What is 7/48 plus 5/21? (Answer: 43/112)

Exact Answer

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Problem: What is 7/48 plus 5/21?
Formula / Expression: 7/48 + 5/21
Final Answer: 43/112
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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 7/48 by 7, and multiply the numerator and denominator of 5/21 by 16 so both fractions share the common base 336.
Working: 7 × 7/48 × 7 = 49/336 and 5 × 16/21 × 16 = 80/336

Step 3: Add the Numerators
Now add the numerators (49 + 80 = 129) and keep the common denominator 336 unchanged.
Working: 49 + 80/336 = 129/336

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 129 and 336, which is 3. Divide both the numerator and denominator by 3.
Working: 129 ÷ 3/336 ÷ 3 = 43/112

Step 5: Decimal & Percentage Representation
Dividing the numerator 43 by denominator 112 produces a repeating decimal (approximately 0.383929, or 38.3929%).
Working: 43 ÷ 112 = 0.383929 (38.3929%)

Key Values:
- Simplified Fraction: 43/112
- Mixed Number Form: 43/112
- Decimal Value: 0.383929
- Percentage: 38.3929%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-7-48-plus-5-21/
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7/48 + 5/21 = 43/112

Simplified Fraction

43/112

Mixed Number

Proper (43/112)

Decimal Value

0.383929

Percentage

38.3929%

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Step-by-Step Solution: 7/48 + 5/21

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 5/21 by 16 so both fractions share the common base 336.

7 × 7/48 × 7 = 49/336 and 5 × 16/21 × 16 = 80/336

Step 3

Add the Numerators

Now add the numerators (49 + 80 = 129) and keep the common denominator 336 unchanged.

49 + 80/336 = 129/336

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 129 and 336, which is 3. Divide both the numerator and denominator by 3.

129 ÷ 3/336 ÷ 3 = 43/112

Step 5

Decimal & Percentage Representation

Dividing the numerator 43 by denominator 112 produces a repeating decimal (approximately 0.383929, or 38.3929%).

43 ÷ 112 = 0.383929 (38.3929%)

Visual Representation

The diagram below illustrates 7/48 plus 5/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`43/112`
Mixed Number Form	`43/112`
Decimal Form	`0.383929`
Percentage	`38.3929%`

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Frequently Asked Questions

What is 7/48 plus 5/21 as a fraction?

7/48 + 5/21 in simplest fraction form is 43/112.

What is 7/48 plus 5/21 as a decimal?

7/48 + 5/21 converted to a decimal is 0.383929.

What is 7/48 plus 5/21 as a percentage?

7/48 + 5/21 expressed as a percentage is 38.3929%.

Does 7/48 plus 5/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.383929...) because the denominator contains prime factors other than 2 and 5.