What is 3/9 plus 7/14? (Answer: 5/6)

Exact Answer

==================================================
Problem: What is 3/9 plus 7/14?
Formula / Expression: 3/9 + 7/14
Final Answer: 5/6
==================================================

Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 9 and 14 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 9 × 14 = 126.
Working: LCD(9, 14) = 126

Step 2: Convert to Equivalent Fractions with Common Denominator 126
Multiply the numerator and denominator of 3/9 by 14, and multiply the numerator and denominator of 7/14 by 9 so both fractions share the common base 126.
Working: 3 × 14/9 × 14 = 42/126 and 7 × 9/14 × 9 = 63/126

Step 3: Add the Numerators
Now add the numerators (42 + 63 = 105) and keep the common denominator 126 unchanged.
Working: 42 + 63/126 = 105/126

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 105 and 126, which is 21. Divide both the numerator and denominator by 21.
Working: 105 ÷ 21/126 ÷ 21 = 5/6

Step 5: Decimal & Percentage Representation
Dividing the numerator 5 by denominator 6 produces a repeating decimal (approximately 0.833333, or 83.3333%).
Working: 5 ÷ 6 = 0.833333 (83.3333%)

Key Values:
- Simplified Fraction: 5/6
- Mixed Number Form: 5/6
- Decimal Value: 0.833333
- Percentage: 83.3333%

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

3/9 + 7/14 = 5/6

Simplified Fraction

5/6

Mixed Number

Proper (5/6)

Decimal Value

0.833333

Percentage

83.3333%

Reduce / Convert Fraction:

Convert Fraction:

Enter Decimal Number:

Enter Percentage: %

What is % of

From Value: To Value:

Simplify Ratio: :

Switch to Proportion / Missing X Solver (A/B = C/D) →

Enter 3 known numbers and leave 1 empty (or type x) to solve:

← Switch to Ratio Simplifier (A:B)

Provide any 2 values below to calculate the remaining:

Price before discount

Discount

Price after discount

You saved

+ Add Sales Tax & Extra Coupon (Optional)

Sales Tax: % Extra Off: %

Provide any 2 values below to calculate the remaining:

Cost

Markup

REVENUE

Gross Profit

Profit Margin

Bill Subtotal

Tip Percentage

Split (People)

👥

Quick Tip:

Total Bill

Split Between

👥

Tip % (Optional)

Include Tip:

Total Price

Quantity

Unit of Measure

← Discount & Sales Tax • Ratio Simplifier (A:B) →

First Number: Second Number:

Find All Factors of:

Dividend: ÷ Divisor:

Number to Round: To Nearest:

Method: Standard (5+ ↑) Always Up (Ceil) Always Down (Floor)

Presets:

√ Square Root of: OR Power (x^y): ^{^}

x² + x + = 0

Number (n! & log):

Circle Radius (r):

Side a: Side b:

Angle (Degrees): °

Numbers (comma separated):

Total Items (n): Choose (r):

Decimal Number:

Number (1–3999):

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

Step 1

Find the Least Common Denominator (LCD)

The denominators 9 and 14 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 9 × 14 = 126.

LCD(9, 14) = 126

Step 2

Convert to Equivalent Fractions with Common Denominator 126

Multiply the numerator and denominator of 3/9 by 14, and multiply the numerator and denominator of 7/14 by 9 so both fractions share the common base 126.

3 × 14/9 × 14 = 42/126 and 7 × 9/14 × 9 = 63/126

Step 3

Add the Numerators

Now add the numerators (42 + 63 = 105) and keep the common denominator 126 unchanged.

42 + 63/126 = 105/126

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 105 and 126, which is 21. Divide both the numerator and denominator by 21.

105 ÷ 21/126 ÷ 21 = 5/6

Step 5

Decimal & Percentage Representation

Dividing the numerator 5 by denominator 6 produces a repeating decimal (approximately 0.833333, or 83.3333%).

5 ÷ 6 = 0.833333 (83.3333%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`5/6`
Mixed Number Form	`5/6`
Decimal Form	`0.833333`
Percentage	`83.3333%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

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

3/9 + 7/14 in simplest fraction form is 5/6.

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

3/9 + 7/14 converted to a decimal is 0.833333.

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

3/9 + 7/14 expressed as a percentage is 83.3333%.

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

It results in a repeating decimal (approximately 0.833333...) because the denominator contains prime factors other than 2 and 5.