What is 3/7 plus 4/9? (Answer: 55/63)

Exact Answer

==================================================
Problem: What is 3/7 plus 4/9?
Formula / Expression: 3/7 + 4/9
Final Answer: 55/63
==================================================

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 3/7 by 9, and multiply the numerator and denominator of 4/9 by 7 so both fractions share the common base 63.
Working: 3 × 9/7 × 9 = 27/63 and 4 × 7/9 × 7 = 28/63

Step 3: Add the Numerators
Now add the numerators (27 + 28 = 55) and keep the common denominator 63 unchanged.
Working: 27 + 28/63 = 55/63

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 55 and 63 is 1, confirming that 55/63 cannot be reduced further—it is already in its simplest irreducible form.
Working: 55/63

Step 5: Decimal & Percentage Representation
Dividing the numerator 55 by denominator 63 produces a repeating decimal (approximately 0.873016, or 87.3016%).
Working: 55 ÷ 63 = 0.873016 (87.3016%)

Key Values:
- Simplified Fraction: 55/63
- Mixed Number Form: 55/63
- Decimal Value: 0.873016
- Percentage: 87.3016%

--------------------------------------------------
Solved with FractionsCalc:
https://fractionscalc.com/what-is-3-7-plus-4-9/
==================================================

3/7 + 4/9 = 55/63

Simplified Fraction

55/63

Mixed Number

Proper (55/63)

Decimal Value

0.873016

Percentage

87.3016%

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: 3/7 + 4/9

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 3/7 by 9, and multiply the numerator and denominator of 4/9 by 7 so both fractions share the common base 63.

3 × 9/7 × 9 = 27/63 and 4 × 7/9 × 7 = 28/63

Step 3

Add the Numerators

Now add the numerators (27 + 28 = 55) and keep the common denominator 63 unchanged.

27 + 28/63 = 55/63

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 55 and 63 is 1, confirming that 55/63 cannot be reduced further—it is already in its simplest irreducible form.

55/63

Step 5

Decimal & Percentage Representation

Dividing the numerator 55 by denominator 63 produces a repeating decimal (approximately 0.873016, or 87.3016%).

55 ÷ 63 = 0.873016 (87.3016%)

Visual Representation

The diagram below illustrates 3/7 plus 4/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`55/63`
Mixed Number Form	`55/63`
Decimal Form	`0.873016`
Percentage	`87.3016%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

What is 3/7 plus 4/9 as a fraction?

3/7 + 4/9 in simplest fraction form is 55/63.

What is 3/7 plus 4/9 as a decimal?

3/7 + 4/9 converted to a decimal is 0.873016.

What is 3/7 plus 4/9 as a percentage?

3/7 + 4/9 expressed as a percentage is 87.3016%.

Does 3/7 plus 4/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.873016...) because the denominator contains prime factors other than 2 and 5.