What is 4/56 plus 3/21? (Answer: 3/14)

Exact Answer

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Problem: What is 4/56 plus 3/21?
Formula / Expression: 4/56 + 3/21
Final Answer: 3/14
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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 3/21 by 8 so both fractions share the common base 168.
Working: 4 × 3/56 × 3 = 12/168 and 3 × 8/21 × 8 = 24/168

Step 3: Add the Numerators
Now add the numerators (12 + 24 = 36) and keep the common denominator 168 unchanged.
Working: 12 + 24/168 = 36/168

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 36 and 168, which is 12. Divide both the numerator and denominator by 12.
Working: 36 ÷ 12/168 ÷ 12 = 3/14

Step 5: Decimal & Percentage Representation
Dividing the numerator 3 by denominator 14 produces a repeating decimal (approximately 0.214286, or 21.4286%).
Working: 3 ÷ 14 = 0.214286 (21.4286%)

Key Values:
- Simplified Fraction: 3/14
- Mixed Number Form: 3/14
- Decimal Value: 0.214286
- Percentage: 21.4286%

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Solved with FractionsCalc:
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4/56 + 3/21 = 3/14

Simplified Fraction

3/14

Mixed Number

Proper (3/14)

Decimal Value

0.214286

Percentage

21.4286%

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Step-by-Step Solution: 4/56 + 3/21

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 3/21 by 8 so both fractions share the common base 168.

4 × 3/56 × 3 = 12/168 and 3 × 8/21 × 8 = 24/168

Step 3

Add the Numerators

Now add the numerators (12 + 24 = 36) and keep the common denominator 168 unchanged.

12 + 24/168 = 36/168

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 36 and 168, which is 12. Divide both the numerator and denominator by 12.

36 ÷ 12/168 ÷ 12 = 3/14

Step 5

Decimal & Percentage Representation

Dividing the numerator 3 by denominator 14 produces a repeating decimal (approximately 0.214286, or 21.4286%).

3 ÷ 14 = 0.214286 (21.4286%)

Visual Representation

The diagram below illustrates 4/56 plus 3/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`3/14`
Mixed Number Form	`3/14`
Decimal Form	`0.214286`
Percentage	`21.4286%`

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Frequently Asked Questions

What is 4/56 plus 3/21 as a fraction?

4/56 + 3/21 in simplest fraction form is 3/14.

What is 4/56 plus 3/21 as a decimal?

4/56 + 3/21 converted to a decimal is 0.214286.

What is 4/56 plus 3/21 as a percentage?

4/56 + 3/21 expressed as a percentage is 21.4286%.

Does 4/56 plus 3/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.214286...) because the denominator contains prime factors other than 2 and 5.