https://r2.erweima.ai/mathbot/image/1726591607621pfsuzrw7.jpg

Here are the steps to solve the problems from the image:

### 1. \( \sqrt{7} + 10 \)

- First, calculate the square root of 7.
  \[
  \sqrt{7} \approx 2.6458
  \]
- Add 10 to this result.
  \[
  2.6458 + 10 = 12.6458
  \]

### 2. \( \frac{1}{2} + \frac{1}{3} + \frac{1}{6} \)

- Find a common denominator. The least common denominator (LCD) of 2, 3, and 6 is 6.
  \[
  \frac{1}{2} = \frac{3}{6}, \quad \frac{1}{3} = \frac{2}{6}, \quad \frac{1}{6} = \frac{1}{6}
  \]
- Now, add the fractions:
  \[
  \frac{3}{6} + \frac{2}{6} + \frac{1}{6} = \frac{6}{6} = 1
  \]

### 3. \( \frac{\frac{1}{2}}{\frac{1}{10}} \)

- When dividing fractions, multiply by the reciprocal:
  \[
  \frac{1}{2} \div \frac{1}{10} = \frac{1}{2} \times \frac{10}{1} = \frac{10}{2} = 5
  \]

### 4. \( 0.833\ldots - 0.666\ldots \)

- Both numbers are repeating decimals. First, approximate them:
  \[
  0.833\ldots \approx \frac{5}{6}, \quad 0.666\ldots \approx \frac{2}{3}
  \]
- To subtract:
  \[
  \frac{5}{6} - \frac{2}{3} = \frac{5}{6} - \frac{4}{6} = \frac{1}{6} \approx 0.166\ldots
  \]

Do you want more details or explanations?

Here are 5 related questions:
1. How do you simplify square roots like \( \sqrt{7} \) more accurately?
2. What are other ways to find a common denominator for adding fractions?
3. Can you explain more complex operations with fractions?
4. How do you convert repeating decimals into fractions?
5. How does dividing fractions differ from multiplying them?

**Tip:** When dividing fractions, always multiply by the reciprocal of the second fraction.

Solve the following problems: 1. √7 + 10, 2. 1/2 + 1/3 + 1/6, 3. (1/2) / (1/10), 4. 0.833... - 0.666...

Learn how to solve problems involving square roots, adding and dividing fractions, and subtracting repeating decimals. This step-by-step guide covers key concepts like simplifying square roots, finding a common denominator, and dividing fractions, with a focus on fractions and decimals suitable for 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