What is 10/49 plus 5/21? (Answer: 65/147)

Exact Answer

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Problem: What is 10/49 plus 5/21?
Formula / Expression: 10/49 + 5/21
Final Answer: 65/147
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 49 and 21 share a common factor (GCD = 7). Finding their Least Common Multiple gives an LCD of 147 (which is smaller than their product 49 × 21 = 1029, keeping the calculation simpler).
Working: LCD(49, 21) = 147

Step 2: Convert to Equivalent Fractions with Common Denominator 147
Multiply the numerator and denominator of 10/49 by 3, and multiply the numerator and denominator of 5/21 by 7 so both fractions share the common base 147.
Working: 10 × 3/49 × 3 = 30/147 and 5 × 7/21 × 7 = 35/147

Step 3: Add the Numerators
Now add the numerators (30 + 35 = 65) and keep the common denominator 147 unchanged.
Working: 30 + 35/147 = 65/147

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 65 and 147 is 1, confirming that 65/147 cannot be reduced further—it is already in its simplest irreducible form.
Working: 65/147

Step 5: Decimal & Percentage Representation
Dividing the numerator 65 by denominator 147 produces a repeating decimal (approximately 0.442177, or 44.2177%).
Working: 65 ÷ 147 = 0.442177 (44.2177%)

Key Values:
- Simplified Fraction: 65/147
- Mixed Number Form: 65/147
- Decimal Value: 0.442177
- Percentage: 44.2177%

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10/49 + 5/21 = 65/147

Simplified Fraction

65/147

Mixed Number

Proper (65/147)

Decimal Value

0.442177

Percentage

44.2177%

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Step-by-Step Solution: 10/49 + 5/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 49 and 21 share a common factor (GCD = 7). Finding their Least Common Multiple gives an LCD of 147 (which is smaller than their product 49 × 21 = 1029, keeping the calculation simpler).

LCD(49, 21) = 147

Step 2

Convert to Equivalent Fractions with Common Denominator 147

Multiply the numerator and denominator of 10/49 by 3, and multiply the numerator and denominator of 5/21 by 7 so both fractions share the common base 147.

10 × 3/49 × 3 = 30/147 and 5 × 7/21 × 7 = 35/147

Step 3

Add the Numerators

Now add the numerators (30 + 35 = 65) and keep the common denominator 147 unchanged.

30 + 35/147 = 65/147

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 65 and 147 is 1, confirming that 65/147 cannot be reduced further—it is already in its simplest irreducible form.

65/147

Step 5

Decimal & Percentage Representation

Dividing the numerator 65 by denominator 147 produces a repeating decimal (approximately 0.442177, or 44.2177%).

65 ÷ 147 = 0.442177 (44.2177%)

Visual Representation

The diagram below illustrates 10/49 plus 5/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`65/147`
Mixed Number Form	`65/147`
Decimal Form	`0.442177`
Percentage	`44.2177%`

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Frequently Asked Questions

What is 10/49 plus 5/21 as a fraction?

10/49 + 5/21 in simplest fraction form is 65/147.

What is 10/49 plus 5/21 as a decimal?

10/49 + 5/21 converted to a decimal is 0.442177.

What is 10/49 plus 5/21 as a percentage?

10/49 + 5/21 expressed as a percentage is 44.2177%.

Does 10/49 plus 5/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.442177...) because the denominator contains prime factors other than 2 and 5.