What is 1/7 plus 3/9? (Answer: 10/21)

Exact Answer

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Problem: What is 1/7 plus 3/9?
Formula / Expression: 1/7 + 3/9
Final Answer: 10/21
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 7 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 7 × 9 = 63.
Working: LCD(7, 9) = 63

Step 2: Convert to Equivalent Fractions with Common Denominator 63
Multiply the numerator and denominator of 1/7 by 9, and multiply the numerator and denominator of 3/9 by 7 so both fractions share the common base 63.
Working: 1 × 9/7 × 9 = 9/63 and 3 × 7/9 × 7 = 21/63

Step 3: Add the Numerators
Now add the numerators (9 + 21 = 30) and keep the common denominator 63 unchanged.
Working: 9 + 21/63 = 30/63

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 30 and 63, which is 3. Divide both the numerator and denominator by 3.
Working: 30 ÷ 3/63 ÷ 3 = 10/21

Step 5: Decimal & Percentage Representation
Dividing the numerator 10 by denominator 21 produces a repeating decimal (approximately 0.47619, or 47.619%).
Working: 10 ÷ 21 = 0.47619 (47.619%)

Key Values:
- Simplified Fraction: 10/21
- Mixed Number Form: 10/21
- Decimal Value: 0.47619
- Percentage: 47.619%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-1-7-plus-3-9/
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1/7 + 3/9 = 10/21

Simplified Fraction

10/21

Mixed Number

Proper (10/21)

Decimal Value

0.47619

Percentage

47.619%

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Step-by-Step Solution: 1/7 + 3/9

Step 1

Find the Least Common Denominator (LCD)

The denominators 7 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 7 × 9 = 63.

LCD(7, 9) = 63

Step 2

Convert to Equivalent Fractions with Common Denominator 63

Multiply the numerator and denominator of 1/7 by 9, and multiply the numerator and denominator of 3/9 by 7 so both fractions share the common base 63.

1 × 9/7 × 9 = 9/63 and 3 × 7/9 × 7 = 21/63

Step 3

Add the Numerators

Now add the numerators (9 + 21 = 30) and keep the common denominator 63 unchanged.

9 + 21/63 = 30/63

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 30 and 63, which is 3. Divide both the numerator and denominator by 3.

30 ÷ 3/63 ÷ 3 = 10/21

Step 5

Decimal & Percentage Representation

Dividing the numerator 10 by denominator 21 produces a repeating decimal (approximately 0.47619, or 47.619%).

10 ÷ 21 = 0.47619 (47.619%)

Visual Representation

The diagram below illustrates 1/7 plus 3/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`10/21`
Mixed Number Form	`10/21`
Decimal Form	`0.47619`
Percentage	`47.619%`

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Frequently Asked Questions

What is 1/7 plus 3/9 as a fraction?

1/7 + 3/9 in simplest fraction form is 10/21.

What is 1/7 plus 3/9 as a decimal?

1/7 + 3/9 converted to a decimal is 0.47619.

What is 1/7 plus 3/9 as a percentage?

1/7 + 3/9 expressed as a percentage is 47.619%.

Does 1/7 plus 3/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.47619...) because the denominator contains prime factors other than 2 and 5.