What is 3/24 plus 10/21? (Answer: 101/168)

Exact Answer

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Problem: What is 3/24 plus 10/21?
Formula / Expression: 3/24 + 10/21
Final Answer: 101/168
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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 3/24 by 7, and multiply the numerator and denominator of 10/21 by 8 so both fractions share the common base 168.
Working: 3 × 7/24 × 7 = 21/168 and 10 × 8/21 × 8 = 80/168

Step 3: Add the Numerators
Now add the numerators (21 + 80 = 101) and keep the common denominator 168 unchanged.
Working: 21 + 80/168 = 101/168

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 101 and 168 is 1, confirming that 101/168 cannot be reduced further—it is already in its simplest irreducible form.
Working: 101/168

Step 5: Decimal & Percentage Representation
Dividing the numerator 101 by denominator 168 produces a repeating decimal (approximately 0.60119, or 60.119%).
Working: 101 ÷ 168 = 0.60119 (60.119%)

Key Values:
- Simplified Fraction: 101/168
- Mixed Number Form: 101/168
- Decimal Value: 0.60119
- Percentage: 60.119%

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Solved with FractionsCalc:
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3/24 + 10/21 = 101/168

Simplified Fraction

101/168

Mixed Number

Proper (101/168)

Decimal Value

0.60119

Percentage

60.119%

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Step-by-Step Solution: 3/24 + 10/21

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 3/24 by 7, and multiply the numerator and denominator of 10/21 by 8 so both fractions share the common base 168.

3 × 7/24 × 7 = 21/168 and 10 × 8/21 × 8 = 80/168

Step 3

Add the Numerators

Now add the numerators (21 + 80 = 101) and keep the common denominator 168 unchanged.

21 + 80/168 = 101/168

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 101 and 168 is 1, confirming that 101/168 cannot be reduced further—it is already in its simplest irreducible form.

101/168

Step 5

Decimal & Percentage Representation

Dividing the numerator 101 by denominator 168 produces a repeating decimal (approximately 0.60119, or 60.119%).

101 ÷ 168 = 0.60119 (60.119%)

Visual Representation

The diagram below illustrates 3/24 plus 10/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`101/168`
Mixed Number Form	`101/168`
Decimal Form	`0.60119`
Percentage	`60.119%`

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Frequently Asked Questions

What is 3/24 plus 10/21 as a fraction?

3/24 + 10/21 in simplest fraction form is 101/168.

What is 3/24 plus 10/21 as a decimal?

3/24 + 10/21 converted to a decimal is 0.60119.

What is 3/24 plus 10/21 as a percentage?

3/24 + 10/21 expressed as a percentage is 60.119%.

Does 3/24 plus 10/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.60119...) because the denominator contains prime factors other than 2 and 5.