What is 4/56 plus 2/21? (Answer: 1/6)

Exact Answer

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Problem: What is 4/56 plus 2/21?
Formula / Expression: 4/56 + 2/21
Final Answer: 1/6
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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 4/56 by 3, and multiply the numerator and denominator of 2/21 by 8 so both fractions share the common base 168.
Working: 4 × 3/56 × 3 = 12/168 and 2 × 8/21 × 8 = 16/168

Step 3: Add the Numerators
Now add the numerators (12 + 16 = 28) and keep the common denominator 168 unchanged.
Working: 12 + 16/168 = 28/168

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 28 and 168, which is 28. Divide both the numerator and denominator by 28.
Working: 28 ÷ 28/168 ÷ 28 = 1/6

Step 5: Decimal & Percentage Representation
Dividing the numerator 1 by denominator 6 produces a repeating decimal (approximately 0.166667, or 16.6667%).
Working: 1 ÷ 6 = 0.166667 (16.6667%)

Key Values:
- Simplified Fraction: 1/6
- Mixed Number Form: 1/6
- Decimal Value: 0.166667
- Percentage: 16.6667%

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Solved with FractionsCalc:
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4/56 + 2/21 = 1/6

Simplified Fraction

1/6

Mixed Number

Proper (1/6)

Decimal Value

0.166667

Percentage

16.6667%

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Step-by-Step Solution: 4/56 + 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 4/56 by 3, and multiply the numerator and denominator of 2/21 by 8 so both fractions share the common base 168.

4 × 3/56 × 3 = 12/168 and 2 × 8/21 × 8 = 16/168

Step 3

Add the Numerators

Now add the numerators (12 + 16 = 28) and keep the common denominator 168 unchanged.

12 + 16/168 = 28/168

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 28 and 168, which is 28. Divide both the numerator and denominator by 28.

28 ÷ 28/168 ÷ 28 = 1/6

Step 5

Decimal & Percentage Representation

Dividing the numerator 1 by denominator 6 produces a repeating decimal (approximately 0.166667, or 16.6667%).

1 ÷ 6 = 0.166667 (16.6667%)

Visual Representation

The diagram below illustrates 4/56 plus 2/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`1/6`
Mixed Number Form	`1/6`
Decimal Form	`0.166667`
Percentage	`16.6667%`

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Frequently Asked Questions

What is 4/56 plus 2/21 as a fraction?

4/56 + 2/21 in simplest fraction form is 1/6.

What is 4/56 plus 2/21 as a decimal?

4/56 + 2/21 converted to a decimal is 0.166667.

What is 4/56 plus 2/21 as a percentage?

4/56 + 2/21 expressed as a percentage is 16.6667%.

Does 4/56 plus 2/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.166667...) because the denominator contains prime factors other than 2 and 5.