What is 13/21 plus 15/21? (Answer: 4/3)

Exact Answer

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Problem: What is 13/21 plus 15/21?
Formula / Expression: 13/21 + 15/21
Final Answer: 1 1/3 (4/3)
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Step-by-Step Solution:

Step 1: Check the Denominators (Like Fractions)
Both fractions already share the identical denominator (21). Because these are like fractions, no conversion to a common denominator is required—we directly add their numerators while keeping the denominator 21.
Working: 13/21 + 15/21

Step 2: Add the Numerators
Now add the numerators (13 + 15 = 28) and keep the common denominator 21 unchanged.
Working: 13 + 15/21 = 28/21

Step 3: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 28 and 21, which is 7. Divide both the numerator and denominator by 7.
Working: 28 ÷ 7/21 ÷ 7 = 4/3

Step 4: Convert Improper Fraction to a Mixed Number
Since the numerator (4) is greater than the denominator (3), divide 4 by 3: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/3.
Working: 4/3 = 1 1/3

Step 5: Decimal & Percentage Representation
Dividing the numerator 4 by denominator 3 produces a repeating decimal (approximately 1.333333, or 133.3333%).
Working: 4 ÷ 3 = 1.333333 (133.3333%)

Key Values:
- Simplified Fraction: 4/3
- Mixed Number Form: 1 1/3
- Decimal Value: 1.333333
- Percentage: 133.3333%

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Solved with FractionsCalc:
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13/21 + 15/21 = 4/3

Simplified Fraction

4/3

Mixed Number

1 1/3

Decimal Value

1.333333

Percentage

133.3333%

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

Step 1

Check the Denominators (Like Fractions)

Both fractions already share the identical denominator (21). Because these are like fractions, no conversion to a common denominator is required—we directly add their numerators while keeping the denominator 21.

13/21 + 15/21

Step 2

Add the Numerators

Now add the numerators (13 + 15 = 28) and keep the common denominator 21 unchanged.

13 + 15/21 = 28/21

Step 3

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 28 and 21, which is 7. Divide both the numerator and denominator by 7.

28 ÷ 7/21 ÷ 7 = 4/3

Step 4

Convert Improper Fraction to a Mixed Number

Since the numerator (4) is greater than the denominator (3), divide 4 by 3: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/3.

4/3 = 11/3

Step 5

Decimal & Percentage Representation

Dividing the numerator 4 by denominator 3 produces a repeating decimal (approximately 1.333333, or 133.3333%).

4 ÷ 3 = 1.333333 (133.3333%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`4/3`
Mixed Number Form	`1 1/3`
Decimal Form	`1.333333`
Percentage	`133.3333%`

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Frequently Asked Questions

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

13/21 + 15/21 in simplest fraction form is 4/3 (or 1 1/3 as a mixed number).

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

13/21 + 15/21 converted to a decimal is 1.333333.

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

13/21 + 15/21 expressed as a percentage is 133.3333%.

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

Because the numerator is greater than the denominator, the improper fraction 4/3 can be written as the mixed number 1 1/3.

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

It results in a repeating decimal (approximately 1.333333...) because the denominator contains prime factors other than 2 and 5.