What is 5/48 plus 4/21? (Answer: 33/112)

Exact Answer

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Problem: What is 5/48 plus 4/21?
Formula / Expression: 5/48 + 4/21
Final Answer: 33/112
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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 5/48 by 7, and multiply the numerator and denominator of 4/21 by 16 so both fractions share the common base 336.
Working: 5 × 7/48 × 7 = 35/336 and 4 × 16/21 × 16 = 64/336

Step 3: Add the Numerators
Now add the numerators (35 + 64 = 99) and keep the common denominator 336 unchanged.
Working: 35 + 64/336 = 99/336

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 99 and 336, which is 3. Divide both the numerator and denominator by 3.
Working: 99 ÷ 3/336 ÷ 3 = 33/112

Step 5: Decimal & Percentage Representation
Dividing the numerator 33 by denominator 112 produces a repeating decimal (approximately 0.294643, or 29.4643%).
Working: 33 ÷ 112 = 0.294643 (29.4643%)

Key Values:
- Simplified Fraction: 33/112
- Mixed Number Form: 33/112
- Decimal Value: 0.294643
- Percentage: 29.4643%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-5-48-plus-4-21/
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5/48 + 4/21 = 33/112

Simplified Fraction

33/112

Mixed Number

Proper (33/112)

Decimal Value

0.294643

Percentage

29.4643%

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Step-by-Step Solution: 5/48 + 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 5/48 by 7, and multiply the numerator and denominator of 4/21 by 16 so both fractions share the common base 336.

5 × 7/48 × 7 = 35/336 and 4 × 16/21 × 16 = 64/336

Step 3

Add the Numerators

Now add the numerators (35 + 64 = 99) and keep the common denominator 336 unchanged.

35 + 64/336 = 99/336

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 99 and 336, which is 3. Divide both the numerator and denominator by 3.

99 ÷ 3/336 ÷ 3 = 33/112

Step 5

Decimal & Percentage Representation

Dividing the numerator 33 by denominator 112 produces a repeating decimal (approximately 0.294643, or 29.4643%).

33 ÷ 112 = 0.294643 (29.4643%)

Visual Representation

The diagram below illustrates 5/48 plus 4/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`33/112`
Mixed Number Form	`33/112`
Decimal Form	`0.294643`
Percentage	`29.4643%`

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Frequently Asked Questions

What is 5/48 plus 4/21 as a fraction?

5/48 + 4/21 in simplest fraction form is 33/112.

What is 5/48 plus 4/21 as a decimal?

5/48 + 4/21 converted to a decimal is 0.294643.

What is 5/48 plus 4/21 as a percentage?

5/48 + 4/21 expressed as a percentage is 29.4643%.

Does 5/48 plus 4/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.294643...) because the denominator contains prime factors other than 2 and 5.