What is 2/21 plus 3/28? (Answer: 17/84)

Exact Answer

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Problem: What is 2/21 plus 3/28?
Formula / Expression: 2/21 + 3/28
Final Answer: 17/84
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 21 and 28 share a common factor (GCD = 7). Finding their Least Common Multiple gives an LCD of 84 (which is smaller than their product 21 × 28 = 588, keeping the calculation simpler).
Working: LCD(21, 28) = 84

Step 2: Convert to Equivalent Fractions with Common Denominator 84
Multiply the numerator and denominator of 2/21 by 4, and multiply the numerator and denominator of 3/28 by 3 so both fractions share the common base 84.
Working: 2 × 4/21 × 4 = 8/84 and 3 × 3/28 × 3 = 9/84

Step 3: Add the Numerators
Now add the numerators (8 + 9 = 17) and keep the common denominator 84 unchanged.
Working: 8 + 9/84 = 17/84

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 17 and 84 is 1, confirming that 17/84 cannot be reduced further—it is already in its simplest irreducible form.
Working: 17/84

Step 5: Decimal & Percentage Representation
Dividing the numerator 17 by denominator 84 produces a repeating decimal (approximately 0.202381, or 20.2381%).
Working: 17 ÷ 84 = 0.202381 (20.2381%)

Key Values:
- Simplified Fraction: 17/84
- Mixed Number Form: 17/84
- Decimal Value: 0.202381
- Percentage: 20.2381%

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Solved with FractionsCalc:
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2/21 + 3/28 = 17/84

Simplified Fraction

17/84

Mixed Number

Proper (17/84)

Decimal Value

0.202381

Percentage

20.2381%

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Step-by-Step Solution: 2/21 + 3/28

Step 1

Find the Least Common Denominator (LCD)

The denominators 21 and 28 share a common factor (GCD = 7). Finding their Least Common Multiple gives an LCD of 84 (which is smaller than their product 21 × 28 = 588, keeping the calculation simpler).

LCD(21, 28) = 84

Step 2

Convert to Equivalent Fractions with Common Denominator 84

Multiply the numerator and denominator of 2/21 by 4, and multiply the numerator and denominator of 3/28 by 3 so both fractions share the common base 84.

2 × 4/21 × 4 = 8/84 and 3 × 3/28 × 3 = 9/84

Step 3

Add the Numerators

Now add the numerators (8 + 9 = 17) and keep the common denominator 84 unchanged.

8 + 9/84 = 17/84

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 17 and 84 is 1, confirming that 17/84 cannot be reduced further—it is already in its simplest irreducible form.

17/84

Step 5

Decimal & Percentage Representation

Dividing the numerator 17 by denominator 84 produces a repeating decimal (approximately 0.202381, or 20.2381%).

17 ÷ 84 = 0.202381 (20.2381%)

Visual Representation

The diagram below illustrates 2/21 plus 3/28 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`17/84`
Mixed Number Form	`17/84`
Decimal Form	`0.202381`
Percentage	`20.2381%`

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Frequently Asked Questions

What is 2/21 plus 3/28 as a fraction?

2/21 + 3/28 in simplest fraction form is 17/84.

What is 2/21 plus 3/28 as a decimal?

2/21 + 3/28 converted to a decimal is 0.202381.

What is 2/21 plus 3/28 as a percentage?

2/21 + 3/28 expressed as a percentage is 20.2381%.

Does 2/21 plus 3/28 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.202381...) because the denominator contains prime factors other than 2 and 5.