What is 3/7 plus 9/14? (Answer: 15/14)

Exact Answer

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Problem: What is 3/7 plus 9/14?
Formula / Expression: 3/7 + 9/14
Final Answer: 1 1/14 (15/14)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
Notice that 14 is an exact multiple of 7 (7 × 2 = 14). The Least Common Denominator (LCD) is simply 14, meaning we only need to scale one fraction.
Working: LCD(7, 14) = 14

Step 2: Convert to Equivalent Fractions with Common Denominator 14
Multiply the numerator and denominator of 3/7 by 2, and multiply the numerator and denominator of 9/14 by 1 so both fractions share the common base 14.
Working: 3 × 2/7 × 2 = 6/14 and 9 × 1/14 × 1 = 9/14

Step 3: Add the Numerators
Now add the numerators (6 + 9 = 15) and keep the common denominator 14 unchanged.
Working: 6 + 9/14 = 15/14

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 15 and 14 is 1, confirming that 15/14 cannot be reduced further—it is already in its simplest irreducible form.
Working: 15/14

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (15) is greater than the denominator (14), divide 15 by 14: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/14.
Working: 15/14 = 1 1/14

Step 6: Decimal & Percentage Representation
Dividing the numerator 15 by denominator 14 produces a repeating decimal (approximately 1.071429, or 107.1429%).
Working: 15 ÷ 14 = 1.071429 (107.1429%)

Key Values:
- Simplified Fraction: 15/14
- Mixed Number Form: 1 1/14
- Decimal Value: 1.071429
- Percentage: 107.1429%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-3-7-plus-9-14/
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3/7 + 9/14 = 15/14

Simplified Fraction

15/14

Mixed Number

1 1/14

Decimal Value

1.071429

Percentage

107.1429%

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Step-by-Step Solution: 3/7 + 9/14

Step 1

Find the Least Common Denominator (LCD)

Notice that 14 is an exact multiple of 7 (7 × 2 = 14). The Least Common Denominator (LCD) is simply 14, meaning we only need to scale one fraction.

LCD(7, 14) = 14

Step 2

Convert to Equivalent Fractions with Common Denominator 14

Multiply the numerator and denominator of 3/7 by 2, and multiply the numerator and denominator of 9/14 by 1 so both fractions share the common base 14.

3 × 2/7 × 2 = 6/14 and 9 × 1/14 × 1 = 9/14

Step 3

Add the Numerators

Now add the numerators (6 + 9 = 15) and keep the common denominator 14 unchanged.

6 + 9/14 = 15/14

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 15 and 14 is 1, confirming that 15/14 cannot be reduced further—it is already in its simplest irreducible form.

15/14

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (15) is greater than the denominator (14), divide 15 by 14: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/14.

15/14 = 11/14

Step 6

Decimal & Percentage Representation

Dividing the numerator 15 by denominator 14 produces a repeating decimal (approximately 1.071429, or 107.1429%).

15 ÷ 14 = 1.071429 (107.1429%)

Visual Representation

The diagram below illustrates 3/7 plus 9/14 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`15/14`
Mixed Number Form	`1 1/14`
Decimal Form	`1.071429`
Percentage	`107.1429%`

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Frequently Asked Questions

What is 3/7 plus 9/14 as a fraction?

3/7 + 9/14 in simplest fraction form is 15/14 (or 1 1/14 as a mixed number).

What is 3/7 plus 9/14 as a decimal?

3/7 + 9/14 converted to a decimal is 1.071429.

What is 3/7 plus 9/14 as a percentage?

3/7 + 9/14 expressed as a percentage is 107.1429%.

How do you write 3/7 plus 9/14 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 15/14 can be written as the mixed number 1 1/14.

Does 3/7 plus 9/14 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.071429...) because the denominator contains prime factors other than 2 and 5.