What is 4/9 plus 7/15? (Answer: 41/45)

Exact Answer

==================================================
Problem: What is 4/9 plus 7/15?
Formula / Expression: 4/9 + 7/15
Final Answer: 41/45
==================================================

Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 9 and 15 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 45 (which is smaller than their product 9 × 15 = 135, keeping the calculation simpler).
Working: LCD(9, 15) = 45

Step 2: Convert to Equivalent Fractions with Common Denominator 45
Multiply the numerator and denominator of 4/9 by 5, and multiply the numerator and denominator of 7/15 by 3 so both fractions share the common base 45.
Working: 4 × 5/9 × 5 = 20/45 and 7 × 3/15 × 3 = 21/45

Step 3: Add the Numerators
Now add the numerators (20 + 21 = 41) and keep the common denominator 45 unchanged.
Working: 20 + 21/45 = 41/45

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 41 and 45 is 1, confirming that 41/45 cannot be reduced further—it is already in its simplest irreducible form.
Working: 41/45

Step 5: Decimal & Percentage Representation
Dividing the numerator 41 by denominator 45 produces a repeating decimal (approximately 0.911111, or 91.1111%).
Working: 41 ÷ 45 = 0.911111 (91.1111%)

Key Values:
- Simplified Fraction: 41/45
- Mixed Number Form: 41/45
- Decimal Value: 0.911111
- Percentage: 91.1111%

--------------------------------------------------
Solved with FractionsCalc:
https://fractionscalc.com/what-is-4-9-plus-7-15/
==================================================

4/9 + 7/15 = 41/45

Simplified Fraction

41/45

Mixed Number

Proper (41/45)

Decimal Value

0.911111

Percentage

91.1111%

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: 4/9 + 7/15

Step 1

Find the Least Common Denominator (LCD)

The denominators 9 and 15 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 45 (which is smaller than their product 9 × 15 = 135, keeping the calculation simpler).

LCD(9, 15) = 45

Step 2

Convert to Equivalent Fractions with Common Denominator 45

Multiply the numerator and denominator of 4/9 by 5, and multiply the numerator and denominator of 7/15 by 3 so both fractions share the common base 45.

4 × 5/9 × 5 = 20/45 and 7 × 3/15 × 3 = 21/45

Step 3

Add the Numerators

Now add the numerators (20 + 21 = 41) and keep the common denominator 45 unchanged.

20 + 21/45 = 41/45

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 41 and 45 is 1, confirming that 41/45 cannot be reduced further—it is already in its simplest irreducible form.

41/45

Step 5

Decimal & Percentage Representation

Dividing the numerator 41 by denominator 45 produces a repeating decimal (approximately 0.911111, or 91.1111%).

41 ÷ 45 = 0.911111 (91.1111%)

Visual Representation

The diagram below illustrates 4/9 plus 7/15 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`41/45`
Mixed Number Form	`41/45`
Decimal Form	`0.911111`
Percentage	`91.1111%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

What is 4/9 plus 7/15 as a fraction?

4/9 + 7/15 in simplest fraction form is 41/45.

What is 4/9 plus 7/15 as a decimal?

4/9 + 7/15 converted to a decimal is 0.911111.

What is 4/9 plus 7/15 as a percentage?

4/9 + 7/15 expressed as a percentage is 91.1111%.

Does 4/9 plus 7/15 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.911111...) because the denominator contains prime factors other than 2 and 5.