Question

multiplication and division equations
solve each equation. check your solution.

1. $7a = 56$
2. $-5b = -20$
3. $14 = 14c$
4. $\frac{e}{-9} = -6$
5. $\frac{k}{12} = 2$
6. $\frac{m}{6} = -10$
7. $66 = -11y$
8. $\frac{x}{19} = 4$
9. $-15 = \frac{z}{-8}$
10. $-3z = 93$
11. $5 = \frac{g}{4}$
12. $\frac{a}{3} = -12$
13. $-8 = \frac{t}{9}$
14. $3c = 15$
15. $-7 = \frac{w}{6}$
16. $-6y = -6$
17. $18 = -9b$
18. $-13c = -52$
19. $4h = -44$
20. $-7x = -63$

Answer:

Let's solve these equations one by one using the inverse operations (multiplication or division) to isolate the variable.

1. \( 7a = 56 \)

Step 1: Divide both sides by 7

To isolate \( a \), divide both sides of the equation by 7.
\( \frac{7a}{7} = \frac{56}{7} \)

Step 2: Simplify

Simplifying both sides gives \( a = 8 \).

2. \( -5b = -20 \)

Step 1: Divide both sides by -5

To isolate \( b \), divide both sides by -5: \( \frac{-5b}{-5} = \frac{-20}{-5} \)

Step 2: Simplify

Simplifying gives \( b = 4 \).

3. \( 14 = 14c \)

Step 1: Divide both sides by 14

Divide both sides by 14: \( \frac{14}{14} = \frac{14c}{14} \)

Step 2: Simplify

Simplifying gives \( 1 = c \) or \( c = 1 \).

4. \( \frac{e}{-9} = -6 \)

Step 1: Multiply both sides by -9

To isolate \( e \), multiply both sides by -9: \( \frac{e}{-9} \times (-9) = -6 \times (-9) \)

Step 2: Simplify

Simplifying gives \( e = 54 \).

5. \( \frac{k}{12} = 2 \)

Step 1: Multiply both sides by 12

Multiply both sides by 12: \( \frac{k}{12} \times 12 = 2 \times 12 \)

Step 2: Simplify

Simplifying gives \( k = 24 \).

6. \( \frac{m}{6} = -10 \)

Step 1: Multiply both sides by 6

Multiply both sides by 6: \( \frac{m}{6} \times 6 = -10 \times 6 \)

Step 2: Simplify

Simplifying gives \( m = -60 \).

7. \( 66 = -11y \)

Step 1: Divide both sides by -11

Divide both sides by -11: \( \frac{66}{-11} = \frac{-11y}{-11} \)

Step 2: Simplify

Simplifying gives \( -6 = y \) or \( y = -6 \).

8. \( \frac{x}{19} = 4 \)

Step 1: Multiply both sides by 19

Multiply both sides by 19: \( \frac{x}{19} \times 19 = 4 \times 19 \)

Step 2: Simplify

Simplifying gives \( x = 76 \).

9. \( -15 = \frac{z}{-8} \)

Step 1: Multiply both sides by -8

Multiply both sides by -8: \( -15 \times (-8) = \frac{z}{-8} \times (-8) \)

Step 2: Simplify

Simplifying gives \( 120 = z \) or \( z = 120 \).

10. \( -3z = 93 \)

Step 1: Divide both sides by -3

Divide both sides by -3: \( \frac{-3z}{-3} = \frac{93}{-3} \)

Step 2: Simplify

Simplifying gives \( z = -31 \).

11. \( 5 = \frac{g}{4} \)

Step 1: Multiply both sides by 4

Multiply both sides by 4: \( 5 \times 4 = \frac{g}{4} \times 4 \)

Step 2: Simplify

Simplifying gives \( 20 = g \) or \( g = 20 \).

12. \( \frac{a}{3} = -12 \)

Step 1: Multiply both sides by 3

Multiply both sides by 3: \( \frac{a}{3} \times 3 = -12 \times 3 \)

Step 2: Simplify

Simplifying gives \( a = -36 \).

13. \( -8 = \frac{t}{9} \)

Step 1: Multiply both sides by 9

Multiply both sides by 9: \( -8 \times 9 = \frac{t}{9} \times 9 \)

Step 2: Simplify

Simplifying gives \( -72 = t \) or \( t = -72 \).

14. \( 3c = 15 \)

Step 1: Divide both sides by 3

Divide both sides by 3: \( \frac{3c}{3} = \frac{15}{3} \)

Step 2: Simplify

Simplifying gives \( c = 5 \).

15. \( -7 = \frac{w}{6} \)

Step 1: Multiply both sides by 6

Multiply both sides by 6: \( -7 \times 6 = \frac{w}{6} \times 6 \)

Step 2: Simplify

Simplifying gives \( -42 = w \) or \( w = -42 \).

16. \( -6y = -6 \)

Step 1: Divide both sides by -6

Divide both sides by -6: \( \frac{-6y}{-6} = \frac{-6}{-6} \)

Step 2: Simplify

Simplifying gives \( y = 1 \).

17. \( 18 = -9b \)

Step 1: Divide both sides by -9

Divide both sides by -9: \( \frac{18}{-9} = \frac{-9b}{-9} \)

Step 2: Simplify

Simplifying gives \( -2 = b \) or \( b = -2 \).

18. \( -13c = -52 \)

Step 1: Divide both sides by -13

Divide both sides by -13: \( \frac{-13c}{-13} = \frac{-52}{-13} \)

Step 2: Simplify

Simplifying gives \( c = 4 \).

19. \( 4h = -44 \)

Step 1: Divide both sides by 4

Divide both sides by 4: \( \frac{4h}{4} = \frac{-44}{4} \)

Step 2: Simplify

Simplifying gives \( h = -11 \).

20. \( -7x = -63 \)

Step 1: Divide both sides by -7

Divide both sides by -7: \( \frac{-7x}{-7} = \frac{-63}{-7} \)

Step 2: Simplify

Simplifying gives \( x = 9 \).

Final Answers:

1. \( \boldsymbol{a = 8} \)
2. \( \boldsymbol{b = 4} \)
3. \( \boldsymbol{c = 1} \)
4. \( \boldsymbol{e = 54} \)
5. \( \boldsymbol{k = 24} \)
6. \( \boldsymbol{m = -60} \)
7. \( \boldsymbol{y = -6} \)
8. \( \boldsymbol{x = 76} \)
9. \( \boldsymbol{z = 120} \)
10. \( \boldsymbol{z = -31} \)
11. \( \boldsymbol{g = 20} \)
12. \( \boldsymbol{a = -36} \)
13. \( \boldsymbol{t = -72} \)
14. \( \boldsymbol{c = 5} \)
15. \( \boldsymbol{w = -42} \)
16. \( \boldsymbol{y = 1} \)
17. \( \boldsymbol{b = -2} \)
18. \( \boldsymbol{c = 4} \)
19. \( \boldsymbol{h = -11} \)
20. \( \boldsymbol{x = 9} \)