Seventh Grade Rational Number Operations Activity - Twinkl - Free Printable

Problem Description:

The task involves solving a series of operations with rational numbers. The operations include addition, subtraction, multiplication, and division. Rational numbers are expressed as fractions or decimals.

Solution:

#### Part 1: Operations with Rational Numbers (Fractions and Decimals)

We will solve each problem step by step.

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Section 1: Fractions

1. \( \frac{1}{4} + \frac{3}{8} \)
- Find a common denominator: \( \text{LCM}(4, 8) = 8 \).
- Convert fractions: \( \frac{1}{4} = \frac{2}{8} \).
- Add: \( \frac{2}{8} + \frac{3}{8} = \frac{5}{8} \).
- Answer: \( \frac{5}{8} \).

2. \( 0.47 + 8.13 \)
- Add directly: \( 0.47 + 8.13 = 8.60 \).
- Answer: \( 8.60 \).

3. \( \frac{1}{7} + \frac{1}{7} \)
- Since the denominators are the same, add the numerators: \( \frac{1}{7} + \frac{1}{7} = \frac{2}{7} \).
- Answer: \( \frac{2}{7} \).

4. \( -0.54 - (-0.8) \)
- Subtracting a negative is the same as adding: \( -0.54 + 0.8 = 0.26 \).
- Answer: \( 0.26 \).

5. \( -4 \times 6.3 \)
- Multiply: \( -4 \times 6.3 = -25.2 \).
- Answer: \( -25.2 \).

6. \( -\frac{4}{9} \div \left( -\frac{2}{3} \right) \)
- Dividing by a fraction is the same as multiplying by its reciprocal:
\[
-\frac{4}{9} \div \left( -\frac{2}{3} \right) = -\frac{4}{9} \times \left( -\frac{3}{2} \right)
\]
- Simplify:
\[
\left( -\frac{4}{9} \right) \times \left( -\frac{3}{2} \right) = \frac{4 \times 3}{9 \times 2} = \frac{12}{18} = \frac{2}{3}
\]
- Answer: \( \frac{2}{3} \).

7. \( 2.4 \times [2.85] \)
- Multiply: \( 2.4 \times 2.85 = 6.84 \).
- Answer: \( 6.84 \).

8. \( -7.9 \times 0 \times 8 \)
- Any number multiplied by 0 is 0: \( -7.9 \times 0 \times 8 = 0 \).
- Answer: \( 0 \).

9. \( -1 \frac{1}{2} \div \left( \frac{1}{3} \right) \)
- Convert mixed number to improper fraction: \( -1 \frac{1}{2} = -\frac{3}{2} \).
- Divide by a fraction:
\[
-\frac{3}{2} \div \frac{1}{3} = -\frac{3}{2} \times 3 = -\frac{3 \times 3}{2} = -\frac{9}{2}
\]
- Answer: \( -\frac{9}{2} \).

10. \( 7 \frac{3}{4} - \frac{1}{4} \)
- Convert mixed number to improper fraction: \( 7 \frac{3}{4} = \frac{31}{4} \).
- Subtract:
\[
\frac{31}{4} - \frac{1}{4} = \frac{31 - 1}{4} = \frac{30}{4} = \frac{15}{2}
\]
- Answer: \( \frac{15}{2} \).

11. \( -29 \times (-5) \)
- Multiply: \( -29 \times (-5) = 145 \).
- Answer: \( 145 \).

12. \( \frac{3}{4} + 2 \div 3 \)
- Perform division first: \( 2 \div 3 = \frac{2}{3} \).
- Add:
\[
\frac{3}{4} + \frac{2}{3} = \frac{9}{12} + \frac{8}{12} = \frac{17}{12}
\]
- Answer: \( \frac{17}{12} \).

13. \( \frac{3}{4} \div \frac{3}{4} \)
- Dividing a number by itself is 1:
\[
\frac{3}{4} \div \frac{3}{4} = 1
\]
- Answer: \( 1 \).

14. \( 2.3 - 3.7 \)
- Subtract: \( 2.3 - 3.7 = -1.4 \).
- Answer: \( -1.4 \).

15. \( 8.14 \div 0.01 \)
- Divide: \( 8.14 \div 0.01 = 814 \).
- Answer: \( 814 \).

16. \( 1 \div 1 \)
- Any number divided by itself is 1:
\[
1 \div 1 = 1
\]
- Answer: \( 1 \).

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Final Answers:

1. \( \frac{5}{8} \)
2. \( 8.60 \)
3. \( \frac{2}{7} \)
4. \( 0.26 \)
5. \( -25.2 \)
6. \( \frac{2}{3} \)
7. \( 6.84 \)
8. \( 0 \)
9. \( -\frac{9}{2} \)
10. \( \frac{15}{2} \)
11. \( 145 \)
12. \( \frac{17}{12} \)
13. \( 1 \)
14. \( -1.4 \)
15. \( 814 \)
16. \( 1 \)

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Boxed Final Answer:

\[
\boxed{
\begin{array}{ll}
1. & \frac{5}{8} \\
2. & 8.60 \\
3. & \frac{2}{7} \\
4. & 0.26 \\
5. & -25.2 \\
6. & \frac{2}{3} \\
7. & 6.84 \\
8. & 0 \\
9. & -\frac{9}{2} \\
10. & \frac{15}{2} \\
11. & 145 \\
12. & \frac{17}{12} \\
13. & 1 \\
14. & -1.4 \\
15. & 814 \\
16. & 1 \\
\end{array}
}
\]