What is 6/43 plus 4/21?
6/43 plus 4/21 equals 298/903 (or 0.330011 in decimal form). Learn the step-by-step solution to add 6/43 and 4/21 using Least Common Denominator and simplification.
Exact Answer
6/43 + 4/21 = 298/903
Simplified Fraction
298/903
Mixed Number
Proper (298/903)
Decimal Value
0.330011
Percentage
33.0011%
Step-by-Step Solution: 6/43 + 4/21
Step 1
Find the Least Common Denominator (LCD)
The denominators 43 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 43 × 21 = 903.
LCD(43, 21) = 903
Step 2
Convert to Equivalent Fractions with Common Denominator 903
Multiply the numerator and denominator of 6/43 by 21, and multiply the numerator and denominator of 4/21 by 43 so both fractions share the common base 903.
6 × 21/43 × 21 = 126/903 and 4 × 43/21 × 43 = 172/903
Step 3
Add the Numerators
Now add the numerators (126 + 172 = 298) and keep the common denominator 903 unchanged.
126 + 172/903 = 298/903
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 298 and 903 is 1, confirming that 298/903 cannot be reduced further—it is already in its simplest irreducible form.
298/903
Step 5
Decimal & Percentage Representation
Dividing the numerator 298 by denominator 903 produces a repeating decimal (approximately 0.330011, or 33.0011%).
298 ÷ 903 = 0.330011 (33.0011%)
Visual Representation
The diagram below illustrates 6/43 plus 4/21 visually:
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Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 298/903 |
| Mixed Number Form | 298/903 |
| Decimal Form | 0.330011 |
| Percentage | 33.0011% |
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Frequently Asked Questions
What is 6/43 plus 4/21 as a fraction?
6/43 + 4/21 in simplest fraction form is 298/903.
What is 6/43 plus 4/21 as a decimal?
6/43 + 4/21 converted to a decimal is 0.330011.
What is 6/43 plus 4/21 as a percentage?
6/43 + 4/21 expressed as a percentage is 33.0011%.
Does 6/43 plus 4/21 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 0.330011...) because the denominator contains prime factors other than 2 and 5.