What is 17/53 plus 7/21? (Answer: 104/159)

Exact Answer

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Problem: What is 17/53 plus 7/21?
Formula / Expression: 17/53 + 7/21
Final Answer: 104/159
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 53 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 53 × 21 = 1113.
Working: LCD(53, 21) = 1113

Step 2: Convert to Equivalent Fractions with Common Denominator 1113
Multiply the numerator and denominator of 17/53 by 21, and multiply the numerator and denominator of 7/21 by 53 so both fractions share the common base 1113.
Working: 17 × 21/53 × 21 = 357/1113 and 7 × 53/21 × 53 = 371/1113

Step 3: Add the Numerators
Now add the numerators (357 + 371 = 728) and keep the common denominator 1113 unchanged.
Working: 357 + 371/1113 = 728/1113

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 728 and 1113, which is 7. Divide both the numerator and denominator by 7.
Working: 728 ÷ 7/1113 ÷ 7 = 104/159

Step 5: Decimal & Percentage Representation
Dividing the numerator 104 by denominator 159 produces a repeating decimal (approximately 0.654088, or 65.4088%).
Working: 104 ÷ 159 = 0.654088 (65.4088%)

Key Values:
- Simplified Fraction: 104/159
- Mixed Number Form: 104/159
- Decimal Value: 0.654088
- Percentage: 65.4088%

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Solved with FractionsCalc:
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17/53 + 7/21 = 104/159

Simplified Fraction

104/159

Mixed Number

Proper (104/159)

Decimal Value

0.654088

Percentage

65.4088%

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Step-by-Step Solution: 17/53 + 7/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 53 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 53 × 21 = 1113.

LCD(53, 21) = 1113

Step 2

Convert to Equivalent Fractions with Common Denominator 1113

Multiply the numerator and denominator of 17/53 by 21, and multiply the numerator and denominator of 7/21 by 53 so both fractions share the common base 1113.

17 × 21/53 × 21 = 357/1113 and 7 × 53/21 × 53 = 371/1113

Step 3

Add the Numerators

Now add the numerators (357 + 371 = 728) and keep the common denominator 1113 unchanged.

357 + 371/1113 = 728/1113

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 728 and 1113, which is 7. Divide both the numerator and denominator by 7.

728 ÷ 7/1113 ÷ 7 = 104/159

Step 5

Decimal & Percentage Representation

Dividing the numerator 104 by denominator 159 produces a repeating decimal (approximately 0.654088, or 65.4088%).

104 ÷ 159 = 0.654088 (65.4088%)

Visual Representation

The diagram below illustrates 17/53 plus 7/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`104/159`
Mixed Number Form	`104/159`
Decimal Form	`0.654088`
Percentage	`65.4088%`

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Frequently Asked Questions

What is 17/53 plus 7/21 as a fraction?

17/53 + 7/21 in simplest fraction form is 104/159.

What is 17/53 plus 7/21 as a decimal?

17/53 + 7/21 converted to a decimal is 0.654088.

What is 17/53 plus 7/21 as a percentage?

17/53 + 7/21 expressed as a percentage is 65.4088%.

Does 17/53 plus 7/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.654088...) because the denominator contains prime factors other than 2 and 5.