What is 7/24 plus 3/9? (Answer: 5/8)

Exact Answer

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Problem: What is 7/24 plus 3/9?
Formula / Expression: 7/24 + 3/9
Final Answer: 5/8
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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 3/9 by 8 so both fractions share the common base 72.
Working: 7 × 3/24 × 3 = 21/72 and 3 × 8/9 × 8 = 24/72

Step 3: Add the Numerators
Now add the numerators (21 + 24 = 45) and keep the common denominator 72 unchanged.
Working: 21 + 24/72 = 45/72

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 45 and 72, which is 9. Divide both the numerator and denominator by 9.
Working: 45 ÷ 9/72 ÷ 9 = 5/8

Step 5: Decimal & Percentage Representation
Dividing the numerator 5 by denominator 8 yields an exact terminating decimal of 0.625 (or 62.5%).
Working: 5 ÷ 8 = 0.625 (62.5%)

Key Values:
- Simplified Fraction: 5/8
- Mixed Number Form: 5/8
- Decimal Value: 0.625
- Percentage: 62.5%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-7-24-plus-3-9/
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7/24 + 3/9 = 5/8

Simplified Fraction

5/8

Mixed Number

Proper (5/8)

Decimal Value

0.625

Percentage

62.5%

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Step-by-Step Solution: 7/24 + 3/9

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 3/9 by 8 so both fractions share the common base 72.

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

Step 3

Add the Numerators

Now add the numerators (21 + 24 = 45) and keep the common denominator 72 unchanged.

21 + 24/72 = 45/72

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 45 and 72, which is 9. Divide both the numerator and denominator by 9.

45 ÷ 9/72 ÷ 9 = 5/8

Step 5

Decimal & Percentage Representation

Dividing the numerator 5 by denominator 8 yields an exact terminating decimal of 0.625 (or 62.5%).

5 ÷ 8 = 0.625 (62.5%)

Visual Representation

The diagram below illustrates 7/24 plus 3/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`5/8`
Mixed Number Form	`5/8`
Decimal Form	`0.625`
Percentage	`62.5%`

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Frequently Asked Questions

What is 7/24 plus 3/9 as a fraction?

7/24 + 3/9 in simplest fraction form is 5/8.

What is 7/24 plus 3/9 as a decimal?

7/24 + 3/9 converted to a decimal is 0.625.

What is 7/24 plus 3/9 as a percentage?

7/24 + 3/9 expressed as a percentage is 62.5%.

Does 7/24 plus 3/9 result in a terminating or repeating decimal?

It results in an exact terminating decimal (0.625) because the denominator in simplest terms contains only prime factors 2 and/or 5.