What is 2/8 plus 9/21? (Answer: 19/28)

Exact Answer

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Problem: What is 2/8 plus 9/21?
Formula / Expression: 2/8 + 9/21
Final Answer: 19/28
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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 2/8 by 21, and multiply the numerator and denominator of 9/21 by 8 so both fractions share the common base 168.
Working: 2 × 21/8 × 21 = 42/168 and 9 × 8/21 × 8 = 72/168

Step 3: Add the Numerators
Now add the numerators (42 + 72 = 114) and keep the common denominator 168 unchanged.
Working: 42 + 72/168 = 114/168

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 114 and 168, which is 6. Divide both the numerator and denominator by 6.
Working: 114 ÷ 6/168 ÷ 6 = 19/28

Step 5: Decimal & Percentage Representation
Dividing the numerator 19 by denominator 28 produces a repeating decimal (approximately 0.678571, or 67.8571%).
Working: 19 ÷ 28 = 0.678571 (67.8571%)

Key Values:
- Simplified Fraction: 19/28
- Mixed Number Form: 19/28
- Decimal Value: 0.678571
- Percentage: 67.8571%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-8-plus-9-21/
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2/8 + 9/21 = 19/28

Simplified Fraction

19/28

Mixed Number

Proper (19/28)

Decimal Value

0.678571

Percentage

67.8571%

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Step-by-Step Solution: 2/8 + 9/21

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 2/8 by 21, and multiply the numerator and denominator of 9/21 by 8 so both fractions share the common base 168.

2 × 21/8 × 21 = 42/168 and 9 × 8/21 × 8 = 72/168

Step 3

Add the Numerators

Now add the numerators (42 + 72 = 114) and keep the common denominator 168 unchanged.

42 + 72/168 = 114/168

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 114 and 168, which is 6. Divide both the numerator and denominator by 6.

114 ÷ 6/168 ÷ 6 = 19/28

Step 5

Decimal & Percentage Representation

Dividing the numerator 19 by denominator 28 produces a repeating decimal (approximately 0.678571, or 67.8571%).

19 ÷ 28 = 0.678571 (67.8571%)

Visual Representation

The diagram below illustrates 2/8 plus 9/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`19/28`
Mixed Number Form	`19/28`
Decimal Form	`0.678571`
Percentage	`67.8571%`

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Frequently Asked Questions

What is 2/8 plus 9/21 as a fraction?

2/8 + 9/21 in simplest fraction form is 19/28.

What is 2/8 plus 9/21 as a decimal?

2/8 + 9/21 converted to a decimal is 0.678571.

What is 2/8 plus 9/21 as a percentage?

2/8 + 9/21 expressed as a percentage is 67.8571%.

Does 2/8 plus 9/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.678571...) because the denominator contains prime factors other than 2 and 5.