What is 13/48 plus 8/21? (Answer: 73/112)

Exact Answer

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Problem: What is 13/48 plus 8/21?
Formula / Expression: 13/48 + 8/21
Final Answer: 73/112
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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 13/48 by 7, and multiply the numerator and denominator of 8/21 by 16 so both fractions share the common base 336.
Working: 13 × 7/48 × 7 = 91/336 and 8 × 16/21 × 16 = 128/336

Step 3: Add the Numerators
Now add the numerators (91 + 128 = 219) and keep the common denominator 336 unchanged.
Working: 91 + 128/336 = 219/336

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 219 and 336, which is 3. Divide both the numerator and denominator by 3.
Working: 219 ÷ 3/336 ÷ 3 = 73/112

Step 5: Decimal & Percentage Representation
Dividing the numerator 73 by denominator 112 produces a repeating decimal (approximately 0.651786, or 65.1786%).
Working: 73 ÷ 112 = 0.651786 (65.1786%)

Key Values:
- Simplified Fraction: 73/112
- Mixed Number Form: 73/112
- Decimal Value: 0.651786
- Percentage: 65.1786%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-13-48-plus-8-21/
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13/48 + 8/21 = 73/112

Simplified Fraction

73/112

Mixed Number

Proper (73/112)

Decimal Value

0.651786

Percentage

65.1786%

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Step-by-Step Solution: 13/48 + 8/21

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 13/48 by 7, and multiply the numerator and denominator of 8/21 by 16 so both fractions share the common base 336.

13 × 7/48 × 7 = 91/336 and 8 × 16/21 × 16 = 128/336

Step 3

Add the Numerators

Now add the numerators (91 + 128 = 219) and keep the common denominator 336 unchanged.

91 + 128/336 = 219/336

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 219 and 336, which is 3. Divide both the numerator and denominator by 3.

219 ÷ 3/336 ÷ 3 = 73/112

Step 5

Decimal & Percentage Representation

Dividing the numerator 73 by denominator 112 produces a repeating decimal (approximately 0.651786, or 65.1786%).

73 ÷ 112 = 0.651786 (65.1786%)

Visual Representation

The diagram below illustrates 13/48 plus 8/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`73/112`
Mixed Number Form	`73/112`
Decimal Form	`0.651786`
Percentage	`65.1786%`

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Frequently Asked Questions

What is 13/48 plus 8/21 as a fraction?

13/48 + 8/21 in simplest fraction form is 73/112.

What is 13/48 plus 8/21 as a decimal?

13/48 + 8/21 converted to a decimal is 0.651786.

What is 13/48 plus 8/21 as a percentage?

13/48 + 8/21 expressed as a percentage is 65.1786%.

Does 13/48 plus 8/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.651786...) because the denominator contains prime factors other than 2 and 5.