What is 1/56 plus 8/21? (Answer: 67/168)

Exact Answer

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Problem: What is 1/56 plus 8/21?
Formula / Expression: 1/56 + 8/21
Final Answer: 67/168
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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 8/21 by 8 so both fractions share the common base 168.
Working: 1 × 3/56 × 3 = 3/168 and 8 × 8/21 × 8 = 64/168

Step 3: Add the Numerators
Now add the numerators (3 + 64 = 67) and keep the common denominator 168 unchanged.
Working: 3 + 64/168 = 67/168

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 67 and 168 is 1, confirming that 67/168 cannot be reduced further—it is already in its simplest irreducible form.
Working: 67/168

Step 5: Decimal & Percentage Representation
Dividing the numerator 67 by denominator 168 produces a repeating decimal (approximately 0.39881, or 39.881%).
Working: 67 ÷ 168 = 0.39881 (39.881%)

Key Values:
- Simplified Fraction: 67/168
- Mixed Number Form: 67/168
- Decimal Value: 0.39881
- Percentage: 39.881%

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Solved with FractionsCalc:
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1/56 + 8/21 = 67/168

Simplified Fraction

67/168

Mixed Number

Proper (67/168)

Decimal Value

0.39881

Percentage

39.881%

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Step-by-Step Solution: 1/56 + 8/21

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

1 × 3/56 × 3 = 3/168 and 8 × 8/21 × 8 = 64/168

Step 3

Add the Numerators

Now add the numerators (3 + 64 = 67) and keep the common denominator 168 unchanged.

3 + 64/168 = 67/168

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 67 and 168 is 1, confirming that 67/168 cannot be reduced further—it is already in its simplest irreducible form.

67/168

Step 5

Decimal & Percentage Representation

Dividing the numerator 67 by denominator 168 produces a repeating decimal (approximately 0.39881, or 39.881%).

67 ÷ 168 = 0.39881 (39.881%)

Visual Representation

The diagram below illustrates 1/56 plus 8/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`67/168`
Mixed Number Form	`67/168`
Decimal Form	`0.39881`
Percentage	`39.881%`

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Frequently Asked Questions

What is 1/56 plus 8/21 as a fraction?

1/56 + 8/21 in simplest fraction form is 67/168.

What is 1/56 plus 8/21 as a decimal?

1/56 + 8/21 converted to a decimal is 0.39881.

What is 1/56 plus 8/21 as a percentage?

1/56 + 8/21 expressed as a percentage is 39.881%.

Does 1/56 plus 8/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.39881...) because the denominator contains prime factors other than 2 and 5.