What is 9/24 plus 12/21? (Answer: 53/56)

Exact Answer

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Problem: What is 9/24 plus 12/21?
Formula / Expression: 9/24 + 12/21
Final Answer: 53/56
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 24 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 168 (which is smaller than their product 24 × 21 = 504, keeping the calculation simpler).
Working: LCD(24, 21) = 168

Step 2: Convert to Equivalent Fractions with Common Denominator 168
Multiply the numerator and denominator of 9/24 by 7, and multiply the numerator and denominator of 12/21 by 8 so both fractions share the common base 168.
Working: 9 × 7/24 × 7 = 63/168 and 12 × 8/21 × 8 = 96/168

Step 3: Add the Numerators
Now add the numerators (63 + 96 = 159) and keep the common denominator 168 unchanged.
Working: 63 + 96/168 = 159/168

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 159 and 168, which is 3. Divide both the numerator and denominator by 3.
Working: 159 ÷ 3/168 ÷ 3 = 53/56

Step 5: Decimal & Percentage Representation
Dividing the numerator 53 by denominator 56 produces a repeating decimal (approximately 0.946429, or 94.6429%).
Working: 53 ÷ 56 = 0.946429 (94.6429%)

Key Values:
- Simplified Fraction: 53/56
- Mixed Number Form: 53/56
- Decimal Value: 0.946429
- Percentage: 94.6429%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-9-24-plus-12-21/
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9/24 + 12/21 = 53/56

Simplified Fraction

53/56

Mixed Number

Proper (53/56)

Decimal Value

0.946429

Percentage

94.6429%

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Step-by-Step Solution: 9/24 + 12/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 24 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 168 (which is smaller than their product 24 × 21 = 504, keeping the calculation simpler).

LCD(24, 21) = 168

Step 2

Convert to Equivalent Fractions with Common Denominator 168

Multiply the numerator and denominator of 9/24 by 7, and multiply the numerator and denominator of 12/21 by 8 so both fractions share the common base 168.

9 × 7/24 × 7 = 63/168 and 12 × 8/21 × 8 = 96/168

Step 3

Add the Numerators

Now add the numerators (63 + 96 = 159) and keep the common denominator 168 unchanged.

63 + 96/168 = 159/168

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 159 and 168, which is 3. Divide both the numerator and denominator by 3.

159 ÷ 3/168 ÷ 3 = 53/56

Step 5

Decimal & Percentage Representation

Dividing the numerator 53 by denominator 56 produces a repeating decimal (approximately 0.946429, or 94.6429%).

53 ÷ 56 = 0.946429 (94.6429%)

Visual Representation

The diagram below illustrates 9/24 plus 12/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`53/56`
Mixed Number Form	`53/56`
Decimal Form	`0.946429`
Percentage	`94.6429%`

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Frequently Asked Questions

What is 9/24 plus 12/21 as a fraction?

9/24 + 12/21 in simplest fraction form is 53/56.

What is 9/24 plus 12/21 as a decimal?

9/24 + 12/21 converted to a decimal is 0.946429.

What is 9/24 plus 12/21 as a percentage?

9/24 + 12/21 expressed as a percentage is 94.6429%.

Does 9/24 plus 12/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.946429...) because the denominator contains prime factors other than 2 and 5.