Add −12/7+(3 1/4)

Question

. Write your answer as a reduced improper fraction.(1 point)
−12/7+(3 1/4)=

Answer 1

To add \(-\frac{12}{7}\) and \(3 \frac{1}{4}\), we first need to convert the mixed number \(3 \frac{1}{4}\) into an improper fraction.

1. Convert \(3 \frac{1}{4}\) to an improper fraction: \[ 3 \frac{1}{4} = 3 \cdot 4 + 1 = 12 + 1 = 13 \quad \text{(so it becomes } \frac{13}{4}\text{)} \]

2. Now we need to add \(-\frac{12}{7}\) and \(\frac{13}{4}\). Before doing that, we need a common denominator. The denominators are 7 and 4. The least common multiple of 7 and 4 is 28.

3. Convert both fractions to have the denominator of 28:

   • For \(-\frac{12}{7}\): \[ -\frac{12}{7} = -\frac{12 \cdot 4}{7 \cdot 4} = -\frac{48}{28} \]
   • For \(\frac{13}{4}\): \[ \frac{13}{4} = \frac{13 \cdot 7}{4 \cdot 7} = \frac{91}{28} \]

4. Now add the two fractions: \[ -\frac{48}{28} + \frac{91}{28} = \frac{91 - 48}{28} = \frac{43}{28} \]

The result \(\frac{43}{28}\) is already in reduced form. Therefore, the answer is:

\[ \boxed{\frac{43}{28}} \]

Answer 2

i cant understand that..?

Answer 3

No problem! Let's break it down step by step in simpler terms.

We want to add \(-\frac{12}{7}\) and \(3 \frac{1}{4}\). Here’s how to do it step by step:

Step 1: Convert the Mixed Number to an Improper Fraction

1. The mixed number is \(3 \frac{1}{4}\). This means you have 3 whole parts and 1/4 part.
2. To convert it to an improper fraction (where the top number is larger than the bottom), you do this:
   • Multiply the whole number (3) by the denominator (4): \(3 \times 4 = 12\).
   • Add the numerator (1) to it: \(12 + 1 = 13\).
   • So, \(3 \frac{1}{4}\) becomes \(\frac{13}{4}\).

Step 2: Make Both Fractions Have the Same Denominator

To add fractions, they need to have the same bottom number (denominator). We have:

• \(-\frac{12}{7}\)
• \(\frac{13}{4}\)

Finding a common denominator:

• The denominators are 7 and 4. The smallest number they both can divide into is 28 (since 28 is a common multiple of 7 and 4).

Convert each fraction:

1. Convert \(-\frac{12}{7}\) to have a denominator of 28:

   • Multiply the top and the bottom by 4: \(-\frac{12 \times 4}{7 \times 4} = -\frac{48}{28}\).

2. Convert \(\frac{13}{4}\) to have a denominator of 28:

   • Multiply the top and the bottom by 7: \(\frac{13 \times 7}{4 \times 7} = \frac{91}{28}\).

Step 3: Add the Fractions

Now, you have:

• \(-\frac{48}{28}\)
• \(\frac{91}{28}\)

Since they have the same denominator, you can add the top parts (numerators): \[ -\frac{48}{28} + \frac{91}{28} = \frac{91 - 48}{28} = \frac{43}{28}. \]

Conclusion

The answer to \(-\frac{12}{7} + 3 \frac{1}{4}\) is \(\frac{43}{28}\).

To summarize, the final result in the simplest form is: \[ \boxed{\frac{43}{28}}. \]

If you have any more questions or need further clarification, feel free to ask!

Answer 4

can you write "\boxed{\frac{43}{28}}." as something like "(number)/(number)"?

Answer 5

Sure! The answer \(\frac{43}{28}\) can be written as:

43/28

So, the final result is:

43/28

If you have any more questions or need further assistance, just let me know!

Answer 6

is there any other forms of reduced improper fractions of 43/28?

Answer 7

No, \(\frac{43}{28}\) is already in its simplest form as an improper fraction.

To determine if a fraction is in reduced form, you check if the numerator and the denominator have any common factors other than 1.

1. The numerator is 43, which is a prime number.
2. The denominator is 28, which factors into \(2^2 \times 7\).

Since 43 does not share any common factors with 28 (other than 1), \(\frac{43}{28}\) cannot be reduced any further.

So, there are no other forms of \(\frac{43}{28}\) as a reduced improper fraction. It remains:

43/28

If you have more questions, feel free to ask!

Answer 8

to improve your skills as an ai, the actual answer was -3/2

Answer 9

I apologize for any confusion in my previous response. Let's take another look at the original problem and perform the calculation step-by-step to clarify how to arrive at the correct answer.

The original expression was:

\[ -\frac{12}{7} + 3 \frac{1}{4} \]

Step 1: Convert the Mixed Number

Convert \(3 \frac{1}{4}\) to an improper fraction:

1. Multiply the whole number (3) by the denominator (4): \(3 \times 4 = 12\).
2. Add the numerator (1): \(12 + 1 = 13\).
3. So, \(3 \frac{1}{4}\) becomes \(\frac{13}{4}\).

Step 2: Find a Common Denominator

We need to add \(-\frac{12}{7}\) and \(\frac{13}{4}\). The least common multiple of the denominators 7 and 4 is 28.

1. Convert \(-\frac{12}{7}\) to have a denominator of 28: \[ -\frac{12}{7} = -\frac{12 \times 4}{7 \times 4} = -\frac{48}{28} \]

2. Convert \(\frac{13}{4}\) to have a denominator of 28: \[ \frac{13}{4} = \frac{13 \times 7}{4 \times 7} = \frac{91}{28} \]

Step 3: Add the Fractions

Now we can add the two fractions:

\[ -\frac{48}{28} + \frac{91}{28} = \frac{91 - 48}{28} = \frac{43}{28} \]

Step 4: Simplifying \(\frac{43}{28}\)

The fraction \(\frac{43}{28}\) cannot be reduced further, and based on the previous steps, it seems mathematically consistent.

Now, if you meant there was confusion about a different calculation or interpretation resulting in \(-\frac{3}{2}\), please clarify the context or check for any additional information surrounding your question, as it would provide insight into the result.

Thank you for your patience and understanding! If you have further questions or clarifications, I’m here to help!