What is 3/56 plus 2/21? (Answer: 25/168)

Exact Answer

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Problem: What is 3/56 plus 2/21?
Formula / Expression: 3/56 + 2/21
Final Answer: 25/168
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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 3/56 by 3, and multiply the numerator and denominator of 2/21 by 8 so both fractions share the common base 168.
Working: 3 × 3/56 × 3 = 9/168 and 2 × 8/21 × 8 = 16/168

Step 3: Add the Numerators
Now add the numerators (9 + 16 = 25) and keep the common denominator 168 unchanged.
Working: 9 + 16/168 = 25/168

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 25 and 168 is 1, confirming that 25/168 cannot be reduced further—it is already in its simplest irreducible form.
Working: 25/168

Step 5: Decimal & Percentage Representation
Dividing the numerator 25 by denominator 168 produces a repeating decimal (approximately 0.14881, or 14.881%).
Working: 25 ÷ 168 = 0.14881 (14.881%)

Key Values:
- Simplified Fraction: 25/168
- Mixed Number Form: 25/168
- Decimal Value: 0.14881
- Percentage: 14.881%

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Solved with FractionsCalc:
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3/56 + 2/21 = 25/168

Simplified Fraction

25/168

Mixed Number

Proper (25/168)

Decimal Value

0.14881

Percentage

14.881%

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

3 × 3/56 × 3 = 9/168 and 2 × 8/21 × 8 = 16/168

Step 3

Add the Numerators

Now add the numerators (9 + 16 = 25) and keep the common denominator 168 unchanged.

9 + 16/168 = 25/168

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 25 and 168 is 1, confirming that 25/168 cannot be reduced further—it is already in its simplest irreducible form.

25/168

Step 5

Decimal & Percentage Representation

Dividing the numerator 25 by denominator 168 produces a repeating decimal (approximately 0.14881, or 14.881%).

25 ÷ 168 = 0.14881 (14.881%)

Visual Representation

The diagram below illustrates 3/56 plus 2/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`25/168`
Mixed Number Form	`25/168`
Decimal Form	`0.14881`
Percentage	`14.881%`

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Frequently Asked Questions

What is 3/56 plus 2/21 as a fraction?

3/56 + 2/21 in simplest fraction form is 25/168.

What is 3/56 plus 2/21 as a decimal?

3/56 + 2/21 converted to a decimal is 0.14881.

What is 3/56 plus 2/21 as a percentage?

3/56 + 2/21 expressed as a percentage is 14.881%.

Does 3/56 plus 2/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.14881...) because the denominator contains prime factors other than 2 and 5.