What is 11/48 plus 7/21? (Answer: 9/16)

Exact Answer

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Problem: What is 11/48 plus 7/21?
Formula / Expression: 11/48 + 7/21
Final Answer: 9/16
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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 11/48 by 7, and multiply the numerator and denominator of 7/21 by 16 so both fractions share the common base 336.
Working: 11 × 7/48 × 7 = 77/336 and 7 × 16/21 × 16 = 112/336

Step 3: Add the Numerators
Now add the numerators (77 + 112 = 189) and keep the common denominator 336 unchanged.
Working: 77 + 112/336 = 189/336

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 189 and 336, which is 21. Divide both the numerator and denominator by 21.
Working: 189 ÷ 21/336 ÷ 21 = 9/16

Step 5: Decimal & Percentage Representation
Dividing the numerator 9 by denominator 16 yields an exact terminating decimal of 0.5625 (or 56.25%).
Working: 9 ÷ 16 = 0.5625 (56.25%)

Key Values:
- Simplified Fraction: 9/16
- Mixed Number Form: 9/16
- Decimal Value: 0.5625
- Percentage: 56.25%

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Solved with FractionsCalc:
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11/48 + 7/21 = 9/16

Simplified Fraction

9/16

Mixed Number

Proper (9/16)

Decimal Value

0.5625

Percentage

56.25%

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Step-by-Step Solution: 11/48 + 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 11/48 by 7, and multiply the numerator and denominator of 7/21 by 16 so both fractions share the common base 336.

11 × 7/48 × 7 = 77/336 and 7 × 16/21 × 16 = 112/336

Step 3

Add the Numerators

Now add the numerators (77 + 112 = 189) and keep the common denominator 336 unchanged.

77 + 112/336 = 189/336

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 189 and 336, which is 21. Divide both the numerator and denominator by 21.

189 ÷ 21/336 ÷ 21 = 9/16

Step 5

Decimal & Percentage Representation

Dividing the numerator 9 by denominator 16 yields an exact terminating decimal of 0.5625 (or 56.25%).

9 ÷ 16 = 0.5625 (56.25%)

Visual Representation

The diagram below illustrates 11/48 plus 7/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`9/16`
Mixed Number Form	`9/16`
Decimal Form	`0.5625`
Percentage	`56.25%`

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Frequently Asked Questions

What is 11/48 plus 7/21 as a fraction?

11/48 + 7/21 in simplest fraction form is 9/16.

What is 11/48 plus 7/21 as a decimal?

11/48 + 7/21 converted to a decimal is 0.5625.

What is 11/48 plus 7/21 as a percentage?

11/48 + 7/21 expressed as a percentage is 56.25%.

Does 11/48 plus 7/21 result in a terminating or repeating decimal?

It results in an exact terminating decimal (0.5625) because the denominator in simplest terms contains only prime factors 2 and/or 5.