What is 10/24 plus 12/21? (Answer: 83/84)

Exact Answer

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Problem: What is 10/24 plus 12/21?
Formula / Expression: 10/24 + 12/21
Final Answer: 83/84
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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 10/24 by 7, and multiply the numerator and denominator of 12/21 by 8 so both fractions share the common base 168.
Working: 10 × 7/24 × 7 = 70/168 and 12 × 8/21 × 8 = 96/168

Step 3: Add the Numerators
Now add the numerators (70 + 96 = 166) and keep the common denominator 168 unchanged.
Working: 70 + 96/168 = 166/168

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 166 and 168, which is 2. Divide both the numerator and denominator by 2.
Working: 166 ÷ 2/168 ÷ 2 = 83/84

Step 5: Decimal & Percentage Representation
Dividing the numerator 83 by denominator 84 produces a repeating decimal (approximately 0.988095, or 98.8095%).
Working: 83 ÷ 84 = 0.988095 (98.8095%)

Key Values:
- Simplified Fraction: 83/84
- Mixed Number Form: 83/84
- Decimal Value: 0.988095
- Percentage: 98.8095%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-10-24-plus-12-21/
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10/24 + 12/21 = 83/84

Simplified Fraction

83/84

Mixed Number

Proper (83/84)

Decimal Value

0.988095

Percentage

98.8095%

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Step-by-Step Solution: 10/24 + 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 10/24 by 7, and multiply the numerator and denominator of 12/21 by 8 so both fractions share the common base 168.

10 × 7/24 × 7 = 70/168 and 12 × 8/21 × 8 = 96/168

Step 3

Add the Numerators

Now add the numerators (70 + 96 = 166) and keep the common denominator 168 unchanged.

70 + 96/168 = 166/168

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 166 and 168, which is 2. Divide both the numerator and denominator by 2.

166 ÷ 2/168 ÷ 2 = 83/84

Step 5

Decimal & Percentage Representation

Dividing the numerator 83 by denominator 84 produces a repeating decimal (approximately 0.988095, or 98.8095%).

83 ÷ 84 = 0.988095 (98.8095%)

Visual Representation

The diagram below illustrates 10/24 plus 12/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`83/84`
Mixed Number Form	`83/84`
Decimal Form	`0.988095`
Percentage	`98.8095%`

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Frequently Asked Questions

What is 10/24 plus 12/21 as a fraction?

10/24 + 12/21 in simplest fraction form is 83/84.

What is 10/24 plus 12/21 as a decimal?

10/24 + 12/21 converted to a decimal is 0.988095.

What is 10/24 plus 12/21 as a percentage?

10/24 + 12/21 expressed as a percentage is 98.8095%.

Does 10/24 plus 12/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.988095...) because the denominator contains prime factors other than 2 and 5.