You’ve uploaded an image containing a set of arithmetic problems — mostly subtraction and addition equations with missing numbers. The hint says: *“Make a fact triangle to help you solve.”*
Let’s break this down step by step.
---
## 🔍 What is a “Fact Triangle”?
A
fact triangle is a visual tool that shows the relationship between three numbers in an addition/subtraction or multiplication/division fact family.
For example, for the numbers 5, 3, and 8:
```
8
/ \
5 3
```
This means:
- 5 + 3 = 8
- 3 + 5 = 8
- 8 - 5 = 3
- 8 - 3 = 5
We’ll use this idea to solve each problem.
---
## ✏️ Solving Each Problem
We’ll go row by row.
---
Row 1:
>
42 - ___ = 38
→ Think: What number subtracted from 42 gives 38?
→ 42 - 38 =
4
✔ Answer:
4
>
___ - 8 = 5
→ Think: What number minus 8 equals 5?
→ 5 + 8 =
13
✔ Answer:
13
---
Row 2:
>
184 - ___ = 65
→ 184 - 65 =
119
✔ Answer:
119
>
39 + ___ = 48
→ 48 - 39 =
9
✔ Answer:
9
---
Row 3:
>
132 - ___ = 101
→ 132 - 101 =
31
✔ Answer:
31
>
___ + 12 = 80
→ 80 - 12 =
68
✔ Answer:
68
---
Row 4:
>
___ - 38 = 174
→ 174 + 38 =
212
✔ Answer:
212
>
27 + ___ = 48
→ 48 - 27 =
21
✔ Answer:
21
---
Row 5:
>
___ - 209 = 116
→ 116 + 209 =
325
✔ Answer:
325
>
___ + 6 = 18
→ 18 - 6 =
12
✔ Answer:
12
---
Row 6:
>
151 - 23 = ___
→ 151 - 23 =
128
✔ Answer:
128
>
___ + 4 = 93
→ 93 - 4 =
89
✔ Answer:
89
---
Row 7:
>
343 - ___ = 91
→ 343 - 91 =
252
✔ Answer:
252
>
31 + ___ = 65
→ 65 - 31 =
34
✔ Answer:
34
---
Row 8:
>
39 - ___ = 38
→ 39 - 38 =
1
✔ Answer:
1
>
152 + 198 = ___
→ 152 + 198 =
350
✔ Answer:
350
---
Row 9:
>
99 - ___ = 72
→ 99 - 72 =
27
✔ Answer:
27
*(Note: There’s no second equation in the last row — only one blank.)*
---
## 🧩 Final Answers (Left to Right, Top to Bottom):
```
4 13
119 9
31 68
212 21
325 12
128 89
252 34
1 350
27
```
---
## 💡 How Fact Triangles Help
For any equation like `A - B = C`, the fact triangle would be:
```
A
/ \
B C
```
So if you know two numbers, you can find the third.
Example: For `___ - 8 = 5`, think of triangle:
```
?
/ \
8 5
```
→ ? = 8 + 5 = 13
Similarly, for `39 + ___ = 48` → think:
```
48
/ \
39 ?
```
→ ? = 48 - 39 = 9
This method reinforces inverse operations and helps build number sense.
---
✔ All problems solved! Let me know if you’d like them formatted in a grid or worksheet style.
Parent Tip: Review the logic above to help your child master the concept of open sentence math worksheet.
