Question

keep in mind the order of operations mdas:multiplication—division (left-to-right)addition—subtraction (left-to-right)1) transform 50 into 10 using subtraction and division:2) transform 30 into 20 using addition and multiplication:3) transform 15 into 10 using subtraction and multiplication:4) transform 100 into 90 using subtraction and division:5) transform 10 into 15 using addition and division:6) transform 0 into 99 using addition and multiplication:7) transform 12 into 0 using subtraction and multiplication:

Explanation:

Step1: Subtract to get divisible value

$(50 - 0) \div 5 = 10$ (Alternatively: $(50 - 20) \div 3 = 10$, but simplest is $(50 - 0) \div 5$; using subtraction of 0, division by 5)
Simpler valid option: $\frac{50 - 0}{5} = 10$, or $\frac{50 - 20}{3} = 10$. The most straightforward: $\frac{50}{5} = 10$, but to include subtraction: $(50 - 0) \div 5 = 10$

Step2: Add then multiply for target

$(30 \div 3) \times 2 = 20$ → to use addition: $(30 + 0) \times \frac{2}{3} = 20$, or $(10 + 20) \times \frac{2}{3} = 20$; better: $(30 + 0) \times \frac{2}{3} = 20$, or $(0 + 30) \times \frac{2}{3} = 20$

Step3: Subtract then multiply for target

$(15 - 5) \times 1 = 10$, or $(15 - 0) \times \frac{2}{3} = 10$; simplest: $(15 - 5) \times 1 = 10$

Step4: Subtract then divide for target

$(100 - 10) \div 1 = 90$, or $\frac{100 - 10}{1} = 90$; or $\frac{100 - 0}{1} - 10 = 90$, but using subtraction + division: $\frac{100 - 10}{1} = 90$

Step5: Divide then add for target

$(10 \div 2) + 10 = 15$, or $\frac{10}{2} + 10 = 15$; or $(10 + 5) \div 1 = 15$, but division + addition: $\frac{10}{2} + 10 = 15$

Step6: Add then multiply for target

$(0 + 99) \times 1 = 99$, or $(0 + 1) \times 99 = 99$

Step7: Subtract then multiply for target

$(12 - 12) \times 5 = 0$, or $(12 - 0) \times 0 = 0$

Answer:

1. $\boldsymbol{(50 - 0) \div 5 = 10}$ (or $\boldsymbol{\frac{50 - 20}{3} = 10}$)
2. $\boldsymbol{(30 + 0) \times \frac{2}{3} = 20}$ (or $\boldsymbol{(10 + 20) \times \frac{2}{3} = 20}$)
3. $\boldsymbol{(15 - 5) \times 1 = 10}$ (or $\boldsymbol{(15 - 0) \times \frac{2}{3} = 10}$)
4. $\boldsymbol{\frac{100 - 10}{1} = 90}$ (or $\boldsymbol{(100 - 10) \div 1 = 90}$)
5. $\boldsymbol{\frac{10}{2} + 10 = 15}$ (or $\boldsymbol{(10 \div 2) + 10 = 15}$)
6. $\boldsymbol{(0 + 1) \times 99 = 99}$ (or $\boldsymbol{(0 + 99) \times 1 = 99}$)
7. $\boldsymbol{(12 - 12) \times 1 = 0}$ (or $\boldsymbol{(12 - 0) \times 0 = 0}$)