What is 7/48 plus 15/21? (Answer: 289/336)

Exact Answer

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Problem: What is 7/48 plus 15/21?
Formula / Expression: 7/48 + 15/21
Final Answer: 289/336
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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 15/21 by 16 so both fractions share the common base 336.
Working: 7 × 7/48 × 7 = 49/336 and 15 × 16/21 × 16 = 240/336

Step 3: Add the Numerators
Now add the numerators (49 + 240 = 289) and keep the common denominator 336 unchanged.
Working: 49 + 240/336 = 289/336

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 289 and 336 is 1, confirming that 289/336 cannot be reduced further—it is already in its simplest irreducible form.
Working: 289/336

Step 5: Decimal & Percentage Representation
Dividing the numerator 289 by denominator 336 produces a repeating decimal (approximately 0.860119, or 86.0119%).
Working: 289 ÷ 336 = 0.860119 (86.0119%)

Key Values:
- Simplified Fraction: 289/336
- Mixed Number Form: 289/336
- Decimal Value: 0.860119
- Percentage: 86.0119%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-7-48-plus-15-21/
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7/48 + 15/21 = 289/336

Simplified Fraction

289/336

Mixed Number

Proper (289/336)

Decimal Value

0.860119

Percentage

86.0119%

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Step-by-Step Solution: 7/48 + 15/21

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 15/21 by 16 so both fractions share the common base 336.

7 × 7/48 × 7 = 49/336 and 15 × 16/21 × 16 = 240/336

Step 3

Add the Numerators

Now add the numerators (49 + 240 = 289) and keep the common denominator 336 unchanged.

49 + 240/336 = 289/336

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 289 and 336 is 1, confirming that 289/336 cannot be reduced further—it is already in its simplest irreducible form.

289/336

Step 5

Decimal & Percentage Representation

Dividing the numerator 289 by denominator 336 produces a repeating decimal (approximately 0.860119, or 86.0119%).

289 ÷ 336 = 0.860119 (86.0119%)

Visual Representation

The diagram below illustrates 7/48 plus 15/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`289/336`
Mixed Number Form	`289/336`
Decimal Form	`0.860119`
Percentage	`86.0119%`

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Frequently Asked Questions

What is 7/48 plus 15/21 as a fraction?

7/48 + 15/21 in simplest fraction form is 289/336.

What is 7/48 plus 15/21 as a decimal?

7/48 + 15/21 converted to a decimal is 0.860119.

What is 7/48 plus 15/21 as a percentage?

7/48 + 15/21 expressed as a percentage is 86.0119%.

Does 7/48 plus 15/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.860119...) because the denominator contains prime factors other than 2 and 5.