What is 10/56 plus 9/13? (Answer: 317/364)

Exact Answer

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Problem: What is 10/56 plus 9/13?
Formula / Expression: 10/56 + 9/13
Final Answer: 317/364
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 56 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 56 × 13 = 728.
Working: LCD(56, 13) = 728

Step 2: Convert to Equivalent Fractions with Common Denominator 728
Multiply the numerator and denominator of 10/56 by 13, and multiply the numerator and denominator of 9/13 by 56 so both fractions share the common base 728.
Working: 10 × 13/56 × 13 = 130/728 and 9 × 56/13 × 56 = 504/728

Step 3: Add the Numerators
Now add the numerators (130 + 504 = 634) and keep the common denominator 728 unchanged.
Working: 130 + 504/728 = 634/728

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 634 and 728, which is 2. Divide both the numerator and denominator by 2.
Working: 634 ÷ 2/728 ÷ 2 = 317/364

Step 5: Decimal & Percentage Representation
Dividing the numerator 317 by denominator 364 produces a repeating decimal (approximately 0.870879, or 87.0879%).
Working: 317 ÷ 364 = 0.870879 (87.0879%)

Key Values:
- Simplified Fraction: 317/364
- Mixed Number Form: 317/364
- Decimal Value: 0.870879
- Percentage: 87.0879%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-10-56-plus-9-13/
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10/56 + 9/13 = 317/364

Simplified Fraction

317/364

Mixed Number

Proper (317/364)

Decimal Value

0.870879

Percentage

87.0879%

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Step-by-Step Solution: 10/56 + 9/13

Step 1

Find the Least Common Denominator (LCD)

The denominators 56 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 56 × 13 = 728.

LCD(56, 13) = 728

Step 2

Convert to Equivalent Fractions with Common Denominator 728

Multiply the numerator and denominator of 10/56 by 13, and multiply the numerator and denominator of 9/13 by 56 so both fractions share the common base 728.

10 × 13/56 × 13 = 130/728 and 9 × 56/13 × 56 = 504/728

Step 3

Add the Numerators

Now add the numerators (130 + 504 = 634) and keep the common denominator 728 unchanged.

130 + 504/728 = 634/728

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 634 and 728, which is 2. Divide both the numerator and denominator by 2.

634 ÷ 2/728 ÷ 2 = 317/364

Step 5

Decimal & Percentage Representation

Dividing the numerator 317 by denominator 364 produces a repeating decimal (approximately 0.870879, or 87.0879%).

317 ÷ 364 = 0.870879 (87.0879%)

Visual Representation

The diagram below illustrates 10/56 plus 9/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`317/364`
Mixed Number Form	`317/364`
Decimal Form	`0.870879`
Percentage	`87.0879%`

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Frequently Asked Questions

What is 10/56 plus 9/13 as a fraction?

10/56 + 9/13 in simplest fraction form is 317/364.

What is 10/56 plus 9/13 as a decimal?

10/56 + 9/13 converted to a decimal is 0.870879.

What is 10/56 plus 9/13 as a percentage?

10/56 + 9/13 expressed as a percentage is 87.0879%.

Does 10/56 plus 9/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.870879...) because the denominator contains prime factors other than 2 and 5.