Question
Jonathan says that when you add 723 to 223 , you must add the whole numbers together first ( 7+2=9 ). Then you just add the numerators together ( 2+2=4 ), and you add the denominators together ( 3+3=6 ). So the answer is 946 . Unfortunately, Jonathan's strategy is incorrect. Solve this problem, and then briefly explain the flaw in Jonathan's reasoning.
Answers
GPT-4o mini
To solve the addition of 723 and 223 properly, we need to add the numbers as whole numbers:
```
723
+ 223
------
946
```
So indeed, the correct answer is **946**. However, let's examine Jonathan's reasoning:
1. Jonathan adds the whole number parts (7 and 2) to get 9, which he places in the hundreds place.
2. He adds the numerators (2 and 2), positioning it into the tens place.
3. He adds the denominators (3 and 3), placing it into the units place.
The flaw in Jonathan's reasoning lies in the misinterpretation of how addition of numbers works.
- **Whole numbers**: 723 and 223 are whole numbers and should be added directly as such.
- **Numerators and denominators**: In this context, numbers should not be treated as fractions, and the method he uses to add numerators and denominators is not applicable here. For whole numbers, you cannot separate the digits and treat them as independent parts that can be added separately in the way he did.
In summary, the error is the misunderstanding of how to properly add whole numbers; the digits should not be added individually as if they represent separate components, as that does not reflect proper arithmetic operations.
```
723
+ 223
------
946
```
So indeed, the correct answer is **946**. However, let's examine Jonathan's reasoning:
1. Jonathan adds the whole number parts (7 and 2) to get 9, which he places in the hundreds place.
2. He adds the numerators (2 and 2), positioning it into the tens place.
3. He adds the denominators (3 and 3), placing it into the units place.
The flaw in Jonathan's reasoning lies in the misinterpretation of how addition of numbers works.
- **Whole numbers**: 723 and 223 are whole numbers and should be added directly as such.
- **Numerators and denominators**: In this context, numbers should not be treated as fractions, and the method he uses to add numerators and denominators is not applicable here. For whole numbers, you cannot separate the digits and treat them as independent parts that can be added separately in the way he did.
In summary, the error is the misunderstanding of how to properly add whole numbers; the digits should not be added individually as if they represent separate components, as that does not reflect proper arithmetic operations.