What is 1/56 plus 7/21? (Answer: 59/168)

Exact Answer

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Problem: What is 1/56 plus 7/21?
Formula / Expression: 1/56 + 7/21
Final Answer: 59/168
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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 7/21 by 8 so both fractions share the common base 168.
Working: 1 × 3/56 × 3 = 3/168 and 7 × 8/21 × 8 = 56/168

Step 3: Add the Numerators
Now add the numerators (3 + 56 = 59) and keep the common denominator 168 unchanged.
Working: 3 + 56/168 = 59/168

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 59 and 168 is 1, confirming that 59/168 cannot be reduced further—it is already in its simplest irreducible form.
Working: 59/168

Step 5: Decimal & Percentage Representation
Dividing the numerator 59 by denominator 168 produces a repeating decimal (approximately 0.35119, or 35.119%).
Working: 59 ÷ 168 = 0.35119 (35.119%)

Key Values:
- Simplified Fraction: 59/168
- Mixed Number Form: 59/168
- Decimal Value: 0.35119
- Percentage: 35.119%

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Solved with FractionsCalc:
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1/56 + 7/21 = 59/168

Simplified Fraction

59/168

Mixed Number

Proper (59/168)

Decimal Value

0.35119

Percentage

35.119%

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Step-by-Step Solution: 1/56 + 7/21

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 7/21 by 8 so both fractions share the common base 168.

1 × 3/56 × 3 = 3/168 and 7 × 8/21 × 8 = 56/168

Step 3

Add the Numerators

Now add the numerators (3 + 56 = 59) and keep the common denominator 168 unchanged.

3 + 56/168 = 59/168

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 59 and 168 is 1, confirming that 59/168 cannot be reduced further—it is already in its simplest irreducible form.

59/168

Step 5

Decimal & Percentage Representation

Dividing the numerator 59 by denominator 168 produces a repeating decimal (approximately 0.35119, or 35.119%).

59 ÷ 168 = 0.35119 (35.119%)

Visual Representation

The diagram below illustrates 1/56 plus 7/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`59/168`
Mixed Number Form	`59/168`
Decimal Form	`0.35119`
Percentage	`35.119%`

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Frequently Asked Questions

What is 1/56 plus 7/21 as a fraction?

1/56 + 7/21 in simplest fraction form is 59/168.

What is 1/56 plus 7/21 as a decimal?

1/56 + 7/21 converted to a decimal is 0.35119.

What is 1/56 plus 7/21 as a percentage?

1/56 + 7/21 expressed as a percentage is 35.119%.

Does 1/56 plus 7/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.35119...) because the denominator contains prime factors other than 2 and 5.