What is 31/45 plus 15/21? (Answer: 442/315)

Exact Answer

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Problem: What is 31/45 plus 15/21?
Formula / Expression: 31/45 + 15/21
Final Answer: 1 127/315 (442/315)
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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 31/45 by 7, and multiply the numerator and denominator of 15/21 by 15 so both fractions share the common base 315.
Working: 31 × 7/45 × 7 = 217/315 and 15 × 15/21 × 15 = 225/315

Step 3: Add the Numerators
Now add the numerators (217 + 225 = 442) and keep the common denominator 315 unchanged.
Working: 217 + 225/315 = 442/315

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 442 and 315 is 1, confirming that 442/315 cannot be reduced further—it is already in its simplest irreducible form.
Working: 442/315

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (442) is greater than the denominator (315), divide 442 by 315: it goes in 1 whole time(s) with a remainder of 127, giving the mixed number 1 127/315.
Working: 442/315 = 1 127/315

Step 6: Decimal & Percentage Representation
Dividing the numerator 442 by denominator 315 produces a repeating decimal (approximately 1.403175, or 140.3175%).
Working: 442 ÷ 315 = 1.403175 (140.3175%)

Key Values:
- Simplified Fraction: 442/315
- Mixed Number Form: 1 127/315
- Decimal Value: 1.403175
- Percentage: 140.3175%

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Solved with FractionsCalc:
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31/45 + 15/21 = 442/315

Simplified Fraction

442/315

Mixed Number

1 127/315

Decimal Value

1.403175

Percentage

140.3175%

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Step-by-Step Solution: 31/45 + 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 31/45 by 7, and multiply the numerator and denominator of 15/21 by 15 so both fractions share the common base 315.

31 × 7/45 × 7 = 217/315 and 15 × 15/21 × 15 = 225/315

Step 3

Add the Numerators

Now add the numerators (217 + 225 = 442) and keep the common denominator 315 unchanged.

217 + 225/315 = 442/315

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 442 and 315 is 1, confirming that 442/315 cannot be reduced further—it is already in its simplest irreducible form.

442/315

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (442) is greater than the denominator (315), divide 442 by 315: it goes in 1 whole time(s) with a remainder of 127, giving the mixed number 1 127/315.

442/315 = 1127/315

Step 6

Decimal & Percentage Representation

Dividing the numerator 442 by denominator 315 produces a repeating decimal (approximately 1.403175, or 140.3175%).

442 ÷ 315 = 1.403175 (140.3175%)

Visual Representation

The diagram below illustrates 31/45 plus 15/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`442/315`
Mixed Number Form	`1 127/315`
Decimal Form	`1.403175`
Percentage	`140.3175%`

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Frequently Asked Questions

What is 31/45 plus 15/21 as a fraction?

31/45 + 15/21 in simplest fraction form is 442/315 (or 1 127/315 as a mixed number).

What is 31/45 plus 15/21 as a decimal?

31/45 + 15/21 converted to a decimal is 1.403175.

What is 31/45 plus 15/21 as a percentage?

31/45 + 15/21 expressed as a percentage is 140.3175%.

How do you write 31/45 plus 15/21 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 442/315 can be written as the mixed number 1 127/315.

Does 31/45 plus 15/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.403175...) because the denominator contains prime factors other than 2 and 5.