What is 10/21 plus 23/48? (Answer: 107/112)

Exact Answer

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Problem: What is 10/21 plus 23/48?
Formula / Expression: 10/21 + 23/48
Final Answer: 107/112
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 336
Multiply the numerator and denominator of 10/21 by 16, and multiply the numerator and denominator of 23/48 by 7 so both fractions share the common base 336.
Working: 10 × 16/21 × 16 = 160/336 and 23 × 7/48 × 7 = 161/336

Step 3: Add the Numerators
Now add the numerators (160 + 161 = 321) and keep the common denominator 336 unchanged.
Working: 160 + 161/336 = 321/336

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 321 and 336, which is 3. Divide both the numerator and denominator by 3.
Working: 321 ÷ 3/336 ÷ 3 = 107/112

Step 5: Decimal & Percentage Representation
Dividing the numerator 107 by denominator 112 produces a repeating decimal (approximately 0.955357, or 95.5357%).
Working: 107 ÷ 112 = 0.955357 (95.5357%)

Key Values:
- Simplified Fraction: 107/112
- Mixed Number Form: 107/112
- Decimal Value: 0.955357
- Percentage: 95.5357%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-10-21-plus-23-48/
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10/21 + 23/48 = 107/112

Simplified Fraction

107/112

Mixed Number

Proper (107/112)

Decimal Value

0.955357

Percentage

95.5357%

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Step-by-Step Solution: 10/21 + 23/48

Step 1

Find the Least Common Denominator (LCD)

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

LCD(21, 48) = 336

Step 2

Convert to Equivalent Fractions with Common Denominator 336

Multiply the numerator and denominator of 10/21 by 16, and multiply the numerator and denominator of 23/48 by 7 so both fractions share the common base 336.

10 × 16/21 × 16 = 160/336 and 23 × 7/48 × 7 = 161/336

Step 3

Add the Numerators

Now add the numerators (160 + 161 = 321) and keep the common denominator 336 unchanged.

160 + 161/336 = 321/336

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 321 and 336, which is 3. Divide both the numerator and denominator by 3.

321 ÷ 3/336 ÷ 3 = 107/112

Step 5

Decimal & Percentage Representation

Dividing the numerator 107 by denominator 112 produces a repeating decimal (approximately 0.955357, or 95.5357%).

107 ÷ 112 = 0.955357 (95.5357%)

Visual Representation

The diagram below illustrates 10/21 plus 23/48 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`107/112`
Mixed Number Form	`107/112`
Decimal Form	`0.955357`
Percentage	`95.5357%`

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Frequently Asked Questions

What is 10/21 plus 23/48 as a fraction?

10/21 + 23/48 in simplest fraction form is 107/112.

What is 10/21 plus 23/48 as a decimal?

10/21 + 23/48 converted to a decimal is 0.955357.

What is 10/21 plus 23/48 as a percentage?

10/21 + 23/48 expressed as a percentage is 95.5357%.

Does 10/21 plus 23/48 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.955357...) because the denominator contains prime factors other than 2 and 5.