What is 10/48 plus 9/21? (Answer: 107/168)

Exact Answer

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Problem: What is 10/48 plus 9/21?
Formula / Expression: 10/48 + 9/21
Final Answer: 107/168
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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 10/48 by 7, and multiply the numerator and denominator of 9/21 by 16 so both fractions share the common base 336.
Working: 10 × 7/48 × 7 = 70/336 and 9 × 16/21 × 16 = 144/336

Step 3: Add the Numerators
Now add the numerators (70 + 144 = 214) and keep the common denominator 336 unchanged.
Working: 70 + 144/336 = 214/336

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 214 and 336, which is 2. Divide both the numerator and denominator by 2.
Working: 214 ÷ 2/336 ÷ 2 = 107/168

Step 5: Decimal & Percentage Representation
Dividing the numerator 107 by denominator 168 produces a repeating decimal (approximately 0.636905, or 63.6905%).
Working: 107 ÷ 168 = 0.636905 (63.6905%)

Key Values:
- Simplified Fraction: 107/168
- Mixed Number Form: 107/168
- Decimal Value: 0.636905
- Percentage: 63.6905%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-10-48-plus-9-21/
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10/48 + 9/21 = 107/168

Simplified Fraction

107/168

Mixed Number

Proper (107/168)

Decimal Value

0.636905

Percentage

63.6905%

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Step-by-Step Solution: 10/48 + 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 10/48 by 7, and multiply the numerator and denominator of 9/21 by 16 so both fractions share the common base 336.

10 × 7/48 × 7 = 70/336 and 9 × 16/21 × 16 = 144/336

Step 3

Add the Numerators

Now add the numerators (70 + 144 = 214) and keep the common denominator 336 unchanged.

70 + 144/336 = 214/336

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 214 and 336, which is 2. Divide both the numerator and denominator by 2.

214 ÷ 2/336 ÷ 2 = 107/168

Step 5

Decimal & Percentage Representation

Dividing the numerator 107 by denominator 168 produces a repeating decimal (approximately 0.636905, or 63.6905%).

107 ÷ 168 = 0.636905 (63.6905%)

Visual Representation

The diagram below illustrates 10/48 plus 9/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`107/168`
Mixed Number Form	`107/168`
Decimal Form	`0.636905`
Percentage	`63.6905%`

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Frequently Asked Questions

What is 10/48 plus 9/21 as a fraction?

10/48 + 9/21 in simplest fraction form is 107/168.

What is 10/48 plus 9/21 as a decimal?

10/48 + 9/21 converted to a decimal is 0.636905.

What is 10/48 plus 9/21 as a percentage?

10/48 + 9/21 expressed as a percentage is 63.6905%.

Does 10/48 plus 9/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.636905...) because the denominator contains prime factors other than 2 and 5.