To subtract the mixed number \(-3 \frac{1}{3}\) and the fraction \(\frac{7}{12}\), let's break it down into steps.

### Step 1: Convert the mixed number to an improper fraction.
\[
-3 \frac{1}{3} = -\frac{10}{3}
\]
This is done by multiplying the whole number \(3\) by the denominator \(3\), and adding the numerator \(1\), then keeping the sign.

### Step 2: Find a common denominator.
The least common denominator (LCD) between \(3\) and \(12\) is \(12\).

- Convert \(-\frac{10}{3}\) to have a denominator of 12:
\[
-\frac{10}{3} = -\frac{40}{12}
\]

### Step 3: Perform the subtraction.
Now, subtract \(\frac{7}{12}\) from \(-\frac{40}{12}\):
\[
-\frac{40}{12} - \frac{7}{12} = -\frac{40 + 7}{12} = -\frac{47}{12}
\]

### Step 4: Simplify the result.
\(-\frac{47}{12}\) is already in its simplest form. As a mixed number:
\[
-\frac{47}{12} = -3 \frac{11}{12}
\]

So, \(-3 \frac{1}{3} - \frac{7}{12} = -3 \frac{11}{12}\).

Would you like any more details or explanations?

---

Here are 5 questions that build on this:
1. How do you find the least common denominator between two fractions?
2. Can you convert \(-3 \frac{11}{12}\) back to an improper fraction?
3. How would you add two mixed numbers?
4. What is the process of simplifying improper fractions?
5. How do you subtract fractions with unlike denominators?

**Tip:** Always remember to simplify fractions after performing operations to get the final answer.

Learn how to subtract mixed numbers and fractions through the example -3 1/3 - 7/12. This detailed step-by-step solution covers converting mixed numbers to improper fractions, finding a common denominator, and simplifying the result. Ideal for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation