What is 19/49 plus 9/21? (Answer: 40/49)

Exact Answer

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Problem: What is 19/49 plus 9/21?
Formula / Expression: 19/49 + 9/21
Final Answer: 40/49
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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 19/49 by 3, and multiply the numerator and denominator of 9/21 by 7 so both fractions share the common base 147.
Working: 19 × 3/49 × 3 = 57/147 and 9 × 7/21 × 7 = 63/147

Step 3: Add the Numerators
Now add the numerators (57 + 63 = 120) and keep the common denominator 147 unchanged.
Working: 57 + 63/147 = 120/147

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 120 and 147, which is 3. Divide both the numerator and denominator by 3.
Working: 120 ÷ 3/147 ÷ 3 = 40/49

Step 5: Decimal & Percentage Representation
Dividing the numerator 40 by denominator 49 produces a repeating decimal (approximately 0.816327, or 81.6327%).
Working: 40 ÷ 49 = 0.816327 (81.6327%)

Key Values:
- Simplified Fraction: 40/49
- Mixed Number Form: 40/49
- Decimal Value: 0.816327
- Percentage: 81.6327%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-19-49-plus-9-21/
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19/49 + 9/21 = 40/49

Simplified Fraction

40/49

Mixed Number

Proper (40/49)

Decimal Value

0.816327

Percentage

81.6327%

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Step-by-Step Solution: 19/49 + 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 19/49 by 3, and multiply the numerator and denominator of 9/21 by 7 so both fractions share the common base 147.

19 × 3/49 × 3 = 57/147 and 9 × 7/21 × 7 = 63/147

Step 3

Add the Numerators

Now add the numerators (57 + 63 = 120) and keep the common denominator 147 unchanged.

57 + 63/147 = 120/147

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 120 and 147, which is 3. Divide both the numerator and denominator by 3.

120 ÷ 3/147 ÷ 3 = 40/49

Step 5

Decimal & Percentage Representation

Dividing the numerator 40 by denominator 49 produces a repeating decimal (approximately 0.816327, or 81.6327%).

40 ÷ 49 = 0.816327 (81.6327%)

Visual Representation

The diagram below illustrates 19/49 plus 9/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`40/49`
Mixed Number Form	`40/49`
Decimal Form	`0.816327`
Percentage	`81.6327%`

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Frequently Asked Questions

What is 19/49 plus 9/21 as a fraction?

19/49 + 9/21 in simplest fraction form is 40/49.

What is 19/49 plus 9/21 as a decimal?

19/49 + 9/21 converted to a decimal is 0.816327.

What is 19/49 plus 9/21 as a percentage?

19/49 + 9/21 expressed as a percentage is 81.6327%.

Does 19/49 plus 9/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.816327...) because the denominator contains prime factors other than 2 and 5.