What is 13/49 plus 10/21? (Answer: 109/147)

Exact Answer

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Problem: What is 13/49 plus 10/21?
Formula / Expression: 13/49 + 10/21
Final Answer: 109/147
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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 13/49 by 3, and multiply the numerator and denominator of 10/21 by 7 so both fractions share the common base 147.
Working: 13 × 3/49 × 3 = 39/147 and 10 × 7/21 × 7 = 70/147

Step 3: Add the Numerators
Now add the numerators (39 + 70 = 109) and keep the common denominator 147 unchanged.
Working: 39 + 70/147 = 109/147

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 109 and 147 is 1, confirming that 109/147 cannot be reduced further—it is already in its simplest irreducible form.
Working: 109/147

Step 5: Decimal & Percentage Representation
Dividing the numerator 109 by denominator 147 produces a repeating decimal (approximately 0.741497, or 74.1497%).
Working: 109 ÷ 147 = 0.741497 (74.1497%)

Key Values:
- Simplified Fraction: 109/147
- Mixed Number Form: 109/147
- Decimal Value: 0.741497
- Percentage: 74.1497%

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13/49 + 10/21 = 109/147

Simplified Fraction

109/147

Mixed Number

Proper (109/147)

Decimal Value

0.741497

Percentage

74.1497%

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Step-by-Step Solution: 13/49 + 10/21

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 13/49 by 3, and multiply the numerator and denominator of 10/21 by 7 so both fractions share the common base 147.

13 × 3/49 × 3 = 39/147 and 10 × 7/21 × 7 = 70/147

Step 3

Add the Numerators

Now add the numerators (39 + 70 = 109) and keep the common denominator 147 unchanged.

39 + 70/147 = 109/147

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 109 and 147 is 1, confirming that 109/147 cannot be reduced further—it is already in its simplest irreducible form.

109/147

Step 5

Decimal & Percentage Representation

Dividing the numerator 109 by denominator 147 produces a repeating decimal (approximately 0.741497, or 74.1497%).

109 ÷ 147 = 0.741497 (74.1497%)

Visual Representation

The diagram below illustrates 13/49 plus 10/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`109/147`
Mixed Number Form	`109/147`
Decimal Form	`0.741497`
Percentage	`74.1497%`

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Frequently Asked Questions

What is 13/49 plus 10/21 as a fraction?

13/49 + 10/21 in simplest fraction form is 109/147.

What is 13/49 plus 10/21 as a decimal?

13/49 + 10/21 converted to a decimal is 0.741497.

What is 13/49 plus 10/21 as a percentage?

13/49 + 10/21 expressed as a percentage is 74.1497%.

Does 13/49 plus 10/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.741497...) because the denominator contains prime factors other than 2 and 5.