What is 10/59 plus 4/21?
10/59 plus 4/21 equals 446/1239 (or 0.359968 in decimal form). Learn the step-by-step solution to add 10/59 and 4/21 using Least Common Denominator and simplification.
Exact Answer
10/59 + 4/21 = 446/1239
Simplified Fraction
446/1239
Mixed Number
Proper (446/1239)
Decimal Value
0.359968
Percentage
35.9968%
Step-by-Step Solution: 10/59 + 4/21
Step 1
Find the Least Common Denominator (LCD)
The denominators 59 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 59 × 21 = 1239.
LCD(59, 21) = 1239
Step 2
Convert to Equivalent Fractions with Common Denominator 1239
Multiply the numerator and denominator of 10/59 by 21, and multiply the numerator and denominator of 4/21 by 59 so both fractions share the common base 1239.
10 × 21/59 × 21 = 210/1239 and 4 × 59/21 × 59 = 236/1239
Step 3
Add the Numerators
Now add the numerators (210 + 236 = 446) and keep the common denominator 1239 unchanged.
210 + 236/1239 = 446/1239
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 446 and 1239 is 1, confirming that 446/1239 cannot be reduced further—it is already in its simplest irreducible form.
446/1239
Step 5
Decimal & Percentage Representation
Dividing the numerator 446 by denominator 1239 produces a repeating decimal (approximately 0.359968, or 35.9968%).
446 ÷ 1239 = 0.359968 (35.9968%)
Visual Representation
The diagram below illustrates 10/59 plus 4/21 visually:
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Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 446/1239 |
| Mixed Number Form | 446/1239 |
| Decimal Form | 0.359968 |
| Percentage | 35.9968% |
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Frequently Asked Questions
What is 10/59 plus 4/21 as a fraction?
10/59 + 4/21 in simplest fraction form is 446/1239.
What is 10/59 plus 4/21 as a decimal?
10/59 + 4/21 converted to a decimal is 0.359968.
What is 10/59 plus 4/21 as a percentage?
10/59 + 4/21 expressed as a percentage is 35.9968%.
Does 10/59 plus 4/21 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 0.359968...) because the denominator contains prime factors other than 2 and 5.