What is 9/14 plus 7/9? (Answer: 179/126)

Exact Answer

==================================================
Problem: What is 9/14 plus 7/9?
Formula / Expression: 9/14 + 7/9
Final Answer: 1 53/126 (179/126)
==================================================

Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 126
Multiply the numerator and denominator of 9/14 by 9, and multiply the numerator and denominator of 7/9 by 14 so both fractions share the common base 126.
Working: 9 × 9/14 × 9 = 81/126 and 7 × 14/9 × 14 = 98/126

Step 3: Add the Numerators
Now add the numerators (81 + 98 = 179) and keep the common denominator 126 unchanged.
Working: 81 + 98/126 = 179/126

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 179 and 126 is 1, confirming that 179/126 cannot be reduced further—it is already in its simplest irreducible form.
Working: 179/126

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (179) is greater than the denominator (126), divide 179 by 126: it goes in 1 whole time(s) with a remainder of 53, giving the mixed number 1 53/126.
Working: 179/126 = 1 53/126

Step 6: Decimal & Percentage Representation
Dividing the numerator 179 by denominator 126 produces a repeating decimal (approximately 1.420635, or 142.0635%).
Working: 179 ÷ 126 = 1.420635 (142.0635%)

Key Values:
- Simplified Fraction: 179/126
- Mixed Number Form: 1 53/126
- Decimal Value: 1.420635
- Percentage: 142.0635%

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

9/14 + 7/9 = 179/126

Simplified Fraction

179/126

Mixed Number

1 53/126

Decimal Value

1.420635

Percentage

142.0635%

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: 9/14 + 7/9

Step 1

Find the Least Common Denominator (LCD)

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

LCD(14, 9) = 126

Step 2

Convert to Equivalent Fractions with Common Denominator 126

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

9 × 9/14 × 9 = 81/126 and 7 × 14/9 × 14 = 98/126

Step 3

Add the Numerators

Now add the numerators (81 + 98 = 179) and keep the common denominator 126 unchanged.

81 + 98/126 = 179/126

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 179 and 126 is 1, confirming that 179/126 cannot be reduced further—it is already in its simplest irreducible form.

179/126

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (179) is greater than the denominator (126), divide 179 by 126: it goes in 1 whole time(s) with a remainder of 53, giving the mixed number 1 53/126.

179/126 = 153/126

Step 6

Decimal & Percentage Representation

Dividing the numerator 179 by denominator 126 produces a repeating decimal (approximately 1.420635, or 142.0635%).

179 ÷ 126 = 1.420635 (142.0635%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`179/126`
Mixed Number Form	`1 53/126`
Decimal Form	`1.420635`
Percentage	`142.0635%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

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

9/14 + 7/9 in simplest fraction form is 179/126 (or 1 53/126 as a mixed number).

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

9/14 + 7/9 converted to a decimal is 1.420635.

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

9/14 + 7/9 expressed as a percentage is 142.0635%.

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

Because the numerator is greater than the denominator, the improper fraction 179/126 can be written as the mixed number 1 53/126.

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

It results in a repeating decimal (approximately 1.420635...) because the denominator contains prime factors other than 2 and 5.