What is 1/56 plus 2/21? (Answer: 19/168)

Exact Answer

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Problem: What is 1/56 plus 2/21?
Formula / Expression: 1/56 + 2/21
Final Answer: 19/168
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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 1/56 by 3, and multiply the numerator and denominator of 2/21 by 8 so both fractions share the common base 168.
Working: 1 × 3/56 × 3 = 3/168 and 2 × 8/21 × 8 = 16/168

Step 3: Add the Numerators
Now add the numerators (3 + 16 = 19) and keep the common denominator 168 unchanged.
Working: 3 + 16/168 = 19/168

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 19 and 168 is 1, confirming that 19/168 cannot be reduced further—it is already in its simplest irreducible form.
Working: 19/168

Step 5: Decimal & Percentage Representation
Dividing the numerator 19 by denominator 168 produces a repeating decimal (approximately 0.113095, or 11.3095%).
Working: 19 ÷ 168 = 0.113095 (11.3095%)

Key Values:
- Simplified Fraction: 19/168
- Mixed Number Form: 19/168
- Decimal Value: 0.113095
- Percentage: 11.3095%

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Solved with FractionsCalc:
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1/56 + 2/21 = 19/168

Simplified Fraction

19/168

Mixed Number

Proper (19/168)

Decimal Value

0.113095

Percentage

11.3095%

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Step-by-Step Solution: 1/56 + 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 1/56 by 3, and multiply the numerator and denominator of 2/21 by 8 so both fractions share the common base 168.

1 × 3/56 × 3 = 3/168 and 2 × 8/21 × 8 = 16/168

Step 3

Add the Numerators

Now add the numerators (3 + 16 = 19) and keep the common denominator 168 unchanged.

3 + 16/168 = 19/168

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 19 and 168 is 1, confirming that 19/168 cannot be reduced further—it is already in its simplest irreducible form.

19/168

Step 5

Decimal & Percentage Representation

Dividing the numerator 19 by denominator 168 produces a repeating decimal (approximately 0.113095, or 11.3095%).

19 ÷ 168 = 0.113095 (11.3095%)

Visual Representation

The diagram below illustrates 1/56 plus 2/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`19/168`
Mixed Number Form	`19/168`
Decimal Form	`0.113095`
Percentage	`11.3095%`

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Frequently Asked Questions

What is 1/56 plus 2/21 as a fraction?

1/56 + 2/21 in simplest fraction form is 19/168.

What is 1/56 plus 2/21 as a decimal?

1/56 + 2/21 converted to a decimal is 0.113095.

What is 1/56 plus 2/21 as a percentage?

1/56 + 2/21 expressed as a percentage is 11.3095%.

Does 1/56 plus 2/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.113095...) because the denominator contains prime factors other than 2 and 5.