What is 29/45 plus 15/21? (Answer: 428/315)

Exact Answer

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Problem: What is 29/45 plus 15/21?
Formula / Expression: 29/45 + 15/21
Final Answer: 1 113/315 (428/315)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 45 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 315 (which is smaller than their product 45 × 21 = 945, keeping the calculation simpler).
Working: LCD(45, 21) = 315

Step 2: Convert to Equivalent Fractions with Common Denominator 315
Multiply the numerator and denominator of 29/45 by 7, and multiply the numerator and denominator of 15/21 by 15 so both fractions share the common base 315.
Working: 29 × 7/45 × 7 = 203/315 and 15 × 15/21 × 15 = 225/315

Step 3: Add the Numerators
Now add the numerators (203 + 225 = 428) and keep the common denominator 315 unchanged.
Working: 203 + 225/315 = 428/315

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 428 and 315 is 1, confirming that 428/315 cannot be reduced further—it is already in its simplest irreducible form.
Working: 428/315

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (428) is greater than the denominator (315), divide 428 by 315: it goes in 1 whole time(s) with a remainder of 113, giving the mixed number 1 113/315.
Working: 428/315 = 1 113/315

Step 6: Decimal & Percentage Representation
Dividing the numerator 428 by denominator 315 produces a repeating decimal (approximately 1.35873, or 135.873%).
Working: 428 ÷ 315 = 1.35873 (135.873%)

Key Values:
- Simplified Fraction: 428/315
- Mixed Number Form: 1 113/315
- Decimal Value: 1.35873
- Percentage: 135.873%

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Solved with FractionsCalc:
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29/45 + 15/21 = 428/315

Simplified Fraction

428/315

Mixed Number

1 113/315

Decimal Value

1.35873

Percentage

135.873%

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Step-by-Step Solution: 29/45 + 15/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 45 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 315 (which is smaller than their product 45 × 21 = 945, keeping the calculation simpler).

LCD(45, 21) = 315

Step 2

Convert to Equivalent Fractions with Common Denominator 315

Multiply the numerator and denominator of 29/45 by 7, and multiply the numerator and denominator of 15/21 by 15 so both fractions share the common base 315.

29 × 7/45 × 7 = 203/315 and 15 × 15/21 × 15 = 225/315

Step 3

Add the Numerators

Now add the numerators (203 + 225 = 428) and keep the common denominator 315 unchanged.

203 + 225/315 = 428/315

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 428 and 315 is 1, confirming that 428/315 cannot be reduced further—it is already in its simplest irreducible form.

428/315

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (428) is greater than the denominator (315), divide 428 by 315: it goes in 1 whole time(s) with a remainder of 113, giving the mixed number 1 113/315.

428/315 = 1113/315

Step 6

Decimal & Percentage Representation

Dividing the numerator 428 by denominator 315 produces a repeating decimal (approximately 1.35873, or 135.873%).

428 ÷ 315 = 1.35873 (135.873%)

Visual Representation

The diagram below illustrates 29/45 plus 15/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`428/315`
Mixed Number Form	`1 113/315`
Decimal Form	`1.35873`
Percentage	`135.873%`

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Frequently Asked Questions

What is 29/45 plus 15/21 as a fraction?

29/45 + 15/21 in simplest fraction form is 428/315 (or 1 113/315 as a mixed number).

What is 29/45 plus 15/21 as a decimal?

29/45 + 15/21 converted to a decimal is 1.35873.

What is 29/45 plus 15/21 as a percentage?

29/45 + 15/21 expressed as a percentage is 135.873%.

How do you write 29/45 plus 15/21 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 428/315 can be written as the mixed number 1 113/315.

Does 29/45 plus 15/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.35873...) because the denominator contains prime factors other than 2 and 5.