What is 6/18 plus 10/21? (Answer: 17/21)

Exact Answer

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Problem: What is 6/18 plus 10/21?
Formula / Expression: 6/18 + 10/21
Final Answer: 17/21
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 18 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 126 (which is smaller than their product 18 × 21 = 378, keeping the calculation simpler).
Working: LCD(18, 21) = 126

Step 2: Convert to Equivalent Fractions with Common Denominator 126
Multiply the numerator and denominator of 6/18 by 7, and multiply the numerator and denominator of 10/21 by 6 so both fractions share the common base 126.
Working: 6 × 7/18 × 7 = 42/126 and 10 × 6/21 × 6 = 60/126

Step 3: Add the Numerators
Now add the numerators (42 + 60 = 102) and keep the common denominator 126 unchanged.
Working: 42 + 60/126 = 102/126

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 102 and 126, which is 6. Divide both the numerator and denominator by 6.
Working: 102 ÷ 6/126 ÷ 6 = 17/21

Step 5: Decimal & Percentage Representation
Dividing the numerator 17 by denominator 21 produces a repeating decimal (approximately 0.809524, or 80.9524%).
Working: 17 ÷ 21 = 0.809524 (80.9524%)

Key Values:
- Simplified Fraction: 17/21
- Mixed Number Form: 17/21
- Decimal Value: 0.809524
- Percentage: 80.9524%

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Solved with FractionsCalc:
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6/18 + 10/21 = 17/21

Simplified Fraction

17/21

Mixed Number

Proper (17/21)

Decimal Value

0.809524

Percentage

80.9524%

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Step-by-Step Solution: 6/18 + 10/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 18 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 126 (which is smaller than their product 18 × 21 = 378, keeping the calculation simpler).

LCD(18, 21) = 126

Step 2

Convert to Equivalent Fractions with Common Denominator 126

Multiply the numerator and denominator of 6/18 by 7, and multiply the numerator and denominator of 10/21 by 6 so both fractions share the common base 126.

6 × 7/18 × 7 = 42/126 and 10 × 6/21 × 6 = 60/126

Step 3

Add the Numerators

Now add the numerators (42 + 60 = 102) and keep the common denominator 126 unchanged.

42 + 60/126 = 102/126

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 102 and 126, which is 6. Divide both the numerator and denominator by 6.

102 ÷ 6/126 ÷ 6 = 17/21

Step 5

Decimal & Percentage Representation

Dividing the numerator 17 by denominator 21 produces a repeating decimal (approximately 0.809524, or 80.9524%).

17 ÷ 21 = 0.809524 (80.9524%)

Visual Representation

The diagram below illustrates 6/18 plus 10/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`17/21`
Mixed Number Form	`17/21`
Decimal Form	`0.809524`
Percentage	`80.9524%`

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Frequently Asked Questions

What is 6/18 plus 10/21 as a fraction?

6/18 + 10/21 in simplest fraction form is 17/21.

What is 6/18 plus 10/21 as a decimal?

6/18 + 10/21 converted to a decimal is 0.809524.

What is 6/18 plus 10/21 as a percentage?

6/18 + 10/21 expressed as a percentage is 80.9524%.

Does 6/18 plus 10/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.809524...) because the denominator contains prime factors other than 2 and 5.