What is 1/4 plus 3/9? (Answer: 7/12)

Exact Answer

==================================================
Problem: What is 1/4 plus 3/9?
Formula / Expression: 1/4 + 3/9
Final Answer: 7/12
==================================================

Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 4 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 4 × 9 = 36.
Working: LCD(4, 9) = 36

Step 2: Convert to Equivalent Fractions with Common Denominator 36
Multiply the numerator and denominator of 1/4 by 9, and multiply the numerator and denominator of 3/9 by 4 so both fractions share the common base 36.
Working: 1 × 9/4 × 9 = 9/36 and 3 × 4/9 × 4 = 12/36

Step 3: Add the Numerators
Now add the numerators (9 + 12 = 21) and keep the common denominator 36 unchanged.
Working: 9 + 12/36 = 21/36

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 21 and 36, which is 3. Divide both the numerator and denominator by 3.
Working: 21 ÷ 3/36 ÷ 3 = 7/12

Step 5: Decimal & Percentage Representation
Dividing the numerator 7 by denominator 12 produces a repeating decimal (approximately 0.583333, or 58.3333%).
Working: 7 ÷ 12 = 0.583333 (58.3333%)

Key Values:
- Simplified Fraction: 7/12
- Mixed Number Form: 7/12
- Decimal Value: 0.583333
- Percentage: 58.3333%

--------------------------------------------------
Solved with FractionsCalc:
https://fractionscalc.com/what-is-1-4-plus-3-9/
==================================================

1/4 + 3/9 = 7/12

Simplified Fraction

7/12

Mixed Number

Proper (7/12)

Decimal Value

0.583333

Percentage

58.3333%

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: 1/4 + 3/9

Step 1

Find the Least Common Denominator (LCD)

The denominators 4 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 4 × 9 = 36.

LCD(4, 9) = 36

Step 2

Convert to Equivalent Fractions with Common Denominator 36

Multiply the numerator and denominator of 1/4 by 9, and multiply the numerator and denominator of 3/9 by 4 so both fractions share the common base 36.

1 × 9/4 × 9 = 9/36 and 3 × 4/9 × 4 = 12/36

Step 3

Add the Numerators

Now add the numerators (9 + 12 = 21) and keep the common denominator 36 unchanged.

9 + 12/36 = 21/36

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 21 and 36, which is 3. Divide both the numerator and denominator by 3.

21 ÷ 3/36 ÷ 3 = 7/12

Step 5

Decimal & Percentage Representation

Dividing the numerator 7 by denominator 12 produces a repeating decimal (approximately 0.583333, or 58.3333%).

7 ÷ 12 = 0.583333 (58.3333%)

Visual Representation

The diagram below illustrates 1/4 plus 3/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`7/12`
Mixed Number Form	`7/12`
Decimal Form	`0.583333`
Percentage	`58.3333%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

What is 1/4 plus 3/9 as a fraction?

1/4 + 3/9 in simplest fraction form is 7/12.

What is 1/4 plus 3/9 as a decimal?

1/4 + 3/9 converted to a decimal is 0.583333.

What is 1/4 plus 3/9 as a percentage?

1/4 + 3/9 expressed as a percentage is 58.3333%.

Does 1/4 plus 3/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.583333...) because the denominator contains prime factors other than 2 and 5.