What is 25/46 plus 15/21? (Answer: 405/322)

Exact Answer

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Problem: What is 25/46 plus 15/21?
Formula / Expression: 25/46 + 15/21
Final Answer: 1 83/322 (405/322)
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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 25/46 by 21, and multiply the numerator and denominator of 15/21 by 46 so both fractions share the common base 966.
Working: 25 × 21/46 × 21 = 525/966 and 15 × 46/21 × 46 = 690/966

Step 3: Add the Numerators
Now add the numerators (525 + 690 = 1215) and keep the common denominator 966 unchanged.
Working: 525 + 690/966 = 1215/966

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 1215 and 966, which is 3. Divide both the numerator and denominator by 3.
Working: 1215 ÷ 3/966 ÷ 3 = 405/322

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (405) is greater than the denominator (322), divide 405 by 322: it goes in 1 whole time(s) with a remainder of 83, giving the mixed number 1 83/322.
Working: 405/322 = 1 83/322

Step 6: Decimal & Percentage Representation
Dividing the numerator 405 by denominator 322 produces a repeating decimal (approximately 1.257764, or 125.7764%).
Working: 405 ÷ 322 = 1.257764 (125.7764%)

Key Values:
- Simplified Fraction: 405/322
- Mixed Number Form: 1 83/322
- Decimal Value: 1.257764
- Percentage: 125.7764%

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25/46 + 15/21 = 405/322

Simplified Fraction

405/322

Mixed Number

1 83/322

Decimal Value

1.257764

Percentage

125.7764%

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Step-by-Step Solution: 25/46 + 15/21

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 25/46 by 21, and multiply the numerator and denominator of 15/21 by 46 so both fractions share the common base 966.

25 × 21/46 × 21 = 525/966 and 15 × 46/21 × 46 = 690/966

Step 3

Add the Numerators

Now add the numerators (525 + 690 = 1215) and keep the common denominator 966 unchanged.

525 + 690/966 = 1215/966

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 1215 and 966, which is 3. Divide both the numerator and denominator by 3.

1215 ÷ 3/966 ÷ 3 = 405/322

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (405) is greater than the denominator (322), divide 405 by 322: it goes in 1 whole time(s) with a remainder of 83, giving the mixed number 1 83/322.

405/322 = 183/322

Step 6

Decimal & Percentage Representation

Dividing the numerator 405 by denominator 322 produces a repeating decimal (approximately 1.257764, or 125.7764%).

405 ÷ 322 = 1.257764 (125.7764%)

Visual Representation

The diagram below illustrates 25/46 plus 15/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`405/322`
Mixed Number Form	`1 83/322`
Decimal Form	`1.257764`
Percentage	`125.7764%`

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Frequently Asked Questions

What is 25/46 plus 15/21 as a fraction?

25/46 + 15/21 in simplest fraction form is 405/322 (or 1 83/322 as a mixed number).

What is 25/46 plus 15/21 as a decimal?

25/46 + 15/21 converted to a decimal is 1.257764.

What is 25/46 plus 15/21 as a percentage?

25/46 + 15/21 expressed as a percentage is 125.7764%.

How do you write 25/46 plus 15/21 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 405/322 can be written as the mixed number 1 83/322.

Does 25/46 plus 15/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.257764...) because the denominator contains prime factors other than 2 and 5.