What is 17/48 plus 10/21? (Answer: 93/112)

Exact Answer

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Problem: What is 17/48 plus 10/21?
Formula / Expression: 17/48 + 10/21
Final Answer: 93/112
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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 17/48 by 7, and multiply the numerator and denominator of 10/21 by 16 so both fractions share the common base 336.
Working: 17 × 7/48 × 7 = 119/336 and 10 × 16/21 × 16 = 160/336

Step 3: Add the Numerators
Now add the numerators (119 + 160 = 279) and keep the common denominator 336 unchanged.
Working: 119 + 160/336 = 279/336

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 279 and 336, which is 3. Divide both the numerator and denominator by 3.
Working: 279 ÷ 3/336 ÷ 3 = 93/112

Step 5: Decimal & Percentage Representation
Dividing the numerator 93 by denominator 112 produces a repeating decimal (approximately 0.830357, or 83.0357%).
Working: 93 ÷ 112 = 0.830357 (83.0357%)

Key Values:
- Simplified Fraction: 93/112
- Mixed Number Form: 93/112
- Decimal Value: 0.830357
- Percentage: 83.0357%

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Solved with FractionsCalc:
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17/48 + 10/21 = 93/112

Simplified Fraction

93/112

Mixed Number

Proper (93/112)

Decimal Value

0.830357

Percentage

83.0357%

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Step-by-Step Solution: 17/48 + 10/21

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 17/48 by 7, and multiply the numerator and denominator of 10/21 by 16 so both fractions share the common base 336.

17 × 7/48 × 7 = 119/336 and 10 × 16/21 × 16 = 160/336

Step 3

Add the Numerators

Now add the numerators (119 + 160 = 279) and keep the common denominator 336 unchanged.

119 + 160/336 = 279/336

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 279 and 336, which is 3. Divide both the numerator and denominator by 3.

279 ÷ 3/336 ÷ 3 = 93/112

Step 5

Decimal & Percentage Representation

Dividing the numerator 93 by denominator 112 produces a repeating decimal (approximately 0.830357, or 83.0357%).

93 ÷ 112 = 0.830357 (83.0357%)

Visual Representation

The diagram below illustrates 17/48 plus 10/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`93/112`
Mixed Number Form	`93/112`
Decimal Form	`0.830357`
Percentage	`83.0357%`

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Frequently Asked Questions

What is 17/48 plus 10/21 as a fraction?

17/48 + 10/21 in simplest fraction form is 93/112.

What is 17/48 plus 10/21 as a decimal?

17/48 + 10/21 converted to a decimal is 0.830357.

What is 17/48 plus 10/21 as a percentage?

17/48 + 10/21 expressed as a percentage is 83.0357%.

Does 17/48 plus 10/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.830357...) because the denominator contains prime factors other than 2 and 5.