What is 3/21 plus 7/48? (Answer: 97/336)

Exact Answer

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Problem: What is 3/21 plus 7/48?
Formula / Expression: 3/21 + 7/48
Final Answer: 97/336
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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 3/21 by 16, and multiply the numerator and denominator of 7/48 by 7 so both fractions share the common base 336.
Working: 3 × 16/21 × 16 = 48/336 and 7 × 7/48 × 7 = 49/336

Step 3: Add the Numerators
Now add the numerators (48 + 49 = 97) and keep the common denominator 336 unchanged.
Working: 48 + 49/336 = 97/336

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 97 and 336 is 1, confirming that 97/336 cannot be reduced further—it is already in its simplest irreducible form.
Working: 97/336

Step 5: Decimal & Percentage Representation
Dividing the numerator 97 by denominator 336 produces a repeating decimal (approximately 0.28869, or 28.869%).
Working: 97 ÷ 336 = 0.28869 (28.869%)

Key Values:
- Simplified Fraction: 97/336
- Mixed Number Form: 97/336
- Decimal Value: 0.28869
- Percentage: 28.869%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-3-21-plus-7-48/
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3/21 + 7/48 = 97/336

Simplified Fraction

97/336

Mixed Number

Proper (97/336)

Decimal Value

0.28869

Percentage

28.869%

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Step-by-Step Solution: 3/21 + 7/48

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 3/21 by 16, and multiply the numerator and denominator of 7/48 by 7 so both fractions share the common base 336.

3 × 16/21 × 16 = 48/336 and 7 × 7/48 × 7 = 49/336

Step 3

Add the Numerators

Now add the numerators (48 + 49 = 97) and keep the common denominator 336 unchanged.

48 + 49/336 = 97/336

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 97 and 336 is 1, confirming that 97/336 cannot be reduced further—it is already in its simplest irreducible form.

97/336

Step 5

Decimal & Percentage Representation

Dividing the numerator 97 by denominator 336 produces a repeating decimal (approximately 0.28869, or 28.869%).

97 ÷ 336 = 0.28869 (28.869%)

Visual Representation

The diagram below illustrates 3/21 plus 7/48 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`97/336`
Mixed Number Form	`97/336`
Decimal Form	`0.28869`
Percentage	`28.869%`

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Frequently Asked Questions

What is 3/21 plus 7/48 as a fraction?

3/21 + 7/48 in simplest fraction form is 97/336.

What is 3/21 plus 7/48 as a decimal?

3/21 + 7/48 converted to a decimal is 0.28869.

What is 3/21 plus 7/48 as a percentage?

3/21 + 7/48 expressed as a percentage is 28.869%.

Does 3/21 plus 7/48 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.28869...) because the denominator contains prime factors other than 2 and 5.