What is 7/48 plus 10/21? (Answer: 209/336)

Exact Answer

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Problem: What is 7/48 plus 10/21?
Formula / Expression: 7/48 + 10/21
Final Answer: 209/336
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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 7/48 by 7, and multiply the numerator and denominator of 10/21 by 16 so both fractions share the common base 336.
Working: 7 × 7/48 × 7 = 49/336 and 10 × 16/21 × 16 = 160/336

Step 3: Add the Numerators
Now add the numerators (49 + 160 = 209) and keep the common denominator 336 unchanged.
Working: 49 + 160/336 = 209/336

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 209 and 336 is 1, confirming that 209/336 cannot be reduced further—it is already in its simplest irreducible form.
Working: 209/336

Step 5: Decimal & Percentage Representation
Dividing the numerator 209 by denominator 336 produces a repeating decimal (approximately 0.622024, or 62.2024%).
Working: 209 ÷ 336 = 0.622024 (62.2024%)

Key Values:
- Simplified Fraction: 209/336
- Mixed Number Form: 209/336
- Decimal Value: 0.622024
- Percentage: 62.2024%

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Solved with FractionsCalc:
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7/48 + 10/21 = 209/336

Simplified Fraction

209/336

Mixed Number

Proper (209/336)

Decimal Value

0.622024

Percentage

62.2024%

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

7 × 7/48 × 7 = 49/336 and 10 × 16/21 × 16 = 160/336

Step 3

Add the Numerators

Now add the numerators (49 + 160 = 209) and keep the common denominator 336 unchanged.

49 + 160/336 = 209/336

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 209 and 336 is 1, confirming that 209/336 cannot be reduced further—it is already in its simplest irreducible form.

209/336

Step 5

Decimal & Percentage Representation

Dividing the numerator 209 by denominator 336 produces a repeating decimal (approximately 0.622024, or 62.2024%).

209 ÷ 336 = 0.622024 (62.2024%)

Visual Representation

The diagram below illustrates 7/48 plus 10/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`209/336`
Mixed Number Form	`209/336`
Decimal Form	`0.622024`
Percentage	`62.2024%`

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Frequently Asked Questions

What is 7/48 plus 10/21 as a fraction?

7/48 + 10/21 in simplest fraction form is 209/336.

What is 7/48 plus 10/21 as a decimal?

7/48 + 10/21 converted to a decimal is 0.622024.

What is 7/48 plus 10/21 as a percentage?

7/48 + 10/21 expressed as a percentage is 62.2024%.

Does 7/48 plus 10/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.622024...) because the denominator contains prime factors other than 2 and 5.