How much is 120 divided by 220 WITHOUT USING CALCULATOR BCZ IT HAS DIFFERENT ANSWER
The Correct Answer and Explanation is:
Answer:
120220=611≈0.545\frac{120}{220} = \frac{6}{11} \approx 0.545220120=116≈0.545
Step-by-Step Explanation (Like in Textbooks)
To divide 120 by 220 without using a calculator, follow these steps:
Step 1: Write as a Fraction
We are given: 120÷220=120220120 \div 220 = \frac{120}{220}120÷220=220120
This is a fraction. The numerator is 120, and the denominator is 220.
Step 2: Simplify the Fraction
To simplify, find the Greatest Common Divisor (GCD) of 120 and 220.
We start with prime factorizations:
- 120=23×3×5120 = 2^3 \times 3 \times 5120=23×3×5
- 220=22×5×11220 = 2^2 \times 5 \times 11220=22×5×11
Now find the common factors:
- Common factors: 22×5=202^2 \times 5 = 2022×5=20
So, GCD = 20.
Now divide both numerator and denominator by 20: 120÷20220÷20=611\frac{120 \div 20}{220 \div 20} = \frac{6}{11}220÷20120÷20=116
So, the simplified form is: 611\frac{6}{11}116
Step 3: Convert to Decimal (Optional, Long Division)
Now, if we want to write this as a decimal without a calculator, we do long division of 6 ÷ 11.
Let’s compute it step-by-step:
- 11 into 6 → 0 times. Write 0.
- Add decimal point and zero: 11 into 60 → 5 times (11 × 5 = 55)
- Remainder: 60 – 55 = 5
- Bring down 0: 11 into 50 → 4 times (11 × 4 = 44)
- Remainder: 6
- Bring down 0: 11 into 60 → 5 again
- Repeats…
So: 611=0.54‾\frac{6}{11} = 0.\overline{54}116=0.54
This means 0.545454… repeating.
Final Answer:
120220=611≈0.54‾\frac{120}{220} = \frac{6}{11} \approx 0.\overline{54}220120=116≈0.54
This is accurate, and if a calculator gives a different answer, it may be due to rounding or entering values incorrectly.
