What is -2 multiplied by 30 and divided by -36?

The answer

Step-by-step solution

Given: -2 × 30 ÷ -36
Step 1: Multiply -2 by 30      -2 × 30 = -60
Step 2: Divide -60 by -36      -60 ÷ -36 = 1.666... (or 5/3)
Step 3: Check the signs        Negative ÷ Negative = Positive
Step 4: Write the answer       5/3 or 1.67 (rounded to two decimals)

Why each step works

1. Multiplication first: Always do multiplication before division (BODMAS rule).
2. Sign rules: Negative × Positive = Negative. Negative ÷ Negative = Positive.
3. Simplify the fraction: -60 ÷ -36 = 60 ÷ 36 (since two negatives make a positive). 60/36 simplifies to 5/3.

Let's understand it simply

Imagine you owe your friend Rs 2, and you do this 30 times. Now you owe Rs 60 (negative because you owe). But then, you split this debt equally among 36 people, and the split is negative (because you are dividing by a negative number). Dividing a negative by a negative flips it to positive. So, each person now gets a positive share.

How it works

1. Multiply -2 × 30 to get -60.
2. Divide -60 by -36.
3. Two negatives cancel, so answer is positive.
4. Simplify 60/36 to 5/3.

Where you see it in real life

• Bank accounts: If you lose Rs 2 every day for 30 days, total loss is -60. If you pay back in 36 equal parts, each part is positive.
• Temperature drops: If temperature drops 2°C every hour for 30 hours, total drop is -60°C. Sharing the drop over -36 hours (going backwards in time) makes it positive.
• Cricket scores: If a team loses 2 runs per over for 30 overs, total loss is -60. Dividing by -36 (maybe a penalty reversed) gives a positive result.
• Sharing debts: If you and your friends share a debt, and both the amount and the number of people are negative (maybe you are paying back a loan to someone who owes you), the share becomes positive.

Why it matters

• Helps in understanding how negative numbers work in real life.
• Important for solving equations in algebra.
• Used in banking, accounting, and science.
• Needed for higher classes and competitive exams.

Common mistakes

• Forgetting that negative divided by negative is positive.
• Not simplifying the fraction (leaving it as 60/36 instead of 5/3).
• Mixing up multiplication and division order.

Remember it

Two negatives in division or multiplication make a positive. Always simplify your answer!