What is 13/46 plus 7/21? (Answer: 85/138)

Exact Answer

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Problem: What is 13/46 plus 7/21?
Formula / Expression: 13/46 + 7/21
Final Answer: 85/138
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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 7/21 by 46 so both fractions share the common base 966.
Working: 13 × 21/46 × 21 = 273/966 and 7 × 46/21 × 46 = 322/966

Step 3: Add the Numerators
Now add the numerators (273 + 322 = 595) and keep the common denominator 966 unchanged.
Working: 273 + 322/966 = 595/966

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 595 and 966, which is 7. Divide both the numerator and denominator by 7.
Working: 595 ÷ 7/966 ÷ 7 = 85/138

Step 5: Decimal & Percentage Representation
Dividing the numerator 85 by denominator 138 produces a repeating decimal (approximately 0.615942, or 61.5942%).
Working: 85 ÷ 138 = 0.615942 (61.5942%)

Key Values:
- Simplified Fraction: 85/138
- Mixed Number Form: 85/138
- Decimal Value: 0.615942
- Percentage: 61.5942%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-13-46-plus-7-21/
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13/46 + 7/21 = 85/138

Simplified Fraction

85/138

Mixed Number

Proper (85/138)

Decimal Value

0.615942

Percentage

61.5942%

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Step-by-Step Solution: 13/46 + 7/21

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 7/21 by 46 so both fractions share the common base 966.

13 × 21/46 × 21 = 273/966 and 7 × 46/21 × 46 = 322/966

Step 3

Add the Numerators

Now add the numerators (273 + 322 = 595) and keep the common denominator 966 unchanged.

273 + 322/966 = 595/966

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 595 and 966, which is 7. Divide both the numerator and denominator by 7.

595 ÷ 7/966 ÷ 7 = 85/138

Step 5

Decimal & Percentage Representation

Dividing the numerator 85 by denominator 138 produces a repeating decimal (approximately 0.615942, or 61.5942%).

85 ÷ 138 = 0.615942 (61.5942%)

Visual Representation

The diagram below illustrates 13/46 plus 7/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`85/138`
Mixed Number Form	`85/138`
Decimal Form	`0.615942`
Percentage	`61.5942%`

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Frequently Asked Questions

What is 13/46 plus 7/21 as a fraction?

13/46 + 7/21 in simplest fraction form is 85/138.

What is 13/46 plus 7/21 as a decimal?

13/46 + 7/21 converted to a decimal is 0.615942.

What is 13/46 plus 7/21 as a percentage?

13/46 + 7/21 expressed as a percentage is 61.5942%.

Does 13/46 plus 7/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.615942...) because the denominator contains prime factors other than 2 and 5.