What is 14/48 plus 7/21? (Answer: 5/8)

Exact Answer

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Problem: What is 14/48 plus 7/21?
Formula / Expression: 14/48 + 7/21
Final Answer: 5/8
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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 14/48 by 7, and multiply the numerator and denominator of 7/21 by 16 so both fractions share the common base 336.
Working: 14 × 7/48 × 7 = 98/336 and 7 × 16/21 × 16 = 112/336

Step 3: Add the Numerators
Now add the numerators (98 + 112 = 210) and keep the common denominator 336 unchanged.
Working: 98 + 112/336 = 210/336

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 210 and 336, which is 42. Divide both the numerator and denominator by 42.
Working: 210 ÷ 42/336 ÷ 42 = 5/8

Step 5: Decimal & Percentage Representation
Dividing the numerator 5 by denominator 8 yields an exact terminating decimal of 0.625 (or 62.5%).
Working: 5 ÷ 8 = 0.625 (62.5%)

Key Values:
- Simplified Fraction: 5/8
- Mixed Number Form: 5/8
- Decimal Value: 0.625
- Percentage: 62.5%

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Solved with FractionsCalc:
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14/48 + 7/21 = 5/8

Simplified Fraction

5/8

Mixed Number

Proper (5/8)

Decimal Value

0.625

Percentage

62.5%

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Step-by-Step Solution: 14/48 + 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 14/48 by 7, and multiply the numerator and denominator of 7/21 by 16 so both fractions share the common base 336.

14 × 7/48 × 7 = 98/336 and 7 × 16/21 × 16 = 112/336

Step 3

Add the Numerators

Now add the numerators (98 + 112 = 210) and keep the common denominator 336 unchanged.

98 + 112/336 = 210/336

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 210 and 336, which is 42. Divide both the numerator and denominator by 42.

210 ÷ 42/336 ÷ 42 = 5/8

Step 5

Decimal & Percentage Representation

Dividing the numerator 5 by denominator 8 yields an exact terminating decimal of 0.625 (or 62.5%).

5 ÷ 8 = 0.625 (62.5%)

Visual Representation

The diagram below illustrates 14/48 plus 7/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`5/8`
Mixed Number Form	`5/8`
Decimal Form	`0.625`
Percentage	`62.5%`

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Frequently Asked Questions

What is 14/48 plus 7/21 as a fraction?

14/48 + 7/21 in simplest fraction form is 5/8.

What is 14/48 plus 7/21 as a decimal?

14/48 + 7/21 converted to a decimal is 0.625.

What is 14/48 plus 7/21 as a percentage?

14/48 + 7/21 expressed as a percentage is 62.5%.

Does 14/48 plus 7/21 result in a terminating or repeating decimal?

It results in an exact terminating decimal (0.625) because the denominator in simplest terms contains only prime factors 2 and/or 5.