What is 3/9 plus 7/19? (Answer: 40/57)

Exact Answer

==================================================
Problem: What is 3/9 plus 7/19?
Formula / Expression: 3/9 + 7/19
Final Answer: 40/57
==================================================

Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 9 and 19 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 9 × 19 = 171.
Working: LCD(9, 19) = 171

Step 2: Convert to Equivalent Fractions with Common Denominator 171
Multiply the numerator and denominator of 3/9 by 19, and multiply the numerator and denominator of 7/19 by 9 so both fractions share the common base 171.
Working: 3 × 19/9 × 19 = 57/171 and 7 × 9/19 × 9 = 63/171

Step 3: Add the Numerators
Now add the numerators (57 + 63 = 120) and keep the common denominator 171 unchanged.
Working: 57 + 63/171 = 120/171

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 120 and 171, which is 3. Divide both the numerator and denominator by 3.
Working: 120 ÷ 3/171 ÷ 3 = 40/57

Step 5: Decimal & Percentage Representation
Dividing the numerator 40 by denominator 57 produces a repeating decimal (approximately 0.701754, or 70.1754%).
Working: 40 ÷ 57 = 0.701754 (70.1754%)

Key Values:
- Simplified Fraction: 40/57
- Mixed Number Form: 40/57
- Decimal Value: 0.701754
- Percentage: 70.1754%

--------------------------------------------------
Solved with FractionsCalc:
https://fractionscalc.com/what-is-3-9-plus-7-19/
==================================================

3/9 + 7/19 = 40/57

Simplified Fraction

40/57

Mixed Number

Proper (40/57)

Decimal Value

0.701754

Percentage

70.1754%

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 + 7/19

Step 1

Find the Least Common Denominator (LCD)

The denominators 9 and 19 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 9 × 19 = 171.

LCD(9, 19) = 171

Step 2

Convert to Equivalent Fractions with Common Denominator 171

Multiply the numerator and denominator of 3/9 by 19, and multiply the numerator and denominator of 7/19 by 9 so both fractions share the common base 171.

3 × 19/9 × 19 = 57/171 and 7 × 9/19 × 9 = 63/171

Step 3

Add the Numerators

Now add the numerators (57 + 63 = 120) and keep the common denominator 171 unchanged.

57 + 63/171 = 120/171

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 120 and 171, which is 3. Divide both the numerator and denominator by 3.

120 ÷ 3/171 ÷ 3 = 40/57

Step 5

Decimal & Percentage Representation

Dividing the numerator 40 by denominator 57 produces a repeating decimal (approximately 0.701754, or 70.1754%).

40 ÷ 57 = 0.701754 (70.1754%)

Visual Representation

The diagram below illustrates 3/9 plus 7/19 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`40/57`
Mixed Number Form	`40/57`
Decimal Form	`0.701754`
Percentage	`70.1754%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

What is 3/9 plus 7/19 as a fraction?

3/9 + 7/19 in simplest fraction form is 40/57.

What is 3/9 plus 7/19 as a decimal?

3/9 + 7/19 converted to a decimal is 0.701754.

What is 3/9 plus 7/19 as a percentage?

3/9 + 7/19 expressed as a percentage is 70.1754%.

Does 3/9 plus 7/19 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.701754...) because the denominator contains prime factors other than 2 and 5.