What is 1/3 plus 5/7? (Answer: 22/21)

Exact Answer

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Problem: What is 1/3 plus 5/7?
Formula / Expression: 1/3 + 5/7
Final Answer: 1 1/21 (22/21)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 3 and 7 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 3 × 7 = 21.
Working: LCD(3, 7) = 21

Step 2: Convert to Equivalent Fractions with Common Denominator 21
Multiply the numerator and denominator of 1/3 by 7, and multiply the numerator and denominator of 5/7 by 3 so both fractions share the common base 21.
Working: 1 × 7/3 × 7 = 7/21 and 5 × 3/7 × 3 = 15/21

Step 3: Add the Numerators
Now add the numerators (7 + 15 = 22) and keep the common denominator 21 unchanged.
Working: 7 + 15/21 = 22/21

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 22 and 21 is 1, confirming that 22/21 cannot be reduced further—it is already in its simplest irreducible form.
Working: 22/21

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (22) is greater than the denominator (21), divide 22 by 21: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/21.
Working: 22/21 = 1 1/21

Step 6: Decimal & Percentage Representation
Dividing the numerator 22 by denominator 21 produces a repeating decimal (approximately 1.047619, or 104.7619%).
Working: 22 ÷ 21 = 1.047619 (104.7619%)

Key Values:
- Simplified Fraction: 22/21
- Mixed Number Form: 1 1/21
- Decimal Value: 1.047619
- Percentage: 104.7619%

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Solved with FractionsCalc:
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1/3 + 5/7 = 22/21

Simplified Fraction

22/21

Mixed Number

1 1/21

Decimal Value

1.047619

Percentage

104.7619%

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Step-by-Step Solution: 1/3 + 5/7

Step 1

Find the Least Common Denominator (LCD)

The denominators 3 and 7 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 3 × 7 = 21.

LCD(3, 7) = 21

Step 2

Convert to Equivalent Fractions with Common Denominator 21

Multiply the numerator and denominator of 1/3 by 7, and multiply the numerator and denominator of 5/7 by 3 so both fractions share the common base 21.

1 × 7/3 × 7 = 7/21 and 5 × 3/7 × 3 = 15/21

Step 3

Add the Numerators

Now add the numerators (7 + 15 = 22) and keep the common denominator 21 unchanged.

7 + 15/21 = 22/21

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 22 and 21 is 1, confirming that 22/21 cannot be reduced further—it is already in its simplest irreducible form.

22/21

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (22) is greater than the denominator (21), divide 22 by 21: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/21.

22/21 = 11/21

Step 6

Decimal & Percentage Representation

Dividing the numerator 22 by denominator 21 produces a repeating decimal (approximately 1.047619, or 104.7619%).

22 ÷ 21 = 1.047619 (104.7619%)

Visual Representation

The diagram below illustrates 1/3 plus 5/7 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`22/21`
Mixed Number Form	`1 1/21`
Decimal Form	`1.047619`
Percentage	`104.7619%`

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Frequently Asked Questions

What is 1/3 plus 5/7 as a fraction?

1/3 + 5/7 in simplest fraction form is 22/21 (or 1 1/21 as a mixed number).

What is 1/3 plus 5/7 as a decimal?

1/3 + 5/7 converted to a decimal is 1.047619.

What is 1/3 plus 5/7 as a percentage?

1/3 + 5/7 expressed as a percentage is 104.7619%.

How do you write 1/3 plus 5/7 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 22/21 can be written as the mixed number 1 1/21.

Does 1/3 plus 5/7 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.047619...) because the denominator contains prime factors other than 2 and 5.