https://file.aiquickdraw.com/mathbot/file/17284846727073yi3kaqp.jpg

Let's break down the problems from the image and solve them one by one:

### 1. A) Finding the Outer Radius of the Pipe:
- The **inner diameter** of the pipe is \( 3 \frac{3}{4} \) cm, which can be written as \( \frac{15}{4} \) cm.
- The **wall thickness** of the pipe is \( \frac{5}{7} \) cm.
- The **outer diameter** will be the sum of the inner diameter and twice the wall thickness, since the thickness is on both sides.

So, the outer diameter is:
\[
\text{Outer Diameter} = \text{Inner Diameter} + 2 \times \text{Wall Thickness}
\]
\[
\text{Outer Diameter} = \frac{15}{4} + 2 \times \frac{5}{7}
\]
Let's first calculate \( 2 \times \frac{5}{7} = \frac{10}{7} \).

Now, let's add \( \frac{15}{4} \) and \( \frac{10}{7} \). To do this, we need a common denominator:
\[
\text{LCD of 4 and 7 is 28}, \quad \frac{15}{4} = \frac{105}{28}, \quad \frac{10}{7} = \frac{40}{28}
\]
Now add:
\[
\text{Outer Diameter} = \frac{105}{28} + \frac{40}{28} = \frac{145}{28}
\]

Finally, the outer **radius** is half of the outer diameter:
\[
\text{Outer Radius} = \frac{1}{2} \times \frac{145}{28} = \frac{145}{56} \, \text{cm} \approx 2.59 \, \text{cm}
\]

### 1. B) What should be added to \( \frac{2}{3} + \frac{4}{5} + \frac{1}{4} \) to get 2?
First, let's find the sum of the fractions:
\[
\frac{2}{3} + \frac{4}{5} + \frac{1}{4}
\]
We need the least common denominator (LCD) of 3, 5, and 4. The LCD is 60.

Now, convert the fractions:
\[
\frac{2}{3} = \frac{40}{60}, \quad \frac{4}{5} = \frac{48}{60}, \quad \frac{1}{4} = \frac{15}{60}
\]
Now add them:
\[
\frac{40}{60} + \frac{48}{60} + \frac{15}{60} = \frac{103}{60}
\]
We want the sum to be 2, which is \( \frac{120}{60} \).

Now, what should be added to \( \frac{103}{60} \) to get \( \frac{120}{60} \)?
\[
\frac{120}{60} - \frac{103}{60} = \frac{17}{60}
\]
So, \( \frac{17}{60} \) should be added.

### 2. Plane Altitude Problem:
- The plane rose to a height of 22,000 feet.
- It then descended by 4,300 feet. After this, its altitude was:
\[
22,000 - 4,300 = 17,700 \, \text{feet}
\]
- The plane then ascended 5,563 feet to avoid another plane:
\[
17,700 + 5,563 = 23,263 \, \text{feet}
\]
- Finally, the plane descended 9,745 feet:
\[
23,263 - 9,745 = 13,518 \, \text{feet}
\]
Thus, the plane is flying at an altitude of **13,518 feet**.

---

Would you like more details or have any questions?

Here are 5 related questions to explore further:
1. What is the formula for converting between fractions and decimals?
2. How can you calculate the volume of a pipe if you know both its inner and outer radius?
3. How would the altitude change if the plane ascended by a different amount?
4. How would you add mixed numbers without converting to improper fractions first?
5. How do you find the least common denominator for fractions quickly?

**Tip**: When adding or subtracting fractions, finding the least common denominator (LCD) first simplifies the process considerably.

1. A) A water pipe has an inner diameter of 3 3/4 cm and a wall thickness of 5/7 cm. What is the outer radius of the pipe? B) What should be added to 2/3 + 4/5 + 1/4 to get 2? 2. A plane took off from the ground and rose to a height of 22,000 feet. It then descended 4,300 feet because of clouds. Another plane was approaching head-on, so it rose 5563 feet. After the oncoming plane passed, it descended 9,745 feet. At what altitude was the plane flying?

Learn how to calculate the outer radius of a pipe with a given inner diameter and wall thickness, and how to solve an altitude problem involving ascent and descent of a plane. This problem involves arithmetic operations with fractions and basic geometry. Suitable for students in Grades 6-8.

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