https://file.aiquickdraw.com/mathbot/file/1724841547008qmu6z95o.jpg

Let's go through the questions from the image one by one. I'll solve them and explain the process.

### **1. Fractions as operators:**
- **Question 1:** Find these fractions of amounts. Work out the answers.
  1. \(\frac{3}{4}\) of 24
  2. \(\frac{2}{3}\) of 15
  3. \(\frac{3}{5}\) of 20
  4. \(\frac{2}{7}\) of 21
  5. \(\frac{1}{8}\) of 32
  6. \(\frac{3}{10}\) of 50

**Solutions:**
1. \(\frac{3}{4}\) of 24:  
   \[
   \frac{3}{4} \times 24 = \frac{3 \times 24}{4} = \frac{72}{4} = 18
   \]

2. \(\frac{2}{3}\) of 15:  
   \[
   \frac{2}{3} \times 15 = \frac{2 \times 15}{3} = \frac{30}{3} = 10
   \]

3. \(\frac{3}{5}\) of 20:  
   \[
   \frac{3}{5} \times 20 = \frac{3 \times 20}{5} = \frac{60}{5} = 12
   \]

4. \(\frac{2}{7}\) of 21:  
   \[
   \frac{2}{7} \times 21 = \frac{2 \times 21}{7} = \frac{42}{7} = 6
   \]

5. \(\frac{1}{8}\) of 32:  
   \[
   \frac{1}{8} \times 32 = \frac{1 \times 32}{8} = \frac{32}{8} = 4
   \]

6. \(\frac{3}{10}\) of 50:  
   \[
   \frac{3}{10} \times 50 = \frac{3 \times 50}{10} = \frac{150}{10} = 15
   \]

### **2. Flower Problem:**
- Out of 200 plants, \(\frac{1}{4}\) have red flowers and \(\frac{1}{5}\) have yellow flowers. The remaining plants have no flowers at all. How many of each plant are there?
  1. Plants with red flowers
  2. Plants with yellow flowers
  3. Plants with no flowers

**Solutions:**
1. **Plants with red flowers:**  
   \[
   \frac{1}{4} \times 200 = \frac{200}{4} = 50
   \]

2. **Plants with yellow flowers:**  
   \[
   \frac{1}{5} \times 200 = \frac{200}{5} = 40
   \]

3. **Plants with no flowers:**  
   \[
   \text{Total without flowers} = 200 - 50 - 40 = 110
   \]

### **3. Ribbon Problem:**
- Pat and Jim have been cutting lengths of ribbon for their kites. Pat has a ribbon that is 45 cm long and wants \(\frac{1}{3}\) of it. Jim has a 48 cm long ribbon and uses \(\frac{5}{8}\) of his ribbon.
  1. What is the length of Pat’s piece of ribbon?
  2. What is the length of Jim’s piece of ribbon?
  3. How much ribbon did Jim not use?

**Solutions:**
1. **Pat's piece of ribbon:**  
   \[
   \frac{1}{3} \times 45 = \frac{45}{3} = 15 \text{ cm}
   \]

2. **Jim's piece of ribbon:**  
   \[
   \frac{5}{8} \times 48 = \frac{5 \times 48}{8} = \frac{240}{8} = 30 \text{ cm}
   \]

3. **Ribbon Jim did not use:**  
   \[
   48 \text{ cm} - 30 \text{ cm} = 18 \text{ cm}
   \]

---

Would you like any more details or explanations on these solutions? 

Here are 5 related questions to practice:

1. What is \(\frac{7}{9}\) of 81?
2. If \(\frac{2}{5}\) of a garden has roses and the rest has tulips, how much area is covered by tulips if the garden is 100 square meters?
3. A ribbon is 60 cm long, and a person cuts off \(\frac{3}{4}\) of it. What is the length of the remaining ribbon?
4. If \(\frac{2}{3}\) of a class of 30 students are girls, how many boys are in the class?
5. Calculate \(\frac{5}{6}\) of 36.

**Tip:** To find a fraction of a number, multiply the number by the numerator of the fraction and then divide by the denominator.

Learn how to solve fraction problems involving finding fractions of amounts and distribution of flowers among plants. Includes step-by-step solutions and practice questions. Suitable for Grades 5-6 students.

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