What is 3/25 plus 4/21?
3/25 plus 4/21 equals 163/525 (or 0.310476 in decimal form). Learn the step-by-step solution to add 3/25 and 4/21 using Least Common Denominator and simplification.
Exact Answer
3/25 + 4/21 = 163/525
Simplified Fraction
163/525
Mixed Number
Proper (163/525)
Decimal Value
0.310476
Percentage
31.0476%
Step-by-Step Solution: 3/25 + 4/21
Step 1
Find the Least Common Denominator (LCD)
The denominators 25 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 25 × 21 = 525.
LCD(25, 21) = 525
Step 2
Convert to Equivalent Fractions with Common Denominator 525
Multiply the numerator and denominator of 3/25 by 21, and multiply the numerator and denominator of 4/21 by 25 so both fractions share the common base 525.
3 × 21/25 × 21 = 63/525 and 4 × 25/21 × 25 = 100/525
Step 3
Add the Numerators
Now add the numerators (63 + 100 = 163) and keep the common denominator 525 unchanged.
63 + 100/525 = 163/525
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 163 and 525 is 1, confirming that 163/525 cannot be reduced further—it is already in its simplest irreducible form.
163/525
Step 5
Decimal & Percentage Representation
Dividing the numerator 163 by denominator 525 produces a repeating decimal (approximately 0.310476, or 31.0476%).
163 ÷ 525 = 0.310476 (31.0476%)
Visual Representation
The diagram below illustrates 3/25 plus 4/21 visually:
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Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 163/525 |
| Mixed Number Form | 163/525 |
| Decimal Form | 0.310476 |
| Percentage | 31.0476% |
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Frequently Asked Questions
What is 3/25 plus 4/21 as a fraction?
3/25 + 4/21 in simplest fraction form is 163/525.
What is 3/25 plus 4/21 as a decimal?
3/25 + 4/21 converted to a decimal is 0.310476.
What is 3/25 plus 4/21 as a percentage?
3/25 + 4/21 expressed as a percentage is 31.0476%.
Does 3/25 plus 4/21 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 0.310476...) because the denominator contains prime factors other than 2 and 5.