What is 10/56 plus 6/21? (Answer: 13/28)

Exact Answer

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Problem: What is 10/56 plus 6/21?
Formula / Expression: 10/56 + 6/21
Final Answer: 13/28
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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 10/56 by 3, and multiply the numerator and denominator of 6/21 by 8 so both fractions share the common base 168.
Working: 10 × 3/56 × 3 = 30/168 and 6 × 8/21 × 8 = 48/168

Step 3: Add the Numerators
Now add the numerators (30 + 48 = 78) and keep the common denominator 168 unchanged.
Working: 30 + 48/168 = 78/168

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 78 and 168, which is 6. Divide both the numerator and denominator by 6.
Working: 78 ÷ 6/168 ÷ 6 = 13/28

Step 5: Decimal & Percentage Representation
Dividing the numerator 13 by denominator 28 produces a repeating decimal (approximately 0.464286, or 46.4286%).
Working: 13 ÷ 28 = 0.464286 (46.4286%)

Key Values:
- Simplified Fraction: 13/28
- Mixed Number Form: 13/28
- Decimal Value: 0.464286
- Percentage: 46.4286%

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Solved with FractionsCalc:
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10/56 + 6/21 = 13/28

Simplified Fraction

13/28

Mixed Number

Proper (13/28)

Decimal Value

0.464286

Percentage

46.4286%

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Step-by-Step Solution: 10/56 + 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 10/56 by 3, and multiply the numerator and denominator of 6/21 by 8 so both fractions share the common base 168.

10 × 3/56 × 3 = 30/168 and 6 × 8/21 × 8 = 48/168

Step 3

Add the Numerators

Now add the numerators (30 + 48 = 78) and keep the common denominator 168 unchanged.

30 + 48/168 = 78/168

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 78 and 168, which is 6. Divide both the numerator and denominator by 6.

78 ÷ 6/168 ÷ 6 = 13/28

Step 5

Decimal & Percentage Representation

Dividing the numerator 13 by denominator 28 produces a repeating decimal (approximately 0.464286, or 46.4286%).

13 ÷ 28 = 0.464286 (46.4286%)

Visual Representation

The diagram below illustrates 10/56 plus 6/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`13/28`
Mixed Number Form	`13/28`
Decimal Form	`0.464286`
Percentage	`46.4286%`

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Frequently Asked Questions

What is 10/56 plus 6/21 as a fraction?

10/56 + 6/21 in simplest fraction form is 13/28.

What is 10/56 plus 6/21 as a decimal?

10/56 + 6/21 converted to a decimal is 0.464286.

What is 10/56 plus 6/21 as a percentage?

10/56 + 6/21 expressed as a percentage is 46.4286%.

Does 10/56 plus 6/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.464286...) because the denominator contains prime factors other than 2 and 5.