What is 2/56 plus 2/21? (Answer: 11/84)

Exact Answer

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Problem: What is 2/56 plus 2/21?
Formula / Expression: 2/56 + 2/21
Final Answer: 11/84
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Step-by-Step Solution:

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

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

Step 3: Add the Numerators
Now add the numerators (6 + 16 = 22) and keep the common denominator 168 unchanged.
Working: 6 + 16/168 = 22/168

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 22 and 168, which is 2. Divide both the numerator and denominator by 2.
Working: 22 ÷ 2/168 ÷ 2 = 11/84

Step 5: Decimal & Percentage Representation
Dividing the numerator 11 by denominator 84 produces a repeating decimal (approximately 0.130952, or 13.0952%).
Working: 11 ÷ 84 = 0.130952 (13.0952%)

Key Values:
- Simplified Fraction: 11/84
- Mixed Number Form: 11/84
- Decimal Value: 0.130952
- Percentage: 13.0952%

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Solved with FractionsCalc:
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2/56 + 2/21 = 11/84

Simplified Fraction

11/84

Mixed Number

Proper (11/84)

Decimal Value

0.130952

Percentage

13.0952%

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Step-by-Step Solution: 2/56 + 2/21

Step 1

Find the Least Common Denominator (LCD)

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

LCD(56, 21) = 168

Step 2

Convert to Equivalent Fractions with Common Denominator 168

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

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

Step 3

Add the Numerators

Now add the numerators (6 + 16 = 22) and keep the common denominator 168 unchanged.

6 + 16/168 = 22/168

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 22 and 168, which is 2. Divide both the numerator and denominator by 2.

22 ÷ 2/168 ÷ 2 = 11/84

Step 5

Decimal & Percentage Representation

Dividing the numerator 11 by denominator 84 produces a repeating decimal (approximately 0.130952, or 13.0952%).

11 ÷ 84 = 0.130952 (13.0952%)

Visual Representation

The diagram below illustrates 2/56 plus 2/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`11/84`
Mixed Number Form	`11/84`
Decimal Form	`0.130952`
Percentage	`13.0952%`

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Frequently Asked Questions

What is 2/56 plus 2/21 as a fraction?

2/56 + 2/21 in simplest fraction form is 11/84.

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

2/56 + 2/21 converted to a decimal is 0.130952.

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

2/56 + 2/21 expressed as a percentage is 13.0952%.

Does 2/56 plus 2/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.130952...) because the denominator contains prime factors other than 2 and 5.