What is 9/48 plus 4/21? (Answer: 127/336)

Exact Answer

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Problem: What is 9/48 plus 4/21?
Formula / Expression: 9/48 + 4/21
Final Answer: 127/336
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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 9/48 by 7, and multiply the numerator and denominator of 4/21 by 16 so both fractions share the common base 336.
Working: 9 × 7/48 × 7 = 63/336 and 4 × 16/21 × 16 = 64/336

Step 3: Add the Numerators
Now add the numerators (63 + 64 = 127) and keep the common denominator 336 unchanged.
Working: 63 + 64/336 = 127/336

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 127 and 336 is 1, confirming that 127/336 cannot be reduced further—it is already in its simplest irreducible form.
Working: 127/336

Step 5: Decimal & Percentage Representation
Dividing the numerator 127 by denominator 336 produces a repeating decimal (approximately 0.377976, or 37.7976%).
Working: 127 ÷ 336 = 0.377976 (37.7976%)

Key Values:
- Simplified Fraction: 127/336
- Mixed Number Form: 127/336
- Decimal Value: 0.377976
- Percentage: 37.7976%

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Solved with FractionsCalc:
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9/48 + 4/21 = 127/336

Simplified Fraction

127/336

Mixed Number

Proper (127/336)

Decimal Value

0.377976

Percentage

37.7976%

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Step-by-Step Solution: 9/48 + 4/21

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 9/48 by 7, and multiply the numerator and denominator of 4/21 by 16 so both fractions share the common base 336.

9 × 7/48 × 7 = 63/336 and 4 × 16/21 × 16 = 64/336

Step 3

Add the Numerators

Now add the numerators (63 + 64 = 127) and keep the common denominator 336 unchanged.

63 + 64/336 = 127/336

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 127 and 336 is 1, confirming that 127/336 cannot be reduced further—it is already in its simplest irreducible form.

127/336

Step 5

Decimal & Percentage Representation

Dividing the numerator 127 by denominator 336 produces a repeating decimal (approximately 0.377976, or 37.7976%).

127 ÷ 336 = 0.377976 (37.7976%)

Visual Representation

The diagram below illustrates 9/48 plus 4/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`127/336`
Mixed Number Form	`127/336`
Decimal Form	`0.377976`
Percentage	`37.7976%`

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Frequently Asked Questions

What is 9/48 plus 4/21 as a fraction?

9/48 + 4/21 in simplest fraction form is 127/336.

What is 9/48 plus 4/21 as a decimal?

9/48 + 4/21 converted to a decimal is 0.377976.

What is 9/48 plus 4/21 as a percentage?

9/48 + 4/21 expressed as a percentage is 37.7976%.

Does 9/48 plus 4/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.377976...) because the denominator contains prime factors other than 2 and 5.