What is 13/46 plus 10/21? (Answer: 733/966)

Exact Answer

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Problem: What is 13/46 plus 10/21?
Formula / Expression: 13/46 + 10/21
Final Answer: 733/966
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 46 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 46 × 21 = 966.
Working: LCD(46, 21) = 966

Step 2: Convert to Equivalent Fractions with Common Denominator 966
Multiply the numerator and denominator of 13/46 by 21, and multiply the numerator and denominator of 10/21 by 46 so both fractions share the common base 966.
Working: 13 × 21/46 × 21 = 273/966 and 10 × 46/21 × 46 = 460/966

Step 3: Add the Numerators
Now add the numerators (273 + 460 = 733) and keep the common denominator 966 unchanged.
Working: 273 + 460/966 = 733/966

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 733 and 966 is 1, confirming that 733/966 cannot be reduced further—it is already in its simplest irreducible form.
Working: 733/966

Step 5: Decimal & Percentage Representation
Dividing the numerator 733 by denominator 966 produces a repeating decimal (approximately 0.758799, or 75.8799%).
Working: 733 ÷ 966 = 0.758799 (75.8799%)

Key Values:
- Simplified Fraction: 733/966
- Mixed Number Form: 733/966
- Decimal Value: 0.758799
- Percentage: 75.8799%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-13-46-plus-10-21/
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13/46 + 10/21 = 733/966

Simplified Fraction

733/966

Mixed Number

Proper (733/966)

Decimal Value

0.758799

Percentage

75.8799%

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Step-by-Step Solution: 13/46 + 10/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 46 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 46 × 21 = 966.

LCD(46, 21) = 966

Step 2

Convert to Equivalent Fractions with Common Denominator 966

Multiply the numerator and denominator of 13/46 by 21, and multiply the numerator and denominator of 10/21 by 46 so both fractions share the common base 966.

13 × 21/46 × 21 = 273/966 and 10 × 46/21 × 46 = 460/966

Step 3

Add the Numerators

Now add the numerators (273 + 460 = 733) and keep the common denominator 966 unchanged.

273 + 460/966 = 733/966

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 733 and 966 is 1, confirming that 733/966 cannot be reduced further—it is already in its simplest irreducible form.

733/966

Step 5

Decimal & Percentage Representation

Dividing the numerator 733 by denominator 966 produces a repeating decimal (approximately 0.758799, or 75.8799%).

733 ÷ 966 = 0.758799 (75.8799%)

Visual Representation

The diagram below illustrates 13/46 plus 10/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`733/966`
Mixed Number Form	`733/966`
Decimal Form	`0.758799`
Percentage	`75.8799%`

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Frequently Asked Questions

What is 13/46 plus 10/21 as a fraction?

13/46 + 10/21 in simplest fraction form is 733/966.

What is 13/46 plus 10/21 as a decimal?

13/46 + 10/21 converted to a decimal is 0.758799.

What is 13/46 plus 10/21 as a percentage?

13/46 + 10/21 expressed as a percentage is 75.8799%.

Does 13/46 plus 10/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.758799...) because the denominator contains prime factors other than 2 and 5.