Converting the decimal number 7.5 into a fraction is a common mathematical operation. In this comprehensive guide, we will walk you through the exact step-by-step process to convert 7.5 into its simplest fractional form.
Conversion Result
15
2
Original Decimal: 7.5
Value Visualization
Converted Fraction
Here is the step-by-step math to convert it:
1
Let x equal the decimal:
Let x = 7.5
2
Multiply by 10 to eliminate the decimal places:
10x = 75
3
Solve for x:
x = 7510
4
Calculate the Greatest Common Divisor (GCD) step by step for easy practice on paper:
💡 Manual Calculation Guide (Euclidean Algorithm):
Objective: Find the greatest common divisor that can evenly divide both numbers (75 and 10).
Rule: Divide the larger number by the smaller number, then take the remainder for the next division step.
• Step 1: 75 ÷ 10 = 7 (remainder 5)
Explanation: 10 × 7 = 70. The remainder from 75 - 70 is 5.
• Step 2: 10 ÷ 5 = 2 (remainder 0)
Explanation: 5 × 2 = 10. The remainder from 10 - 10 is 0.
• Since the remainder is now 0, the process stops here.
The last divisor (5) is the GCD!
→ Conclusion GCD = 5
Objective: Find the greatest common divisor that can evenly divide both numbers (75 and 10).
Rule: Divide the larger number by the smaller number, then take the remainder for the next division step.
• Step 1: 75 ÷ 10 = 7 (remainder 5)
Explanation: 10 × 7 = 70. The remainder from 75 - 70 is 5.
• Step 2: 10 ÷ 5 = 2 (remainder 0)
Explanation: 5 × 2 = 10. The remainder from 10 - 10 is 0.
• Since the remainder is now 0, the process stops here.
The last divisor (5) is the GCD!
→ Conclusion GCD = 5
5
Simplify the fraction by dividing the numerator and denominator by their GCD (5):
x = 75 ÷ 510 ÷ 5 = 152
6
Final fraction conversion result:
Result =
15
2
Conclusion
By following the steps above, we have successfully converted the decimal 7.5 into the simplified fraction 15/2.