What is 13/49 plus 9/21? (Answer: 34/49)

Exact Answer

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Problem: What is 13/49 plus 9/21?
Formula / Expression: 13/49 + 9/21
Final Answer: 34/49
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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 9/21 by 7 so both fractions share the common base 147.
Working: 13 × 3/49 × 3 = 39/147 and 9 × 7/21 × 7 = 63/147

Step 3: Add the Numerators
Now add the numerators (39 + 63 = 102) and keep the common denominator 147 unchanged.
Working: 39 + 63/147 = 102/147

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 102 and 147, which is 3. Divide both the numerator and denominator by 3.
Working: 102 ÷ 3/147 ÷ 3 = 34/49

Step 5: Decimal & Percentage Representation
Dividing the numerator 34 by denominator 49 produces a repeating decimal (approximately 0.693878, or 69.3878%).
Working: 34 ÷ 49 = 0.693878 (69.3878%)

Key Values:
- Simplified Fraction: 34/49
- Mixed Number Form: 34/49
- Decimal Value: 0.693878
- Percentage: 69.3878%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-13-49-plus-9-21/
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13/49 + 9/21 = 34/49

Simplified Fraction

34/49

Mixed Number

Proper (34/49)

Decimal Value

0.693878

Percentage

69.3878%

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Step-by-Step Solution: 13/49 + 9/21

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 9/21 by 7 so both fractions share the common base 147.

13 × 3/49 × 3 = 39/147 and 9 × 7/21 × 7 = 63/147

Step 3

Add the Numerators

Now add the numerators (39 + 63 = 102) and keep the common denominator 147 unchanged.

39 + 63/147 = 102/147

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 102 and 147, which is 3. Divide both the numerator and denominator by 3.

102 ÷ 3/147 ÷ 3 = 34/49

Step 5

Decimal & Percentage Representation

Dividing the numerator 34 by denominator 49 produces a repeating decimal (approximately 0.693878, or 69.3878%).

34 ÷ 49 = 0.693878 (69.3878%)

Visual Representation

The diagram below illustrates 13/49 plus 9/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`34/49`
Mixed Number Form	`34/49`
Decimal Form	`0.693878`
Percentage	`69.3878%`

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Frequently Asked Questions

What is 13/49 plus 9/21 as a fraction?

13/49 + 9/21 in simplest fraction form is 34/49.

What is 13/49 plus 9/21 as a decimal?

13/49 + 9/21 converted to a decimal is 0.693878.

What is 13/49 plus 9/21 as a percentage?

13/49 + 9/21 expressed as a percentage is 69.3878%.

Does 13/49 plus 9/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.693878...) because the denominator contains prime factors other than 2 and 5.