What is 17/30 plus 15/21? (Answer: 269/210)

Exact Answer

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Problem: What is 17/30 plus 15/21?
Formula / Expression: 17/30 + 15/21
Final Answer: 1 59/210 (269/210)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 30 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 210 (which is smaller than their product 30 × 21 = 630, keeping the calculation simpler).
Working: LCD(30, 21) = 210

Step 2: Convert to Equivalent Fractions with Common Denominator 210
Multiply the numerator and denominator of 17/30 by 7, and multiply the numerator and denominator of 15/21 by 10 so both fractions share the common base 210.
Working: 17 × 7/30 × 7 = 119/210 and 15 × 10/21 × 10 = 150/210

Step 3: Add the Numerators
Now add the numerators (119 + 150 = 269) and keep the common denominator 210 unchanged.
Working: 119 + 150/210 = 269/210

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 269 and 210 is 1, confirming that 269/210 cannot be reduced further—it is already in its simplest irreducible form.
Working: 269/210

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (269) is greater than the denominator (210), divide 269 by 210: it goes in 1 whole time(s) with a remainder of 59, giving the mixed number 1 59/210.
Working: 269/210 = 1 59/210

Step 6: Decimal & Percentage Representation
Dividing the numerator 269 by denominator 210 produces a repeating decimal (approximately 1.280952, or 128.0952%).
Working: 269 ÷ 210 = 1.280952 (128.0952%)

Key Values:
- Simplified Fraction: 269/210
- Mixed Number Form: 1 59/210
- Decimal Value: 1.280952
- Percentage: 128.0952%

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17/30 + 15/21 = 269/210

Simplified Fraction

269/210

Mixed Number

1 59/210

Decimal Value

1.280952

Percentage

128.0952%

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Step-by-Step Solution: 17/30 + 15/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 30 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 210 (which is smaller than their product 30 × 21 = 630, keeping the calculation simpler).

LCD(30, 21) = 210

Step 2

Convert to Equivalent Fractions with Common Denominator 210

Multiply the numerator and denominator of 17/30 by 7, and multiply the numerator and denominator of 15/21 by 10 so both fractions share the common base 210.

17 × 7/30 × 7 = 119/210 and 15 × 10/21 × 10 = 150/210

Step 3

Add the Numerators

Now add the numerators (119 + 150 = 269) and keep the common denominator 210 unchanged.

119 + 150/210 = 269/210

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 269 and 210 is 1, confirming that 269/210 cannot be reduced further—it is already in its simplest irreducible form.

269/210

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (269) is greater than the denominator (210), divide 269 by 210: it goes in 1 whole time(s) with a remainder of 59, giving the mixed number 1 59/210.

269/210 = 159/210

Step 6

Decimal & Percentage Representation

Dividing the numerator 269 by denominator 210 produces a repeating decimal (approximately 1.280952, or 128.0952%).

269 ÷ 210 = 1.280952 (128.0952%)

Visual Representation

The diagram below illustrates 17/30 plus 15/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`269/210`
Mixed Number Form	`1 59/210`
Decimal Form	`1.280952`
Percentage	`128.0952%`

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Frequently Asked Questions

What is 17/30 plus 15/21 as a fraction?

17/30 + 15/21 in simplest fraction form is 269/210 (or 1 59/210 as a mixed number).

What is 17/30 plus 15/21 as a decimal?

17/30 + 15/21 converted to a decimal is 1.280952.

What is 17/30 plus 15/21 as a percentage?

17/30 + 15/21 expressed as a percentage is 128.0952%.

How do you write 17/30 plus 15/21 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 269/210 can be written as the mixed number 1 59/210.

Does 17/30 plus 15/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.280952...) because the denominator contains prime factors other than 2 and 5.