What is 1/6 plus 8/21? (Answer: 23/42)

Exact Answer

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Problem: What is 1/6 plus 8/21?
Formula / Expression: 1/6 + 8/21
Final Answer: 23/42
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 6 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 42 (which is smaller than their product 6 × 21 = 126, keeping the calculation simpler).
Working: LCD(6, 21) = 42

Step 2: Convert to Equivalent Fractions with Common Denominator 42
Multiply the numerator and denominator of 1/6 by 7, and multiply the numerator and denominator of 8/21 by 2 so both fractions share the common base 42.
Working: 1 × 7/6 × 7 = 7/42 and 8 × 2/21 × 2 = 16/42

Step 3: Add the Numerators
Now add the numerators (7 + 16 = 23) and keep the common denominator 42 unchanged.
Working: 7 + 16/42 = 23/42

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 23 and 42 is 1, confirming that 23/42 cannot be reduced further—it is already in its simplest irreducible form.
Working: 23/42

Step 5: Decimal & Percentage Representation
Dividing the numerator 23 by denominator 42 produces a repeating decimal (approximately 0.547619, or 54.7619%).
Working: 23 ÷ 42 = 0.547619 (54.7619%)

Key Values:
- Simplified Fraction: 23/42
- Mixed Number Form: 23/42
- Decimal Value: 0.547619
- Percentage: 54.7619%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-1-6-plus-8-21/
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1/6 + 8/21 = 23/42

Simplified Fraction

23/42

Mixed Number

Proper (23/42)

Decimal Value

0.547619

Percentage

54.7619%

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

Step 1

Find the Least Common Denominator (LCD)

The denominators 6 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 42 (which is smaller than their product 6 × 21 = 126, keeping the calculation simpler).

LCD(6, 21) = 42

Step 2

Convert to Equivalent Fractions with Common Denominator 42

Multiply the numerator and denominator of 1/6 by 7, and multiply the numerator and denominator of 8/21 by 2 so both fractions share the common base 42.

1 × 7/6 × 7 = 7/42 and 8 × 2/21 × 2 = 16/42

Step 3

Add the Numerators

Now add the numerators (7 + 16 = 23) and keep the common denominator 42 unchanged.

7 + 16/42 = 23/42

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 23 and 42 is 1, confirming that 23/42 cannot be reduced further—it is already in its simplest irreducible form.

23/42

Step 5

Decimal & Percentage Representation

Dividing the numerator 23 by denominator 42 produces a repeating decimal (approximately 0.547619, or 54.7619%).

23 ÷ 42 = 0.547619 (54.7619%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`23/42`
Mixed Number Form	`23/42`
Decimal Form	`0.547619`
Percentage	`54.7619%`

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Frequently Asked Questions

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

1/6 + 8/21 in simplest fraction form is 23/42.

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

1/6 + 8/21 converted to a decimal is 0.547619.

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

1/6 + 8/21 expressed as a percentage is 54.7619%.

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

It results in a repeating decimal (approximately 0.547619...) because the denominator contains prime factors other than 2 and 5.