What is 10/23 plus 2/4? (Answer: 43/46)

Exact Answer

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Problem: What is 10/23 plus 2/4?
Formula / Expression: 10/23 + 2/4
Final Answer: 43/46
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 23 and 4 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 23 × 4 = 92.
Working: LCD(23, 4) = 92

Step 2: Convert to Equivalent Fractions with Common Denominator 92
Multiply the numerator and denominator of 10/23 by 4, and multiply the numerator and denominator of 2/4 by 23 so both fractions share the common base 92.
Working: 10 × 4/23 × 4 = 40/92 and 2 × 23/4 × 23 = 46/92

Step 3: Add the Numerators
Now add the numerators (40 + 46 = 86) and keep the common denominator 92 unchanged.
Working: 40 + 46/92 = 86/92

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 86 and 92, which is 2. Divide both the numerator and denominator by 2.
Working: 86 ÷ 2/92 ÷ 2 = 43/46

Step 5: Decimal & Percentage Representation
Dividing the numerator 43 by denominator 46 produces a repeating decimal (approximately 0.934783, or 93.4783%).
Working: 43 ÷ 46 = 0.934783 (93.4783%)

Key Values:
- Simplified Fraction: 43/46
- Mixed Number Form: 43/46
- Decimal Value: 0.934783
- Percentage: 93.4783%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-10-23-plus-2-4/
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10/23 + 2/4 = 43/46

Simplified Fraction

43/46

Mixed Number

Proper (43/46)

Decimal Value

0.934783

Percentage

93.4783%

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Step-by-Step Solution: 10/23 + 2/4

Step 1

Find the Least Common Denominator (LCD)

The denominators 23 and 4 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 23 × 4 = 92.

LCD(23, 4) = 92

Step 2

Convert to Equivalent Fractions with Common Denominator 92

Multiply the numerator and denominator of 10/23 by 4, and multiply the numerator and denominator of 2/4 by 23 so both fractions share the common base 92.

10 × 4/23 × 4 = 40/92 and 2 × 23/4 × 23 = 46/92

Step 3

Add the Numerators

Now add the numerators (40 + 46 = 86) and keep the common denominator 92 unchanged.

40 + 46/92 = 86/92

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 86 and 92, which is 2. Divide both the numerator and denominator by 2.

86 ÷ 2/92 ÷ 2 = 43/46

Step 5

Decimal & Percentage Representation

Dividing the numerator 43 by denominator 46 produces a repeating decimal (approximately 0.934783, or 93.4783%).

43 ÷ 46 = 0.934783 (93.4783%)

Visual Representation

The diagram below illustrates 10/23 plus 2/4 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`43/46`
Mixed Number Form	`43/46`
Decimal Form	`0.934783`
Percentage	`93.4783%`

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Frequently Asked Questions

What is 10/23 plus 2/4 as a fraction?

10/23 + 2/4 in simplest fraction form is 43/46.

What is 10/23 plus 2/4 as a decimal?

10/23 + 2/4 converted to a decimal is 0.934783.

What is 10/23 plus 2/4 as a percentage?

10/23 + 2/4 expressed as a percentage is 93.4783%.

Does 10/23 plus 2/4 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.934783...) because the denominator contains prime factors other than 2 and 5.