What is 4/48 plus 7/21? (Answer: 5/12)

Exact Answer

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Problem: What is 4/48 plus 7/21?
Formula / Expression: 4/48 + 7/21
Final Answer: 5/12
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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 4/48 by 7, and multiply the numerator and denominator of 7/21 by 16 so both fractions share the common base 336.
Working: 4 × 7/48 × 7 = 28/336 and 7 × 16/21 × 16 = 112/336

Step 3: Add the Numerators
Now add the numerators (28 + 112 = 140) and keep the common denominator 336 unchanged.
Working: 28 + 112/336 = 140/336

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 140 and 336, which is 28. Divide both the numerator and denominator by 28.
Working: 140 ÷ 28/336 ÷ 28 = 5/12

Step 5: Decimal & Percentage Representation
Dividing the numerator 5 by denominator 12 produces a repeating decimal (approximately 0.416667, or 41.6667%).
Working: 5 ÷ 12 = 0.416667 (41.6667%)

Key Values:
- Simplified Fraction: 5/12
- Mixed Number Form: 5/12
- Decimal Value: 0.416667
- Percentage: 41.6667%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-4-48-plus-7-21/
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4/48 + 7/21 = 5/12

Simplified Fraction

5/12

Mixed Number

Proper (5/12)

Decimal Value

0.416667

Percentage

41.6667%

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Step-by-Step Solution: 4/48 + 7/21

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

4 × 7/48 × 7 = 28/336 and 7 × 16/21 × 16 = 112/336

Step 3

Add the Numerators

Now add the numerators (28 + 112 = 140) and keep the common denominator 336 unchanged.

28 + 112/336 = 140/336

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 140 and 336, which is 28. Divide both the numerator and denominator by 28.

140 ÷ 28/336 ÷ 28 = 5/12

Step 5

Decimal & Percentage Representation

Dividing the numerator 5 by denominator 12 produces a repeating decimal (approximately 0.416667, or 41.6667%).

5 ÷ 12 = 0.416667 (41.6667%)

Visual Representation

The diagram below illustrates 4/48 plus 7/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`5/12`
Mixed Number Form	`5/12`
Decimal Form	`0.416667`
Percentage	`41.6667%`

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Frequently Asked Questions

What is 4/48 plus 7/21 as a fraction?

4/48 + 7/21 in simplest fraction form is 5/12.

What is 4/48 plus 7/21 as a decimal?

4/48 + 7/21 converted to a decimal is 0.416667.

What is 4/48 plus 7/21 as a percentage?

4/48 + 7/21 expressed as a percentage is 41.6667%.

Does 4/48 plus 7/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.416667...) because the denominator contains prime factors other than 2 and 5.