What is 10/53 plus 10/21?
10/53 plus 10/21 equals 740/1113 (or 0.66487 in decimal form). Learn the step-by-step solution to add 10/53 and 10/21 using Least Common Denominator and simplification.
Exact Answer
10/53 + 10/21 = 740/1113
Simplified Fraction
740/1113
Mixed Number
Proper (740/1113)
Decimal Value
0.66487
Percentage
66.487%
Step-by-Step Solution: 10/53 + 10/21
Step 1
Find the Least Common Denominator (LCD)
The denominators 53 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 53 × 21 = 1113.
LCD(53, 21) = 1113
Step 2
Convert to Equivalent Fractions with Common Denominator 1113
Multiply the numerator and denominator of 10/53 by 21, and multiply the numerator and denominator of 10/21 by 53 so both fractions share the common base 1113.
10 × 21/53 × 21 = 210/1113 and 10 × 53/21 × 53 = 530/1113
Step 3
Add the Numerators
Now add the numerators (210 + 530 = 740) and keep the common denominator 1113 unchanged.
210 + 530/1113 = 740/1113
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 740 and 1113 is 1, confirming that 740/1113 cannot be reduced further—it is already in its simplest irreducible form.
740/1113
Step 5
Decimal & Percentage Representation
Dividing the numerator 740 by denominator 1113 produces a repeating decimal (approximately 0.66487, or 66.487%).
740 ÷ 1113 = 0.66487 (66.487%)
Visual Representation
The diagram below illustrates 10/53 plus 10/21 visually:
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Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 740/1113 |
| Mixed Number Form | 740/1113 |
| Decimal Form | 0.66487 |
| Percentage | 66.487% |
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Frequently Asked Questions
What is 10/53 plus 10/21 as a fraction?
10/53 + 10/21 in simplest fraction form is 740/1113.
What is 10/53 plus 10/21 as a decimal?
10/53 + 10/21 converted to a decimal is 0.66487.
What is 10/53 plus 10/21 as a percentage?
10/53 + 10/21 expressed as a percentage is 66.487%.
Does 10/53 plus 10/21 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 0.66487...) because the denominator contains prime factors other than 2 and 5.