What is 1/6 plus 9/21? (Answer: 25/42)

Exact Answer

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Problem: What is 1/6 plus 9/21?
Formula / Expression: 1/6 + 9/21
Final Answer: 25/42
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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 9/21 by 2 so both fractions share the common base 42.
Working: 1 × 7/6 × 7 = 7/42 and 9 × 2/21 × 2 = 18/42

Step 3: Add the Numerators
Now add the numerators (7 + 18 = 25) and keep the common denominator 42 unchanged.
Working: 7 + 18/42 = 25/42

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 25 and 42 is 1, confirming that 25/42 cannot be reduced further—it is already in its simplest irreducible form.
Working: 25/42

Step 5: Decimal & Percentage Representation
Dividing the numerator 25 by denominator 42 produces a repeating decimal (approximately 0.595238, or 59.5238%).
Working: 25 ÷ 42 = 0.595238 (59.5238%)

Key Values:
- Simplified Fraction: 25/42
- Mixed Number Form: 25/42
- Decimal Value: 0.595238
- Percentage: 59.5238%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-1-6-plus-9-21/
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1/6 + 9/21 = 25/42

Simplified Fraction

25/42

Mixed Number

Proper (25/42)

Decimal Value

0.595238

Percentage

59.5238%

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Step-by-Step Solution: 1/6 + 9/21

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 9/21 by 2 so both fractions share the common base 42.

1 × 7/6 × 7 = 7/42 and 9 × 2/21 × 2 = 18/42

Step 3

Add the Numerators

Now add the numerators (7 + 18 = 25) and keep the common denominator 42 unchanged.

7 + 18/42 = 25/42

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 25 and 42 is 1, confirming that 25/42 cannot be reduced further—it is already in its simplest irreducible form.

25/42

Step 5

Decimal & Percentage Representation

Dividing the numerator 25 by denominator 42 produces a repeating decimal (approximately 0.595238, or 59.5238%).

25 ÷ 42 = 0.595238 (59.5238%)

Visual Representation

The diagram below illustrates 1/6 plus 9/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`25/42`
Mixed Number Form	`25/42`
Decimal Form	`0.595238`
Percentage	`59.5238%`

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Frequently Asked Questions

What is 1/6 plus 9/21 as a fraction?

1/6 + 9/21 in simplest fraction form is 25/42.

What is 1/6 plus 9/21 as a decimal?

1/6 + 9/21 converted to a decimal is 0.595238.

What is 1/6 plus 9/21 as a percentage?

1/6 + 9/21 expressed as a percentage is 59.5238%.

Does 1/6 plus 9/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.595238...) because the denominator contains prime factors other than 2 and 5.