What is 25/36 plus 15/21? (Answer: 355/252)

Exact Answer

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Problem: What is 25/36 plus 15/21?
Formula / Expression: 25/36 + 15/21
Final Answer: 1 103/252 (355/252)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 36 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 252 (which is smaller than their product 36 × 21 = 756, keeping the calculation simpler).
Working: LCD(36, 21) = 252

Step 2: Convert to Equivalent Fractions with Common Denominator 252
Multiply the numerator and denominator of 25/36 by 7, and multiply the numerator and denominator of 15/21 by 12 so both fractions share the common base 252.
Working: 25 × 7/36 × 7 = 175/252 and 15 × 12/21 × 12 = 180/252

Step 3: Add the Numerators
Now add the numerators (175 + 180 = 355) and keep the common denominator 252 unchanged.
Working: 175 + 180/252 = 355/252

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 355 and 252 is 1, confirming that 355/252 cannot be reduced further—it is already in its simplest irreducible form.
Working: 355/252

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (355) is greater than the denominator (252), divide 355 by 252: it goes in 1 whole time(s) with a remainder of 103, giving the mixed number 1 103/252.
Working: 355/252 = 1 103/252

Step 6: Decimal & Percentage Representation
Dividing the numerator 355 by denominator 252 produces a repeating decimal (approximately 1.40873, or 140.873%).
Working: 355 ÷ 252 = 1.40873 (140.873%)

Key Values:
- Simplified Fraction: 355/252
- Mixed Number Form: 1 103/252
- Decimal Value: 1.40873
- Percentage: 140.873%

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Solved with FractionsCalc:
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25/36 + 15/21 = 355/252

Simplified Fraction

355/252

Mixed Number

1 103/252

Decimal Value

1.40873

Percentage

140.873%

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Step-by-Step Solution: 25/36 + 15/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 36 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 252 (which is smaller than their product 36 × 21 = 756, keeping the calculation simpler).

LCD(36, 21) = 252

Step 2

Convert to Equivalent Fractions with Common Denominator 252

Multiply the numerator and denominator of 25/36 by 7, and multiply the numerator and denominator of 15/21 by 12 so both fractions share the common base 252.

25 × 7/36 × 7 = 175/252 and 15 × 12/21 × 12 = 180/252

Step 3

Add the Numerators

Now add the numerators (175 + 180 = 355) and keep the common denominator 252 unchanged.

175 + 180/252 = 355/252

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 355 and 252 is 1, confirming that 355/252 cannot be reduced further—it is already in its simplest irreducible form.

355/252

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (355) is greater than the denominator (252), divide 355 by 252: it goes in 1 whole time(s) with a remainder of 103, giving the mixed number 1 103/252.

355/252 = 1103/252

Step 6

Decimal & Percentage Representation

Dividing the numerator 355 by denominator 252 produces a repeating decimal (approximately 1.40873, or 140.873%).

355 ÷ 252 = 1.40873 (140.873%)

Visual Representation

The diagram below illustrates 25/36 plus 15/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`355/252`
Mixed Number Form	`1 103/252`
Decimal Form	`1.40873`
Percentage	`140.873%`

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Frequently Asked Questions

What is 25/36 plus 15/21 as a fraction?

25/36 + 15/21 in simplest fraction form is 355/252 (or 1 103/252 as a mixed number).

What is 25/36 plus 15/21 as a decimal?

25/36 + 15/21 converted to a decimal is 1.40873.

What is 25/36 plus 15/21 as a percentage?

25/36 + 15/21 expressed as a percentage is 140.873%.

How do you write 25/36 plus 15/21 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 355/252 can be written as the mixed number 1 103/252.

Does 25/36 plus 15/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.40873...) because the denominator contains prime factors other than 2 and 5.