What is 5/24 plus 8/21? (Answer: 33/56)

Exact Answer

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Problem: What is 5/24 plus 8/21?
Formula / Expression: 5/24 + 8/21
Final Answer: 33/56
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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 5/24 by 7, and multiply the numerator and denominator of 8/21 by 8 so both fractions share the common base 168.
Working: 5 × 7/24 × 7 = 35/168 and 8 × 8/21 × 8 = 64/168

Step 3: Add the Numerators
Now add the numerators (35 + 64 = 99) and keep the common denominator 168 unchanged.
Working: 35 + 64/168 = 99/168

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 99 and 168, which is 3. Divide both the numerator and denominator by 3.
Working: 99 ÷ 3/168 ÷ 3 = 33/56

Step 5: Decimal & Percentage Representation
Dividing the numerator 33 by denominator 56 produces a repeating decimal (approximately 0.589286, or 58.9286%).
Working: 33 ÷ 56 = 0.589286 (58.9286%)

Key Values:
- Simplified Fraction: 33/56
- Mixed Number Form: 33/56
- Decimal Value: 0.589286
- Percentage: 58.9286%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-5-24-plus-8-21/
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5/24 + 8/21 = 33/56

Simplified Fraction

33/56

Mixed Number

Proper (33/56)

Decimal Value

0.589286

Percentage

58.9286%

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Step-by-Step Solution: 5/24 + 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 5/24 by 7, and multiply the numerator and denominator of 8/21 by 8 so both fractions share the common base 168.

5 × 7/24 × 7 = 35/168 and 8 × 8/21 × 8 = 64/168

Step 3

Add the Numerators

Now add the numerators (35 + 64 = 99) and keep the common denominator 168 unchanged.

35 + 64/168 = 99/168

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 99 and 168, which is 3. Divide both the numerator and denominator by 3.

99 ÷ 3/168 ÷ 3 = 33/56

Step 5

Decimal & Percentage Representation

Dividing the numerator 33 by denominator 56 produces a repeating decimal (approximately 0.589286, or 58.9286%).

33 ÷ 56 = 0.589286 (58.9286%)

Visual Representation

The diagram below illustrates 5/24 plus 8/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`33/56`
Mixed Number Form	`33/56`
Decimal Form	`0.589286`
Percentage	`58.9286%`

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Frequently Asked Questions

What is 5/24 plus 8/21 as a fraction?

5/24 + 8/21 in simplest fraction form is 33/56.

What is 5/24 plus 8/21 as a decimal?

5/24 + 8/21 converted to a decimal is 0.589286.

What is 5/24 plus 8/21 as a percentage?

5/24 + 8/21 expressed as a percentage is 58.9286%.

Does 5/24 plus 8/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.589286...) because the denominator contains prime factors other than 2 and 5.