What is 2/9 plus 7/24? (Answer: 37/72)

Exact Answer

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Problem: What is 2/9 plus 7/24?
Formula / Expression: 2/9 + 7/24
Final Answer: 37/72
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 9 and 24 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 72 (which is smaller than their product 9 × 24 = 216, keeping the calculation simpler).
Working: LCD(9, 24) = 72

Step 2: Convert to Equivalent Fractions with Common Denominator 72
Multiply the numerator and denominator of 2/9 by 8, and multiply the numerator and denominator of 7/24 by 3 so both fractions share the common base 72.
Working: 2 × 8/9 × 8 = 16/72 and 7 × 3/24 × 3 = 21/72

Step 3: Add the Numerators
Now add the numerators (16 + 21 = 37) and keep the common denominator 72 unchanged.
Working: 16 + 21/72 = 37/72

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 37 and 72 is 1, confirming that 37/72 cannot be reduced further—it is already in its simplest irreducible form.
Working: 37/72

Step 5: Decimal & Percentage Representation
Dividing the numerator 37 by denominator 72 produces a repeating decimal (approximately 0.513889, or 51.3889%).
Working: 37 ÷ 72 = 0.513889 (51.3889%)

Key Values:
- Simplified Fraction: 37/72
- Mixed Number Form: 37/72
- Decimal Value: 0.513889
- Percentage: 51.3889%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-9-plus-7-24/
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2/9 + 7/24 = 37/72

Simplified Fraction

37/72

Mixed Number

Proper (37/72)

Decimal Value

0.513889

Percentage

51.3889%

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Step-by-Step Solution: 2/9 + 7/24

Step 1

Find the Least Common Denominator (LCD)

The denominators 9 and 24 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 72 (which is smaller than their product 9 × 24 = 216, keeping the calculation simpler).

LCD(9, 24) = 72

Step 2

Convert to Equivalent Fractions with Common Denominator 72

Multiply the numerator and denominator of 2/9 by 8, and multiply the numerator and denominator of 7/24 by 3 so both fractions share the common base 72.

2 × 8/9 × 8 = 16/72 and 7 × 3/24 × 3 = 21/72

Step 3

Add the Numerators

Now add the numerators (16 + 21 = 37) and keep the common denominator 72 unchanged.

16 + 21/72 = 37/72

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 37 and 72 is 1, confirming that 37/72 cannot be reduced further—it is already in its simplest irreducible form.

37/72

Step 5

Decimal & Percentage Representation

Dividing the numerator 37 by denominator 72 produces a repeating decimal (approximately 0.513889, or 51.3889%).

37 ÷ 72 = 0.513889 (51.3889%)

Visual Representation

The diagram below illustrates 2/9 plus 7/24 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`37/72`
Mixed Number Form	`37/72`
Decimal Form	`0.513889`
Percentage	`51.3889%`

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Frequently Asked Questions

What is 2/9 plus 7/24 as a fraction?

2/9 + 7/24 in simplest fraction form is 37/72.

What is 2/9 plus 7/24 as a decimal?

2/9 + 7/24 converted to a decimal is 0.513889.

What is 2/9 plus 7/24 as a percentage?

2/9 + 7/24 expressed as a percentage is 51.3889%.

Does 2/9 plus 7/24 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.513889...) because the denominator contains prime factors other than 2 and 5.