What is 13/20 plus 15/21? (Answer: 191/140)

Exact Answer

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Problem: What is 13/20 plus 15/21?
Formula / Expression: 13/20 + 15/21
Final Answer: 1 51/140 (191/140)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 20 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 20 × 21 = 420.
Working: LCD(20, 21) = 420

Step 2: Convert to Equivalent Fractions with Common Denominator 420
Multiply the numerator and denominator of 13/20 by 21, and multiply the numerator and denominator of 15/21 by 20 so both fractions share the common base 420.
Working: 13 × 21/20 × 21 = 273/420 and 15 × 20/21 × 20 = 300/420

Step 3: Add the Numerators
Now add the numerators (273 + 300 = 573) and keep the common denominator 420 unchanged.
Working: 273 + 300/420 = 573/420

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 573 and 420, which is 3. Divide both the numerator and denominator by 3.
Working: 573 ÷ 3/420 ÷ 3 = 191/140

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (191) is greater than the denominator (140), divide 191 by 140: it goes in 1 whole time(s) with a remainder of 51, giving the mixed number 1 51/140.
Working: 191/140 = 1 51/140

Step 6: Decimal & Percentage Representation
Dividing the numerator 191 by denominator 140 produces a repeating decimal (approximately 1.364286, or 136.4286%).
Working: 191 ÷ 140 = 1.364286 (136.4286%)

Key Values:
- Simplified Fraction: 191/140
- Mixed Number Form: 1 51/140
- Decimal Value: 1.364286
- Percentage: 136.4286%

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13/20 + 15/21 = 191/140

Simplified Fraction

191/140

Mixed Number

1 51/140

Decimal Value

1.364286

Percentage

136.4286%

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Step-by-Step Solution: 13/20 + 15/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 20 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 20 × 21 = 420.

LCD(20, 21) = 420

Step 2

Convert to Equivalent Fractions with Common Denominator 420

Multiply the numerator and denominator of 13/20 by 21, and multiply the numerator and denominator of 15/21 by 20 so both fractions share the common base 420.

13 × 21/20 × 21 = 273/420 and 15 × 20/21 × 20 = 300/420

Step 3

Add the Numerators

Now add the numerators (273 + 300 = 573) and keep the common denominator 420 unchanged.

273 + 300/420 = 573/420

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 573 and 420, which is 3. Divide both the numerator and denominator by 3.

573 ÷ 3/420 ÷ 3 = 191/140

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (191) is greater than the denominator (140), divide 191 by 140: it goes in 1 whole time(s) with a remainder of 51, giving the mixed number 1 51/140.

191/140 = 151/140

Step 6

Decimal & Percentage Representation

Dividing the numerator 191 by denominator 140 produces a repeating decimal (approximately 1.364286, or 136.4286%).

191 ÷ 140 = 1.364286 (136.4286%)

Visual Representation

The diagram below illustrates 13/20 plus 15/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`191/140`
Mixed Number Form	`1 51/140`
Decimal Form	`1.364286`
Percentage	`136.4286%`

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Frequently Asked Questions

What is 13/20 plus 15/21 as a fraction?

13/20 + 15/21 in simplest fraction form is 191/140 (or 1 51/140 as a mixed number).

What is 13/20 plus 15/21 as a decimal?

13/20 + 15/21 converted to a decimal is 1.364286.

What is 13/20 plus 15/21 as a percentage?

13/20 + 15/21 expressed as a percentage is 136.4286%.

How do you write 13/20 plus 15/21 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 191/140 can be written as the mixed number 1 51/140.

Does 13/20 plus 15/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.364286...) because the denominator contains prime factors other than 2 and 5.