What is 1/8 plus 6/21? (Answer: 23/56)

Exact Answer

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Problem: What is 1/8 plus 6/21?
Formula / Expression: 1/8 + 6/21
Final Answer: 23/56
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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 6/21 by 8 so both fractions share the common base 168.
Working: 1 × 21/8 × 21 = 21/168 and 6 × 8/21 × 8 = 48/168

Step 3: Add the Numerators
Now add the numerators (21 + 48 = 69) and keep the common denominator 168 unchanged.
Working: 21 + 48/168 = 69/168

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 69 and 168, which is 3. Divide both the numerator and denominator by 3.
Working: 69 ÷ 3/168 ÷ 3 = 23/56

Step 5: Decimal & Percentage Representation
Dividing the numerator 23 by denominator 56 produces a repeating decimal (approximately 0.410714, or 41.0714%).
Working: 23 ÷ 56 = 0.410714 (41.0714%)

Key Values:
- Simplified Fraction: 23/56
- Mixed Number Form: 23/56
- Decimal Value: 0.410714
- Percentage: 41.0714%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-1-8-plus-6-21/
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1/8 + 6/21 = 23/56

Simplified Fraction

23/56

Mixed Number

Proper (23/56)

Decimal Value

0.410714

Percentage

41.0714%

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Step-by-Step Solution: 1/8 + 6/21

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 6/21 by 8 so both fractions share the common base 168.

1 × 21/8 × 21 = 21/168 and 6 × 8/21 × 8 = 48/168

Step 3

Add the Numerators

Now add the numerators (21 + 48 = 69) and keep the common denominator 168 unchanged.

21 + 48/168 = 69/168

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 69 and 168, which is 3. Divide both the numerator and denominator by 3.

69 ÷ 3/168 ÷ 3 = 23/56

Step 5

Decimal & Percentage Representation

Dividing the numerator 23 by denominator 56 produces a repeating decimal (approximately 0.410714, or 41.0714%).

23 ÷ 56 = 0.410714 (41.0714%)

Visual Representation

The diagram below illustrates 1/8 plus 6/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`23/56`
Mixed Number Form	`23/56`
Decimal Form	`0.410714`
Percentage	`41.0714%`

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Frequently Asked Questions

What is 1/8 plus 6/21 as a fraction?

1/8 + 6/21 in simplest fraction form is 23/56.

What is 1/8 plus 6/21 as a decimal?

1/8 + 6/21 converted to a decimal is 0.410714.

What is 1/8 plus 6/21 as a percentage?

1/8 + 6/21 expressed as a percentage is 41.0714%.

Does 1/8 plus 6/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.410714...) because the denominator contains prime factors other than 2 and 5.