What is 10/43 plus 10/21?
10/43 plus 10/21 equals 640/903 (or 0.708749 in decimal form). Learn the step-by-step solution to add 10/43 and 10/21 using Least Common Denominator and simplification.
Exact Answer
10/43 + 10/21 = 640/903
Simplified Fraction
640/903
Mixed Number
Proper (640/903)
Decimal Value
0.708749
Percentage
70.8749%
Step-by-Step Solution: 10/43 + 10/21
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 10/43 by 21, and multiply the numerator and denominator of 10/21 by 43 so both fractions share the common base 903.
10 × 21/43 × 21 = 210/903 and 10 × 43/21 × 43 = 430/903
Step 3
Add the Numerators
Now add the numerators (210 + 430 = 640) and keep the common denominator 903 unchanged.
210 + 430/903 = 640/903
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 640 and 903 is 1, confirming that 640/903 cannot be reduced further—it is already in its simplest irreducible form.
640/903
Step 5
Decimal & Percentage Representation
Dividing the numerator 640 by denominator 903 produces a repeating decimal (approximately 0.708749, or 70.8749%).
640 ÷ 903 = 0.708749 (70.8749%)
Visual Representation
The diagram below illustrates 10/43 plus 10/21 visually:
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Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 640/903 |
| Mixed Number Form | 640/903 |
| Decimal Form | 0.708749 |
| Percentage | 70.8749% |
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Frequently Asked Questions
What is 10/43 plus 10/21 as a fraction?
10/43 + 10/21 in simplest fraction form is 640/903.
What is 10/43 plus 10/21 as a decimal?
10/43 + 10/21 converted to a decimal is 0.708749.
What is 10/43 plus 10/21 as a percentage?
10/43 + 10/21 expressed as a percentage is 70.8749%.
Does 10/43 plus 10/21 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 0.708749...) because the denominator contains prime factors other than 2 and 5.