What is 10/63 plus 5/21? (Answer: 25/63)

Exact Answer

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Problem: What is 10/63 plus 5/21?
Formula / Expression: 10/63 + 5/21
Final Answer: 25/63
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
Notice that 63 is an exact multiple of 21 (21 × 3 = 63). The Least Common Denominator (LCD) is simply 63, meaning we only need to scale one fraction.
Working: LCD(63, 21) = 63

Step 2: Convert to Equivalent Fractions with Common Denominator 63
Multiply the numerator and denominator of 10/63 by 1, and multiply the numerator and denominator of 5/21 by 3 so both fractions share the common base 63.
Working: 10 × 1/63 × 1 = 10/63 and 5 × 3/21 × 3 = 15/63

Step 3: Add the Numerators
Now add the numerators (10 + 15 = 25) and keep the common denominator 63 unchanged.
Working: 10 + 15/63 = 25/63

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 25 and 63 is 1, confirming that 25/63 cannot be reduced further—it is already in its simplest irreducible form.
Working: 25/63

Step 5: Decimal & Percentage Representation
Dividing the numerator 25 by denominator 63 produces a repeating decimal (approximately 0.396825, or 39.6825%).
Working: 25 ÷ 63 = 0.396825 (39.6825%)

Key Values:
- Simplified Fraction: 25/63
- Mixed Number Form: 25/63
- Decimal Value: 0.396825
- Percentage: 39.6825%

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Solved with FractionsCalc:
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10/63 + 5/21 = 25/63

Simplified Fraction

25/63

Mixed Number

Proper (25/63)

Decimal Value

0.396825

Percentage

39.6825%

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Step-by-Step Solution: 10/63 + 5/21

Step 1

Find the Least Common Denominator (LCD)

Notice that 63 is an exact multiple of 21 (21 × 3 = 63). The Least Common Denominator (LCD) is simply 63, meaning we only need to scale one fraction.

LCD(63, 21) = 63

Step 2

Convert to Equivalent Fractions with Common Denominator 63

Multiply the numerator and denominator of 10/63 by 1, and multiply the numerator and denominator of 5/21 by 3 so both fractions share the common base 63.

10 × 1/63 × 1 = 10/63 and 5 × 3/21 × 3 = 15/63

Step 3

Add the Numerators

Now add the numerators (10 + 15 = 25) and keep the common denominator 63 unchanged.

10 + 15/63 = 25/63

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 25 and 63 is 1, confirming that 25/63 cannot be reduced further—it is already in its simplest irreducible form.

25/63

Step 5

Decimal & Percentage Representation

Dividing the numerator 25 by denominator 63 produces a repeating decimal (approximately 0.396825, or 39.6825%).

25 ÷ 63 = 0.396825 (39.6825%)

Visual Representation

The diagram below illustrates 10/63 plus 5/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`25/63`
Mixed Number Form	`25/63`
Decimal Form	`0.396825`
Percentage	`39.6825%`

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Frequently Asked Questions

What is 10/63 plus 5/21 as a fraction?

10/63 + 5/21 in simplest fraction form is 25/63.

What is 10/63 plus 5/21 as a decimal?

10/63 + 5/21 converted to a decimal is 0.396825.

What is 10/63 plus 5/21 as a percentage?

10/63 + 5/21 expressed as a percentage is 39.6825%.

Does 10/63 plus 5/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.396825...) because the denominator contains prime factors other than 2 and 5.