What is 17/57 plus 7/21? (Answer: 12/19)

Exact Answer

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Problem: What is 17/57 plus 7/21?
Formula / Expression: 17/57 + 7/21
Final Answer: 12/19
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 57 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 399 (which is smaller than their product 57 × 21 = 1197, keeping the calculation simpler).
Working: LCD(57, 21) = 399

Step 2: Convert to Equivalent Fractions with Common Denominator 399
Multiply the numerator and denominator of 17/57 by 7, and multiply the numerator and denominator of 7/21 by 19 so both fractions share the common base 399.
Working: 17 × 7/57 × 7 = 119/399 and 7 × 19/21 × 19 = 133/399

Step 3: Add the Numerators
Now add the numerators (119 + 133 = 252) and keep the common denominator 399 unchanged.
Working: 119 + 133/399 = 252/399

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 252 and 399, which is 21. Divide both the numerator and denominator by 21.
Working: 252 ÷ 21/399 ÷ 21 = 12/19

Step 5: Decimal & Percentage Representation
Dividing the numerator 12 by denominator 19 produces a repeating decimal (approximately 0.631579, or 63.1579%).
Working: 12 ÷ 19 = 0.631579 (63.1579%)

Key Values:
- Simplified Fraction: 12/19
- Mixed Number Form: 12/19
- Decimal Value: 0.631579
- Percentage: 63.1579%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-17-57-plus-7-21/
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17/57 + 7/21 = 12/19

Simplified Fraction

12/19

Mixed Number

Proper (12/19)

Decimal Value

0.631579

Percentage

63.1579%

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Step-by-Step Solution: 17/57 + 7/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 57 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 399 (which is smaller than their product 57 × 21 = 1197, keeping the calculation simpler).

LCD(57, 21) = 399

Step 2

Convert to Equivalent Fractions with Common Denominator 399

Multiply the numerator and denominator of 17/57 by 7, and multiply the numerator and denominator of 7/21 by 19 so both fractions share the common base 399.

17 × 7/57 × 7 = 119/399 and 7 × 19/21 × 19 = 133/399

Step 3

Add the Numerators

Now add the numerators (119 + 133 = 252) and keep the common denominator 399 unchanged.

119 + 133/399 = 252/399

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 252 and 399, which is 21. Divide both the numerator and denominator by 21.

252 ÷ 21/399 ÷ 21 = 12/19

Step 5

Decimal & Percentage Representation

Dividing the numerator 12 by denominator 19 produces a repeating decimal (approximately 0.631579, or 63.1579%).

12 ÷ 19 = 0.631579 (63.1579%)

Visual Representation

The diagram below illustrates 17/57 plus 7/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`12/19`
Mixed Number Form	`12/19`
Decimal Form	`0.631579`
Percentage	`63.1579%`

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Frequently Asked Questions

What is 17/57 plus 7/21 as a fraction?

17/57 + 7/21 in simplest fraction form is 12/19.

What is 17/57 plus 7/21 as a decimal?

17/57 + 7/21 converted to a decimal is 0.631579.

What is 17/57 plus 7/21 as a percentage?

17/57 + 7/21 expressed as a percentage is 63.1579%.

Does 17/57 plus 7/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.631579...) because the denominator contains prime factors other than 2 and 5.