Question

mixed review 13-20: balance the equations to find the value of each variable. remember to check your answers.

1. \\(\frac{m}{5} = 30\\)
2. \\(v \div 5 = 12\\)
3. \\(\frac{70}{y} = 10\\)
4. \\(\frac{w}{25} = 5\\)
5. \\(y \div 20 = 10\\)
6. \\(100 \div h = 4\\)
7. \\(x \div 15 = 60\\)
8. \\(100 \div k = 2\\)

Explanation:

Solve division equations with variable in numerator

Using the One-Step Equations and Division Equations knowledge points, we solve equations where the variable is divided by a constant. We apply Inverse Operations by multiplying both sides by the divisor.

For Question 13:

$$ \frac{m}{5} = 30 \implies m = 30 \times 5 = 150 $$

For Question 14:

$$ v \div 5 = 12 \implies v = 12 \times 5 = 60 $$

For Question 16:

$$ \frac{w}{25} = 5 \implies w = 5 \times 25 = 125 $$

For Question 17:

$$ y \div 20 = 10 \implies y = 10 \times 20 = 200 $$

For Question 19:

$$ x \div 15 = 60 \implies x = 60 \times 15 = 900 $$

Solve division equations with variable in denominator

Using the One-Step Equations and Division Equations knowledge points, we solve equations where the variable is the divisor. We multiply both sides by the variable, then divide by the constant.

For Question 15:

$$ \frac{70}{y} = 10 \implies 70 = 10y \implies y = \frac{70}{10} = 7 $$

For Question 18:

$$ 100 \div h = 4 \implies 100 = 4h \implies h = \frac{100}{4} = 25 $$

For Question 20:

$$ 100 \div k = 2 \implies 100 = 2k \implies k = \frac{100}{2} = 50 $$

Answer:

No.	Problem	Answer
14	\(v \div 5 = 12\)	\(v = 60\)
15	\(\frac{70}{y} = 10\)	\(y = 7\)
16	\(\frac{w}{25} = 5\)	\(w = 125\)
17	\(y \div 20 = 10\)	\(y = 200\)
18	\(100 \div h = 4\)	\(h = 25\)
19	\(x \div 15 = 60\)	\(x = 900\)
20	\(100 \div k = 2\)	\(k = 50\)