangle: -0.9
8. Left Rectangle: 3.2, Right Rectangle: 2.1, Bottom-Right Circle: 0.6
9. Bottom-Left Circle: 0.8, Left Rectangle: 2.5, Right Rectangle: 2.6
Parent Tip: Review the logic above to help your child master the concept of mathematics puzzle worksheets.
