What is 2/21 plus 6/56? (Answer: 17/84)

Exact Answer

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Problem: What is 2/21 plus 6/56?
Formula / Expression: 2/21 + 6/56
Final Answer: 17/84
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 21 and 56 share a common factor (GCD = 7). Finding their Least Common Multiple gives an LCD of 168 (which is smaller than their product 21 × 56 = 1176, keeping the calculation simpler).
Working: LCD(21, 56) = 168

Step 2: Convert to Equivalent Fractions with Common Denominator 168
Multiply the numerator and denominator of 2/21 by 8, and multiply the numerator and denominator of 6/56 by 3 so both fractions share the common base 168.
Working: 2 × 8/21 × 8 = 16/168 and 6 × 3/56 × 3 = 18/168

Step 3: Add the Numerators
Now add the numerators (16 + 18 = 34) and keep the common denominator 168 unchanged.
Working: 16 + 18/168 = 34/168

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 34 and 168, which is 2. Divide both the numerator and denominator by 2.
Working: 34 ÷ 2/168 ÷ 2 = 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:
https://fractionscalc.com/what-is-2-21-plus-6-56/
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2/21 + 6/56 = 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 + 6/56

Step 1

Find the Least Common Denominator (LCD)

The denominators 21 and 56 share a common factor (GCD = 7). Finding their Least Common Multiple gives an LCD of 168 (which is smaller than their product 21 × 56 = 1176, keeping the calculation simpler).

LCD(21, 56) = 168

Step 2

Convert to Equivalent Fractions with Common Denominator 168

Multiply the numerator and denominator of 2/21 by 8, and multiply the numerator and denominator of 6/56 by 3 so both fractions share the common base 168.

2 × 8/21 × 8 = 16/168 and 6 × 3/56 × 3 = 18/168

Step 3

Add the Numerators

Now add the numerators (16 + 18 = 34) and keep the common denominator 168 unchanged.

16 + 18/168 = 34/168

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 34 and 168, which is 2. Divide both the numerator and denominator by 2.

34 ÷ 2/168 ÷ 2 = 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 6/56 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 6/56 as a fraction?

2/21 + 6/56 in simplest fraction form is 17/84.

What is 2/21 plus 6/56 as a decimal?

2/21 + 6/56 converted to a decimal is 0.202381.

What is 2/21 plus 6/56 as a percentage?

2/21 + 6/56 expressed as a percentage is 20.2381%.

Does 2/21 plus 6/56 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.