What is 21/39 plus 15/21? (Answer: 114/91)

Exact Answer

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Problem: What is 21/39 plus 15/21?
Formula / Expression: 21/39 + 15/21
Final Answer: 1 23/91 (114/91)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 39 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 273 (which is smaller than their product 39 × 21 = 819, keeping the calculation simpler).
Working: LCD(39, 21) = 273

Step 2: Convert to Equivalent Fractions with Common Denominator 273
Multiply the numerator and denominator of 21/39 by 7, and multiply the numerator and denominator of 15/21 by 13 so both fractions share the common base 273.
Working: 21 × 7/39 × 7 = 147/273 and 15 × 13/21 × 13 = 195/273

Step 3: Add the Numerators
Now add the numerators (147 + 195 = 342) and keep the common denominator 273 unchanged.
Working: 147 + 195/273 = 342/273

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 342 and 273, which is 3. Divide both the numerator and denominator by 3.
Working: 342 ÷ 3/273 ÷ 3 = 114/91

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (114) is greater than the denominator (91), divide 114 by 91: it goes in 1 whole time(s) with a remainder of 23, giving the mixed number 1 23/91.
Working: 114/91 = 1 23/91

Step 6: Decimal & Percentage Representation
Dividing the numerator 114 by denominator 91 produces a repeating decimal (approximately 1.252747, or 125.2747%).
Working: 114 ÷ 91 = 1.252747 (125.2747%)

Key Values:
- Simplified Fraction: 114/91
- Mixed Number Form: 1 23/91
- Decimal Value: 1.252747
- Percentage: 125.2747%

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Solved with FractionsCalc:
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21/39 + 15/21 = 114/91

Simplified Fraction

114/91

Mixed Number

1 23/91

Decimal Value

1.252747

Percentage

125.2747%

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Step-by-Step Solution: 21/39 + 15/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 39 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 273 (which is smaller than their product 39 × 21 = 819, keeping the calculation simpler).

LCD(39, 21) = 273

Step 2

Convert to Equivalent Fractions with Common Denominator 273

Multiply the numerator and denominator of 21/39 by 7, and multiply the numerator and denominator of 15/21 by 13 so both fractions share the common base 273.

21 × 7/39 × 7 = 147/273 and 15 × 13/21 × 13 = 195/273

Step 3

Add the Numerators

Now add the numerators (147 + 195 = 342) and keep the common denominator 273 unchanged.

147 + 195/273 = 342/273

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 342 and 273, which is 3. Divide both the numerator and denominator by 3.

342 ÷ 3/273 ÷ 3 = 114/91

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (114) is greater than the denominator (91), divide 114 by 91: it goes in 1 whole time(s) with a remainder of 23, giving the mixed number 1 23/91.

114/91 = 123/91

Step 6

Decimal & Percentage Representation

Dividing the numerator 114 by denominator 91 produces a repeating decimal (approximately 1.252747, or 125.2747%).

114 ÷ 91 = 1.252747 (125.2747%)

Visual Representation

The diagram below illustrates 21/39 plus 15/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`114/91`
Mixed Number Form	`1 23/91`
Decimal Form	`1.252747`
Percentage	`125.2747%`

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Frequently Asked Questions

What is 21/39 plus 15/21 as a fraction?

21/39 + 15/21 in simplest fraction form is 114/91 (or 1 23/91 as a mixed number).

What is 21/39 plus 15/21 as a decimal?

21/39 + 15/21 converted to a decimal is 1.252747.

What is 21/39 plus 15/21 as a percentage?

21/39 + 15/21 expressed as a percentage is 125.2747%.

How do you write 21/39 plus 15/21 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 114/91 can be written as the mixed number 1 23/91.

Does 21/39 plus 15/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.252747...) because the denominator contains prime factors other than 2 and 5.