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I see that you've uploaded an image of a math worksheet titled "Summer Homework Worksheet 1 – Integers and Fractions". Let me extract the content from the image and assist you with the solutions.

**Here is what I see on the worksheet:**

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### **Exercise 1 - Operations with Integers**
Solve the following problems:

a. \( 5 - 3 - 7 + (4 + 7) = \)

b. \( 23 - (7 \times 4 - 5) = \)

c. \( -10 + (-8) - 3 = \)

d. \( 4^2 - (8 \div 4 + 9 \times 2) = \)

e. \( [5^2 - (7 + (-6))] \times (-4)^2 - (4)^3 - (7 - (-4)) \times (-2)^3 = \)

---

### **Exercise 2 - Prime Factorization**
Find the prime factorization of the following numbers:

a. 72 =

b. 154 =

---

### **Exercise 3 - Greatest Common Factor (GCF)**
Find the GCF for each pair of numbers:

a. 36, 144 =

b. 102, 222 =

---

### **Exercise 4 - Least Common Multiple (LCM)**
Find the LCM for each set of numbers:

a. 12, 20 =

b. 25, 30 =

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### **Exercise 5 - Representing Fractions on a Number Line**
Plot the following fractions on the number line:

\[ \frac{1}{2}, \frac{5}{6}, \frac{1}{3}, \frac{2}{3}, \frac{7}{6} \]

---

Let me now solve each section of the worksheet.

### **Exercise 1 - Operations with Integers**
Let's solve these step by step.

a. \( 5 - 3 - 7 + (4 + 7) \)
\[
= 5 - 3 - 7 + 11 = -4 + 11 = 7
\]

b. \( 23 - (7 \times 4 - 5) \)
\[
= 23 - (28 - 5) = 23 - 23 = 0
\]

c. \( -10 + (-8) - 3 \)
\[
= -10 - 8 - 3 = -21
\]

d. \( 4^2 - (8 \div 4 + 9 \times 2) \)
\[
= 16 - (2 + 18) = 16 - 20 = -4
\]

e. \( [5^2 - (7 + (-6))] \times (-4)^2 - (4)^3 - (7 - (-4)) \times (-2)^3 \)
\[
= [25 - (7 - 6)] \times 16 - 64 - (7 + 4) \times (-8)
\]
\[
= [25 - 1] \times 16 - 64 - 11 \times (-8)
\]
\[
= 24 \times 16 - 64 + 88 = 384 - 64 + 88 = 408
\]

---

### **Exercise 2 - Prime Factorization**

a. 72:
\[
72 = 2^3 \times 3^2
\]

b. 154:
\[
154 = 2 \times 7 \times 11
\]

---

### **Exercise 3 - Greatest Common Factor (GCF)**

a. 36, 144:
\[
\text{GCF}(36, 144) = 36
\]

b. 102, 222:
\[
\text{GCF}(102, 222) = 6
\]

---

### **Exercise 4 - Least Common Multiple (LCM)**

Summer Homework Worksheet 1 – Integers and Fractions with exercises on operations with integers, prime factorization, greatest common factor, least common multiple, and representing fractions on a number line.

Explore detailed solutions for a math worksheet on integers and fractions, including operations with integers, prime factorization, GCF, LCM, and fraction representation on a number line. Suitable for students in Grades 5-7.

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