What is 7/24 plus 4/9? (Answer: 53/72)

Exact Answer

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Problem: What is 7/24 plus 4/9?
Formula / Expression: 7/24 + 4/9
Final Answer: 53/72
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 72
Multiply the numerator and denominator of 7/24 by 3, and multiply the numerator and denominator of 4/9 by 8 so both fractions share the common base 72.
Working: 7 × 3/24 × 3 = 21/72 and 4 × 8/9 × 8 = 32/72

Step 3: Add the Numerators
Now add the numerators (21 + 32 = 53) and keep the common denominator 72 unchanged.
Working: 21 + 32/72 = 53/72

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 53 and 72 is 1, confirming that 53/72 cannot be reduced further—it is already in its simplest irreducible form.
Working: 53/72

Step 5: Decimal & Percentage Representation
Dividing the numerator 53 by denominator 72 produces a repeating decimal (approximately 0.736111, or 73.6111%).
Working: 53 ÷ 72 = 0.736111 (73.6111%)

Key Values:
- Simplified Fraction: 53/72
- Mixed Number Form: 53/72
- Decimal Value: 0.736111
- Percentage: 73.6111%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-7-24-plus-4-9/
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7/24 + 4/9 = 53/72

Simplified Fraction

53/72

Mixed Number

Proper (53/72)

Decimal Value

0.736111

Percentage

73.6111%

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Step-by-Step Solution: 7/24 + 4/9

Step 1

Find the Least Common Denominator (LCD)

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

LCD(24, 9) = 72

Step 2

Convert to Equivalent Fractions with Common Denominator 72

Multiply the numerator and denominator of 7/24 by 3, and multiply the numerator and denominator of 4/9 by 8 so both fractions share the common base 72.

7 × 3/24 × 3 = 21/72 and 4 × 8/9 × 8 = 32/72

Step 3

Add the Numerators

Now add the numerators (21 + 32 = 53) and keep the common denominator 72 unchanged.

21 + 32/72 = 53/72

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 53 and 72 is 1, confirming that 53/72 cannot be reduced further—it is already in its simplest irreducible form.

53/72

Step 5

Decimal & Percentage Representation

Dividing the numerator 53 by denominator 72 produces a repeating decimal (approximately 0.736111, or 73.6111%).

53 ÷ 72 = 0.736111 (73.6111%)

Visual Representation

The diagram below illustrates 7/24 plus 4/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`53/72`
Mixed Number Form	`53/72`
Decimal Form	`0.736111`
Percentage	`73.6111%`

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Frequently Asked Questions

What is 7/24 plus 4/9 as a fraction?

7/24 + 4/9 in simplest fraction form is 53/72.

What is 7/24 plus 4/9 as a decimal?

7/24 + 4/9 converted to a decimal is 0.736111.

What is 7/24 plus 4/9 as a percentage?

7/24 + 4/9 expressed as a percentage is 73.6111%.

Does 7/24 plus 4/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.736111...) because the denominator contains prime factors other than 2 and 5.