What is 2/10 plus 9/24? (Answer: 23/40)

Exact Answer

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Problem: What is 2/10 plus 9/24?
Formula / Expression: 2/10 + 9/24
Final Answer: 23/40
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 10 and 24 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 120 (which is smaller than their product 10 × 24 = 240, keeping the calculation simpler).
Working: LCD(10, 24) = 120

Step 2: Convert to Equivalent Fractions with Common Denominator 120
Multiply the numerator and denominator of 2/10 by 12, and multiply the numerator and denominator of 9/24 by 5 so both fractions share the common base 120.
Working: 2 × 12/10 × 12 = 24/120 and 9 × 5/24 × 5 = 45/120

Step 3: Add the Numerators
Now add the numerators (24 + 45 = 69) and keep the common denominator 120 unchanged.
Working: 24 + 45/120 = 69/120

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 69 and 120, which is 3. Divide both the numerator and denominator by 3.
Working: 69 ÷ 3/120 ÷ 3 = 23/40

Step 5: Decimal & Percentage Representation
Dividing the numerator 23 by denominator 40 yields an exact terminating decimal of 0.575 (or 57.5%).
Working: 23 ÷ 40 = 0.575 (57.5%)

Key Values:
- Simplified Fraction: 23/40
- Mixed Number Form: 23/40
- Decimal Value: 0.575
- Percentage: 57.5%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-10-plus-9-24/
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2/10 + 9/24 = 23/40

Simplified Fraction

23/40

Mixed Number

Proper (23/40)

Decimal Value

0.575

Percentage

57.5%

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Step-by-Step Solution: 2/10 + 9/24

Step 1

Find the Least Common Denominator (LCD)

The denominators 10 and 24 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 120 (which is smaller than their product 10 × 24 = 240, keeping the calculation simpler).

LCD(10, 24) = 120

Step 2

Convert to Equivalent Fractions with Common Denominator 120

Multiply the numerator and denominator of 2/10 by 12, and multiply the numerator and denominator of 9/24 by 5 so both fractions share the common base 120.

2 × 12/10 × 12 = 24/120 and 9 × 5/24 × 5 = 45/120

Step 3

Add the Numerators

Now add the numerators (24 + 45 = 69) and keep the common denominator 120 unchanged.

24 + 45/120 = 69/120

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 69 and 120, which is 3. Divide both the numerator and denominator by 3.

69 ÷ 3/120 ÷ 3 = 23/40

Step 5

Decimal & Percentage Representation

Dividing the numerator 23 by denominator 40 yields an exact terminating decimal of 0.575 (or 57.5%).

23 ÷ 40 = 0.575 (57.5%)

Visual Representation

The diagram below illustrates 2/10 plus 9/24 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`23/40`
Mixed Number Form	`23/40`
Decimal Form	`0.575`
Percentage	`57.5%`

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Frequently Asked Questions

What is 2/10 plus 9/24 as a fraction?

2/10 + 9/24 in simplest fraction form is 23/40.

What is 2/10 plus 9/24 as a decimal?

2/10 + 9/24 converted to a decimal is 0.575.

What is 2/10 plus 9/24 as a percentage?

2/10 + 9/24 expressed as a percentage is 57.5%.

Does 2/10 plus 9/24 result in a terminating or repeating decimal?

It results in an exact terminating decimal (0.575) because the denominator in simplest terms contains only prime factors 2 and/or 5.