What is 7/21 plus 20/59? (Answer: 119/177)

Exact Answer

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Problem: What is 7/21 plus 20/59?
Formula / Expression: 7/21 + 20/59
Final Answer: 119/177
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 21 and 59 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 21 × 59 = 1239.
Working: LCD(21, 59) = 1239

Step 2: Convert to Equivalent Fractions with Common Denominator 1239
Multiply the numerator and denominator of 7/21 by 59, and multiply the numerator and denominator of 20/59 by 21 so both fractions share the common base 1239.
Working: 7 × 59/21 × 59 = 413/1239 and 20 × 21/59 × 21 = 420/1239

Step 3: Add the Numerators
Now add the numerators (413 + 420 = 833) and keep the common denominator 1239 unchanged.
Working: 413 + 420/1239 = 833/1239

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 833 and 1239, which is 7. Divide both the numerator and denominator by 7.
Working: 833 ÷ 7/1239 ÷ 7 = 119/177

Step 5: Decimal & Percentage Representation
Dividing the numerator 119 by denominator 177 produces a repeating decimal (approximately 0.672316, or 67.2316%).
Working: 119 ÷ 177 = 0.672316 (67.2316%)

Key Values:
- Simplified Fraction: 119/177
- Mixed Number Form: 119/177
- Decimal Value: 0.672316
- Percentage: 67.2316%

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Solved with FractionsCalc:
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7/21 + 20/59 = 119/177

Simplified Fraction

119/177

Mixed Number

Proper (119/177)

Decimal Value

0.672316

Percentage

67.2316%

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Step-by-Step Solution: 7/21 + 20/59

Step 1

Find the Least Common Denominator (LCD)

The denominators 21 and 59 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 21 × 59 = 1239.

LCD(21, 59) = 1239

Step 2

Convert to Equivalent Fractions with Common Denominator 1239

Multiply the numerator and denominator of 7/21 by 59, and multiply the numerator and denominator of 20/59 by 21 so both fractions share the common base 1239.

7 × 59/21 × 59 = 413/1239 and 20 × 21/59 × 21 = 420/1239

Step 3

Add the Numerators

Now add the numerators (413 + 420 = 833) and keep the common denominator 1239 unchanged.

413 + 420/1239 = 833/1239

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 833 and 1239, which is 7. Divide both the numerator and denominator by 7.

833 ÷ 7/1239 ÷ 7 = 119/177

Step 5

Decimal & Percentage Representation

Dividing the numerator 119 by denominator 177 produces a repeating decimal (approximately 0.672316, or 67.2316%).

119 ÷ 177 = 0.672316 (67.2316%)

Visual Representation

The diagram below illustrates 7/21 plus 20/59 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`119/177`
Mixed Number Form	`119/177`
Decimal Form	`0.672316`
Percentage	`67.2316%`

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Frequently Asked Questions

What is 7/21 plus 20/59 as a fraction?

7/21 + 20/59 in simplest fraction form is 119/177.

What is 7/21 plus 20/59 as a decimal?

7/21 + 20/59 converted to a decimal is 0.672316.

What is 7/21 plus 20/59 as a percentage?

7/21 + 20/59 expressed as a percentage is 67.2316%.

Does 7/21 plus 20/59 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.672316...) because the denominator contains prime factors other than 2 and 5.