What is 6/24 plus 8/21? (Answer: 53/84)

Exact Answer

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Problem: What is 6/24 plus 8/21?
Formula / Expression: 6/24 + 8/21
Final Answer: 53/84
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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 6/24 by 7, and multiply the numerator and denominator of 8/21 by 8 so both fractions share the common base 168.
Working: 6 × 7/24 × 7 = 42/168 and 8 × 8/21 × 8 = 64/168

Step 3: Add the Numerators
Now add the numerators (42 + 64 = 106) and keep the common denominator 168 unchanged.
Working: 42 + 64/168 = 106/168

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 106 and 168, which is 2. Divide both the numerator and denominator by 2.
Working: 106 ÷ 2/168 ÷ 2 = 53/84

Step 5: Decimal & Percentage Representation
Dividing the numerator 53 by denominator 84 produces a repeating decimal (approximately 0.630952, or 63.0952%).
Working: 53 ÷ 84 = 0.630952 (63.0952%)

Key Values:
- Simplified Fraction: 53/84
- Mixed Number Form: 53/84
- Decimal Value: 0.630952
- Percentage: 63.0952%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-6-24-plus-8-21/
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6/24 + 8/21 = 53/84

Simplified Fraction

53/84

Mixed Number

Proper (53/84)

Decimal Value

0.630952

Percentage

63.0952%

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Step-by-Step Solution: 6/24 + 8/21

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 6/24 by 7, and multiply the numerator and denominator of 8/21 by 8 so both fractions share the common base 168.

6 × 7/24 × 7 = 42/168 and 8 × 8/21 × 8 = 64/168

Step 3

Add the Numerators

Now add the numerators (42 + 64 = 106) and keep the common denominator 168 unchanged.

42 + 64/168 = 106/168

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 106 and 168, which is 2. Divide both the numerator and denominator by 2.

106 ÷ 2/168 ÷ 2 = 53/84

Step 5

Decimal & Percentage Representation

Dividing the numerator 53 by denominator 84 produces a repeating decimal (approximately 0.630952, or 63.0952%).

53 ÷ 84 = 0.630952 (63.0952%)

Visual Representation

The diagram below illustrates 6/24 plus 8/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`53/84`
Mixed Number Form	`53/84`
Decimal Form	`0.630952`
Percentage	`63.0952%`

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Frequently Asked Questions

What is 6/24 plus 8/21 as a fraction?

6/24 + 8/21 in simplest fraction form is 53/84.

What is 6/24 plus 8/21 as a decimal?

6/24 + 8/21 converted to a decimal is 0.630952.

What is 6/24 plus 8/21 as a percentage?

6/24 + 8/21 expressed as a percentage is 63.0952%.

Does 6/24 plus 8/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.630952...) because the denominator contains prime factors other than 2 and 5.