What is 2/10 plus 1/4? (Answer: 9/20)

Exact Answer

==================================================
Problem: What is 2/10 plus 1/4?
Formula / Expression: 2/10 + 1/4
Final Answer: 9/20
==================================================

Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 10 and 4 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 20 (which is smaller than their product 10 × 4 = 40, keeping the calculation simpler).
Working: LCD(10, 4) = 20

Step 2: Convert to Equivalent Fractions with Common Denominator 20
Multiply the numerator and denominator of 2/10 by 2, and multiply the numerator and denominator of 1/4 by 5 so both fractions share the common base 20.
Working: 2 × 2/10 × 2 = 4/20 and 1 × 5/4 × 5 = 5/20

Step 3: Add the Numerators
Now add the numerators (4 + 5 = 9) and keep the common denominator 20 unchanged.
Working: 4 + 5/20 = 9/20

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 9 and 20 is 1, confirming that 9/20 cannot be reduced further—it is already in its simplest irreducible form.
Working: 9/20

Step 5: Decimal & Percentage Representation
Dividing the numerator 9 by denominator 20 yields an exact terminating decimal of 0.45 (or 45%).
Working: 9 ÷ 20 = 0.45 (45%)

Key Values:
- Simplified Fraction: 9/20
- Mixed Number Form: 9/20
- Decimal Value: 0.45
- Percentage: 45%

--------------------------------------------------
Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-10-plus-1-4/
==================================================

2/10 + 1/4 = 9/20

Simplified Fraction

9/20

Mixed Number

Proper (9/20)

Decimal Value

0.45

Percentage

45%

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: 2/10 + 1/4

Step 1

Find the Least Common Denominator (LCD)

The denominators 10 and 4 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 20 (which is smaller than their product 10 × 4 = 40, keeping the calculation simpler).

LCD(10, 4) = 20

Step 2

Convert to Equivalent Fractions with Common Denominator 20

Multiply the numerator and denominator of 2/10 by 2, and multiply the numerator and denominator of 1/4 by 5 so both fractions share the common base 20.

2 × 2/10 × 2 = 4/20 and 1 × 5/4 × 5 = 5/20

Step 3

Add the Numerators

Now add the numerators (4 + 5 = 9) and keep the common denominator 20 unchanged.

4 + 5/20 = 9/20

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 9 and 20 is 1, confirming that 9/20 cannot be reduced further—it is already in its simplest irreducible form.

9/20

Step 5

Decimal & Percentage Representation

Dividing the numerator 9 by denominator 20 yields an exact terminating decimal of 0.45 (or 45%).

9 ÷ 20 = 0.45 (45%)

Visual Representation

The diagram below illustrates 2/10 plus 1/4 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`9/20`
Mixed Number Form	`9/20`
Decimal Form	`0.45`
Percentage	`45%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

What is 2/10 plus 1/4 as a fraction?

2/10 + 1/4 in simplest fraction form is 9/20.

What is 2/10 plus 1/4 as a decimal?

2/10 + 1/4 converted to a decimal is 0.45.

What is 2/10 plus 1/4 as a percentage?

2/10 + 1/4 expressed as a percentage is 45%.

Does 2/10 plus 1/4 result in a terminating or repeating decimal?

It results in an exact terminating decimal (0.45) because the denominator in simplest terms contains only prime factors 2 and/or 5.