What is 19/48 plus 9/21? (Answer: 277/336)

Exact Answer

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Problem: What is 19/48 plus 9/21?
Formula / Expression: 19/48 + 9/21
Final Answer: 277/336
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 48 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 336 (which is smaller than their product 48 × 21 = 1008, keeping the calculation simpler).
Working: LCD(48, 21) = 336

Step 2: Convert to Equivalent Fractions with Common Denominator 336
Multiply the numerator and denominator of 19/48 by 7, and multiply the numerator and denominator of 9/21 by 16 so both fractions share the common base 336.
Working: 19 × 7/48 × 7 = 133/336 and 9 × 16/21 × 16 = 144/336

Step 3: Add the Numerators
Now add the numerators (133 + 144 = 277) and keep the common denominator 336 unchanged.
Working: 133 + 144/336 = 277/336

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 277 and 336 is 1, confirming that 277/336 cannot be reduced further—it is already in its simplest irreducible form.
Working: 277/336

Step 5: Decimal & Percentage Representation
Dividing the numerator 277 by denominator 336 produces a repeating decimal (approximately 0.824405, or 82.4405%).
Working: 277 ÷ 336 = 0.824405 (82.4405%)

Key Values:
- Simplified Fraction: 277/336
- Mixed Number Form: 277/336
- Decimal Value: 0.824405
- Percentage: 82.4405%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-19-48-plus-9-21/
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19/48 + 9/21 = 277/336

Simplified Fraction

277/336

Mixed Number

Proper (277/336)

Decimal Value

0.824405

Percentage

82.4405%

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Step-by-Step Solution: 19/48 + 9/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 48 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 336 (which is smaller than their product 48 × 21 = 1008, keeping the calculation simpler).

LCD(48, 21) = 336

Step 2

Convert to Equivalent Fractions with Common Denominator 336

Multiply the numerator and denominator of 19/48 by 7, and multiply the numerator and denominator of 9/21 by 16 so both fractions share the common base 336.

19 × 7/48 × 7 = 133/336 and 9 × 16/21 × 16 = 144/336

Step 3

Add the Numerators

Now add the numerators (133 + 144 = 277) and keep the common denominator 336 unchanged.

133 + 144/336 = 277/336

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 277 and 336 is 1, confirming that 277/336 cannot be reduced further—it is already in its simplest irreducible form.

277/336

Step 5

Decimal & Percentage Representation

Dividing the numerator 277 by denominator 336 produces a repeating decimal (approximately 0.824405, or 82.4405%).

277 ÷ 336 = 0.824405 (82.4405%)

Visual Representation

The diagram below illustrates 19/48 plus 9/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`277/336`
Mixed Number Form	`277/336`
Decimal Form	`0.824405`
Percentage	`82.4405%`

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Frequently Asked Questions

What is 19/48 plus 9/21 as a fraction?

19/48 + 9/21 in simplest fraction form is 277/336.

What is 19/48 plus 9/21 as a decimal?

19/48 + 9/21 converted to a decimal is 0.824405.

What is 19/48 plus 9/21 as a percentage?

19/48 + 9/21 expressed as a percentage is 82.4405%.

Does 19/48 plus 9/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.824405...) because the denominator contains prime factors other than 2 and 5.