What is 7/62 plus 8/21? (Answer: 643/1302)

Exact Answer

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Problem: What is 7/62 plus 8/21?
Formula / Expression: 7/62 + 8/21
Final Answer: 643/1302
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 62 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 62 × 21 = 1302.
Working: LCD(62, 21) = 1302

Step 2: Convert to Equivalent Fractions with Common Denominator 1302
Multiply the numerator and denominator of 7/62 by 21, and multiply the numerator and denominator of 8/21 by 62 so both fractions share the common base 1302.
Working: 7 × 21/62 × 21 = 147/1302 and 8 × 62/21 × 62 = 496/1302

Step 3: Add the Numerators
Now add the numerators (147 + 496 = 643) and keep the common denominator 1302 unchanged.
Working: 147 + 496/1302 = 643/1302

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 643 and 1302 is 1, confirming that 643/1302 cannot be reduced further—it is already in its simplest irreducible form.
Working: 643/1302

Step 5: Decimal & Percentage Representation
Dividing the numerator 643 by denominator 1302 produces a repeating decimal (approximately 0.493856, or 49.3856%).
Working: 643 ÷ 1302 = 0.493856 (49.3856%)

Key Values:
- Simplified Fraction: 643/1302
- Mixed Number Form: 643/1302
- Decimal Value: 0.493856
- Percentage: 49.3856%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-7-62-plus-8-21/
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7/62 + 8/21 = 643/1302

Simplified Fraction

643/1302

Mixed Number

Proper (643/1302)

Decimal Value

0.493856

Percentage

49.3856%

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Step-by-Step Solution: 7/62 + 8/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 62 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 62 × 21 = 1302.

LCD(62, 21) = 1302

Step 2

Convert to Equivalent Fractions with Common Denominator 1302

Multiply the numerator and denominator of 7/62 by 21, and multiply the numerator and denominator of 8/21 by 62 so both fractions share the common base 1302.

7 × 21/62 × 21 = 147/1302 and 8 × 62/21 × 62 = 496/1302

Step 3

Add the Numerators

Now add the numerators (147 + 496 = 643) and keep the common denominator 1302 unchanged.

147 + 496/1302 = 643/1302

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 643 and 1302 is 1, confirming that 643/1302 cannot be reduced further—it is already in its simplest irreducible form.

643/1302

Step 5

Decimal & Percentage Representation

Dividing the numerator 643 by denominator 1302 produces a repeating decimal (approximately 0.493856, or 49.3856%).

643 ÷ 1302 = 0.493856 (49.3856%)

Visual Representation

The diagram below illustrates 7/62 plus 8/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`643/1302`
Mixed Number Form	`643/1302`
Decimal Form	`0.493856`
Percentage	`49.3856%`

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Frequently Asked Questions

What is 7/62 plus 8/21 as a fraction?

7/62 + 8/21 in simplest fraction form is 643/1302.

What is 7/62 plus 8/21 as a decimal?

7/62 + 8/21 converted to a decimal is 0.493856.

What is 7/62 plus 8/21 as a percentage?

7/62 + 8/21 expressed as a percentage is 49.3856%.

Does 7/62 plus 8/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.493856...) because the denominator contains prime factors other than 2 and 5.