What is 1/8 plus 8/21? (Answer: 85/168)

Exact Answer

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Problem: What is 1/8 plus 8/21?
Formula / Expression: 1/8 + 8/21
Final Answer: 85/168
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 8 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 8 × 21 = 168.
Working: LCD(8, 21) = 168

Step 2: Convert to Equivalent Fractions with Common Denominator 168
Multiply the numerator and denominator of 1/8 by 21, and multiply the numerator and denominator of 8/21 by 8 so both fractions share the common base 168.
Working: 1 × 21/8 × 21 = 21/168 and 8 × 8/21 × 8 = 64/168

Step 3: Add the Numerators
Now add the numerators (21 + 64 = 85) and keep the common denominator 168 unchanged.
Working: 21 + 64/168 = 85/168

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 85 and 168 is 1, confirming that 85/168 cannot be reduced further—it is already in its simplest irreducible form.
Working: 85/168

Step 5: Decimal & Percentage Representation
Dividing the numerator 85 by denominator 168 produces a repeating decimal (approximately 0.505952, or 50.5952%).
Working: 85 ÷ 168 = 0.505952 (50.5952%)

Key Values:
- Simplified Fraction: 85/168
- Mixed Number Form: 85/168
- Decimal Value: 0.505952
- Percentage: 50.5952%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-1-8-plus-8-21/
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1/8 + 8/21 = 85/168

Simplified Fraction

85/168

Mixed Number

Proper (85/168)

Decimal Value

0.505952

Percentage

50.5952%

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Step-by-Step Solution: 1/8 + 8/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 8 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 8 × 21 = 168.

LCD(8, 21) = 168

Step 2

Convert to Equivalent Fractions with Common Denominator 168

Multiply the numerator and denominator of 1/8 by 21, and multiply the numerator and denominator of 8/21 by 8 so both fractions share the common base 168.

1 × 21/8 × 21 = 21/168 and 8 × 8/21 × 8 = 64/168

Step 3

Add the Numerators

Now add the numerators (21 + 64 = 85) and keep the common denominator 168 unchanged.

21 + 64/168 = 85/168

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 85 and 168 is 1, confirming that 85/168 cannot be reduced further—it is already in its simplest irreducible form.

85/168

Step 5

Decimal & Percentage Representation

Dividing the numerator 85 by denominator 168 produces a repeating decimal (approximately 0.505952, or 50.5952%).

85 ÷ 168 = 0.505952 (50.5952%)

Visual Representation

The diagram below illustrates 1/8 plus 8/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`85/168`
Mixed Number Form	`85/168`
Decimal Form	`0.505952`
Percentage	`50.5952%`

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Frequently Asked Questions

What is 1/8 plus 8/21 as a fraction?

1/8 + 8/21 in simplest fraction form is 85/168.

What is 1/8 plus 8/21 as a decimal?

1/8 + 8/21 converted to a decimal is 0.505952.

What is 1/8 plus 8/21 as a percentage?

1/8 + 8/21 expressed as a percentage is 50.5952%.

Does 1/8 plus 8/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.505952...) because the denominator contains prime factors other than 2 and 5.