Question

write the operation that would undo the operation in each equation.

1. $5 \times n = 40$ ______
2. $\frac{y}{5} = 80$ ______
3. $\frac{x}{2} = 8$ ______
4. $a \times 7 = 42$ ______

solve each equation.

1. $3 \times a = 9$ ______
2. $\frac{x}{5} = 5$ ______
3. $\frac{x}{3} = 3$ ______
4. $n \times 4 = 4$ ______
5. $5 \times b = 10$ ______
6. $\frac{b}{8} = 2$ ______
7. $\frac{m}{3} = 1$ ______
8. $8 \times n = 20$ ______
9. $4 \times n = 1$ ______
10. $\frac{n}{4} = 5$ ______
11. $n \times 15 = 30$ ______
12. $\frac{n}{4} = 10$ ______
13. $\frac{n}{18} = 2$ ______
14. $n \times 3 = 18$ ______
15. $\frac{n}{2} = 20$ ______
16. $\frac{n}{16} = 1$ ______

Answer:

Part 1: Write the undo operation

1. Explanation for 1: The operation is multiplication by 5, so undo with division by 5.

• Step 1: Identify operation: \( 5 \times n \), undo is \( \div 5 \)
• Answer: Divide by 5 (or \( \div 5 \))

1. Explanation for 2: The operation is division by 5, so undo with multiplication by 5.

• Step 1: Identify operation: \( \frac{y}{5} \), undo is \( \times 5 \)
• Answer: Multiply by 5 (or \( \times 5 \))

1. Explanation for 3: The operation is division by 2, so undo with multiplication by 2.

• Step 1: Identify operation: \( \frac{x}{2} \), undo is \( \times 2 \)
• Answer: Multiply by 2 (or \( \times 2 \))

1. Explanation for 4: The operation is multiplication by 7, so undo with division by 7.

• Step 1: Identify operation: \( a \times 7 \), undo is \( \div 7 \)
• Answer: Divide by 7 (or \( \div 7 \))

Part 2: Solve each equation

1. Explanation for 5:

• Step 1: Equation: \( 3 \times a = 9 \), divide both sides by 3.
• Step 2: \( a = \frac{9}{3} = 3 \)
• Answer: \( a = 3 \)

1. Explanation for 6:

• Step 1: Equation: \( \frac{x}{5} = 5 \), multiply both sides by 5.
• Step 2: \( x = 5 \times 5 = 25 \)
• Answer: \( x = 25 \)

1. Explanation for 7:

• Step 1: Equation: \( \frac{x}{3} = 3 \), multiply both sides by 3.
• Step 2: \( x = 3 \times 3 = 9 \)
• Answer: \( x = 9 \)

1. Explanation for 8:

• Step 1: Equation: \( n \times 4 = 4 \), divide both sides by 4.
• Step 2: \( n = \frac{4}{4} = 1 \)
• Answer: \( n = 1 \)

1. Explanation for 9:

• Step 1: Equation: \( 5 \times b = 10 \), divide both sides by 5.
• Step 2: \( b = \frac{10}{5} = 2 \)
• Answer: \( b = 2 \)

1. Explanation for 10:

• Step 1: Equation: \( \frac{b}{8} = 2 \), multiply both sides by 8.
• Step 2: \( b = 2 \times 8 = 16 \)
• Answer: \( b = 16 \)

1. Explanation for 11:

• Step 1: Equation: \( \frac{m}{3} = 1 \), multiply both sides by 3.
• Step 2: \( m = 1 \times 3 = 3 \)
• Answer: \( m = 3 \)

1. Explanation for 12:

• Step 1: Equation: \( 8 \times n = 20 \), divide both sides by 8.
• Step 2: \( n = \frac{20}{8} = 2.5 \) (or \( \frac{5}{2} \))
• Answer: \( n = 2.5 \) (or \( \frac{5}{2} \))

1. Explanation for 13:

• Step 1: Equation: \( 4 \times n = 1 \), divide both sides by 4.
• Step 2: \( n = \frac{1}{4} = 0.25 \)
• Answer: \( n = \frac{1}{4} \) (or \( 0.25 \))

1. Explanation for 14:

• Step 1: Equation: \( \frac{n}{4} = 5 \), multiply both sides by 4.
• Step 2: \( n = 5 \times 4 = 20 \)
• Answer: \( n = 20 \)

1. Explanation for 15:

• Step 1: Equation: \( n \times 15 = 30 \), divide both sides by 15.
• Step 2: \( n = \frac{30}{15} = 2 \)
• Answer: \( n = 2 \)

1. Explanation for 16:

• Step 1: Equation: \( \frac{n}{4} = 10 \), multiply both sides by 4.
• Step 2: \( n = 10 \times 4 = 40 \)
• Answer: \( n = 40 \)

1. Explanation for 17:

• Step 1: Equation: \( \frac{n}{18} = 2 \), multiply both sides by 18.
• Step 2: \( n = 2 \times 18 = 36 \)
• Answer: \( n = 36 \)

1. Explanation for 18:

• Step 1: Equation: \( n \times 3 = 18 \), divide both sides by 3.
• Step 2: \( n = \frac{18}{3} = 6 \)
• Answer: \( n = 6 \)

1. Explanation for 19:

• Step 1: Equation: \( \frac{n}{2} = 20 \), multiply both sides by 2.
• Step 2: \( n = 20 \times 2 = 40 \)
• Answer: \( n = 40 \)

1. Explanation for 20:

• Step 1: Equation: \( \frac{n}{16} = 1 \), multiply both sides by 16.
• Step 2: \( n = 1 \times 16 = 16 \)
• Answer: \( n = 16 \)