What is 6/56 plus 6/21? (Answer: 11/28)

Exact Answer

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Problem: What is 6/56 plus 6/21?
Formula / Expression: 6/56 + 6/21
Final Answer: 11/28
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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 6/56 by 3, and multiply the numerator and denominator of 6/21 by 8 so both fractions share the common base 168.
Working: 6 × 3/56 × 3 = 18/168 and 6 × 8/21 × 8 = 48/168

Step 3: Add the Numerators
Now add the numerators (18 + 48 = 66) and keep the common denominator 168 unchanged.
Working: 18 + 48/168 = 66/168

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 66 and 168, which is 6. Divide both the numerator and denominator by 6.
Working: 66 ÷ 6/168 ÷ 6 = 11/28

Step 5: Decimal & Percentage Representation
Dividing the numerator 11 by denominator 28 produces a repeating decimal (approximately 0.392857, or 39.2857%).
Working: 11 ÷ 28 = 0.392857 (39.2857%)

Key Values:
- Simplified Fraction: 11/28
- Mixed Number Form: 11/28
- Decimal Value: 0.392857
- Percentage: 39.2857%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-6-56-plus-6-21/
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6/56 + 6/21 = 11/28

Simplified Fraction

11/28

Mixed Number

Proper (11/28)

Decimal Value

0.392857

Percentage

39.2857%

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Step-by-Step Solution: 6/56 + 6/21

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 6/56 by 3, and multiply the numerator and denominator of 6/21 by 8 so both fractions share the common base 168.

6 × 3/56 × 3 = 18/168 and 6 × 8/21 × 8 = 48/168

Step 3

Add the Numerators

Now add the numerators (18 + 48 = 66) and keep the common denominator 168 unchanged.

18 + 48/168 = 66/168

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 66 and 168, which is 6. Divide both the numerator and denominator by 6.

66 ÷ 6/168 ÷ 6 = 11/28

Step 5

Decimal & Percentage Representation

Dividing the numerator 11 by denominator 28 produces a repeating decimal (approximately 0.392857, or 39.2857%).

11 ÷ 28 = 0.392857 (39.2857%)

Visual Representation

The diagram below illustrates 6/56 plus 6/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`11/28`
Mixed Number Form	`11/28`
Decimal Form	`0.392857`
Percentage	`39.2857%`

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Frequently Asked Questions

What is 6/56 plus 6/21 as a fraction?

6/56 + 6/21 in simplest fraction form is 11/28.

What is 6/56 plus 6/21 as a decimal?

6/56 + 6/21 converted to a decimal is 0.392857.

What is 6/56 plus 6/21 as a percentage?

6/56 + 6/21 expressed as a percentage is 39.2857%.

Does 6/56 plus 6/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.392857...) because the denominator contains prime factors other than 2 and 5.