Math worksheet for Grade 6 students focusing on operations with rational numbers, including addition, subtraction, multiplication, and division of fractions.

Let's solve each problem step by step, following the format provided in the worksheet. We'll perform operations with rational numbers (fractions) and simplify answers.

---

1) $\frac{2}{3} + \frac{7}{2}$

To add fractions, find a common denominator. The least common denominator (LCD) of 3 and 2 is 6.

$$
\frac{2}{3} + \frac{7}{2} = \frac{2 \cdot 2}{3 \cdot 2} + \frac{7 \cdot 3}{2 \cdot 3} = \frac{4}{6} + \frac{21}{6} = \frac{25}{6}
$$

Now fill in the blanks:

$$
= \frac{2(2) + 7(3)}{(3)(2)} = \frac{4 + 21}{6} = \frac{25}{6}
$$

✔ Answer: $\boxed{\frac{25}{6}}$

---

2) $-\frac{4}{5} + \frac{7}{10}$

LCD of 5 and 10 is 10.

$$
-\frac{4}{5} = -\frac{8}{10}, \quad \frac{7}{10} = \frac{7}{10}
$$

$$
-\frac{8}{10} + \frac{7}{10} = \frac{-8 + 7}{10} = \frac{-1}{10}
$$

Fill in the blanks:

$$
= \frac{-4(2) + 7(1)}{(5)(2)} = \frac{-8 + 7}{10} = \frac{-1}{10} = -\frac{1}{10}
$$

✔ Answer: $\boxed{-\frac{1}{10}}$

---

3) $\frac{6}{5} - 5$

Convert 5 to a fraction: $5 = \frac{5}{1}$

$$
\frac{6}{5} - \frac{5}{1} = \frac{6 \cdot 1 - 5 \cdot 5}{5 \cdot 1} = \frac{6 - 25}{5} = \frac{-19}{5}
$$

Fill in the blanks:

$$
= \frac{6(1) - 5(5)}{(5)(1)} = \frac{6 - 25}{5} = \frac{-19}{5}
$$

✔ Answer: $\boxed{-\frac{19}{5}}$

---

4) $-\frac{7}{4} - \frac{3}{2}$

LCD of 4 and 2 is 4

$$
-\frac{7}{4} - \frac{3}{2} = -\frac{7}{4} - \frac{6}{4} = \frac{-7 - 6}{4} = \frac{-13}{4}
$$

Fill in the blanks:

$$
= \frac{(-7)(1) - (3)(2)}{(4)(2)} = \frac{-7 - 6}{4} = \frac{-13}{4}
$$

Wait — actually, let's use correct cross-multiplication:

$$
= \frac{(-7)(2) - (3)(4)}{(4)(2)} = \frac{-14 - 12}{8} = \frac{-26}{8} = \frac{-13}{4}
$$

But we can simplify directly:

$$
-\frac{7}{4} - \frac{3}{2} = -\frac{7}{4} - \frac{6}{4} = \frac{-13}{4}
$$

So better way: use LCD 4:

$$
= \frac{-7 - 6}{4} = \frac{-13}{4}
$$

But since the blank format uses $(a)(b)$, we do:

$$
= \frac{(-7)(2) - (3)(4)}{(4)(2)} = \frac{-14 - 12}{8} = \frac{-26}{8} = \frac{-13}{4}
$$

✔ Answer: $\boxed{-\frac{13}{4}}$

---

5) $\frac{2}{3} \cdot \left(-\frac{7}{4}\right)$

Multiply numerators and denominators:

$$
= \frac{2 \cdot (-7)}{3 \cdot 4} = \frac{-14}{12}
$$

Simplify: divide numerator and denominator by 2

$$
= \frac{-7}{6}
$$

Fill in:

$$
= \frac{-14}{12} = \frac{-7}{6}
$$

✔ Answer: $\boxed{-\frac{7}{6}}$

---

6) $-4 \cdot \left(-\frac{3}{2}\right)$

Multiply:

$$
= \frac{-4 \cdot (-3)}{2} = \frac{12}{2} = 6
$$

Or write as:

$$
= \frac{12}{2} = 6
$$

Fill in:

$$
= \frac{12}{2} = 6
$$

✔ Answer: $\boxed{6}$

---

7) $-\frac{3}{4} \div \frac{2}{5}$

Dividing fractions: multiply by reciprocal

$$
= -\frac{3}{4} \cdot \frac{5}{2} = \frac{-15}{8}
$$

✔ Answer: $\boxed{-\frac{15}{8}}$

---

## ✔ Final Answers:

1) $\frac{2}{3} + \frac{7}{2} = \frac{2(2)+7(3)}{(3)(2)} = \frac{4+21}{6} = \frac{25}{6}$
2) $-\frac{4}{5} + \frac{7}{10} = \frac{-4(2)+7(1)}{(5)(2)} = \frac{-8+7}{10} = \frac{-1}{10}$
3) $\frac{6}{5} - 5 = \frac{6(1)-5(5)}{(5)(1)} = \frac{6-25}{5} = \frac{-19}{5}$
4) $-\frac{7}{4} - \frac{3}{2} = \frac{(-7)(2)-(3)(4)}{(4)(2)} = \frac{-14-12}{8} = \frac{-26}{8} = \frac{-13}{4}$
5) $\frac{2}{3} \cdot \left(-\frac{7}{4}\right) = \frac{-14}{12} = \frac{-7}{6}$
6) $-4 \cdot \left(-\frac{3}{2}\right) = \frac{12}{2} = 6$
7) $-\frac{3}{4} \div \frac{2}{5} = -\frac{15}{8}$

---

Let me know if you'd like this formatted for printing or need explanations in simpler terms!