What is 7/21 plus 19/57? (Answer: 2/3)

Exact Answer

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Problem: What is 7/21 plus 19/57?
Formula / Expression: 7/21 + 19/57
Final Answer: 2/3
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Step-by-Step Solution:

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

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

Step 3: Add the Numerators
Now add the numerators (133 + 133 = 266) and keep the common denominator 399 unchanged.
Working: 133 + 133/399 = 266/399

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 266 and 399, which is 133. Divide both the numerator and denominator by 133.
Working: 266 ÷ 133/399 ÷ 133 = 2/3

Step 5: Decimal & Percentage Representation
Dividing the numerator 2 by denominator 3 produces a repeating decimal (approximately 0.666667, or 66.6667%).
Working: 2 ÷ 3 = 0.666667 (66.6667%)

Key Values:
- Simplified Fraction: 2/3
- Mixed Number Form: 2/3
- Decimal Value: 0.666667
- Percentage: 66.6667%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-7-21-plus-19-57/
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7/21 + 19/57 = 2/3

Simplified Fraction

2/3

Mixed Number

Proper (2/3)

Decimal Value

0.666667

Percentage

66.6667%

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Step-by-Step Solution: 7/21 + 19/57

Step 1

Find the Least Common Denominator (LCD)

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

LCD(21, 57) = 399

Step 2

Convert to Equivalent Fractions with Common Denominator 399

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

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

Step 3

Add the Numerators

Now add the numerators (133 + 133 = 266) and keep the common denominator 399 unchanged.

133 + 133/399 = 266/399

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 266 and 399, which is 133. Divide both the numerator and denominator by 133.

266 ÷ 133/399 ÷ 133 = 2/3

Step 5

Decimal & Percentage Representation

Dividing the numerator 2 by denominator 3 produces a repeating decimal (approximately 0.666667, or 66.6667%).

2 ÷ 3 = 0.666667 (66.6667%)

Visual Representation

The diagram below illustrates 7/21 plus 19/57 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`2/3`
Mixed Number Form	`2/3`
Decimal Form	`0.666667`
Percentage	`66.6667%`

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Frequently Asked Questions

What is 7/21 plus 19/57 as a fraction?

7/21 + 19/57 in simplest fraction form is 2/3.

What is 7/21 plus 19/57 as a decimal?

7/21 + 19/57 converted to a decimal is 0.666667.

What is 7/21 plus 19/57 as a percentage?

7/21 + 19/57 expressed as a percentage is 66.6667%.

Does 7/21 plus 19/57 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.666667...) because the denominator contains prime factors other than 2 and 5.