What is 6/48 plus 11/21? (Answer: 109/168)

Exact Answer

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Problem: What is 6/48 plus 11/21?
Formula / Expression: 6/48 + 11/21
Final Answer: 109/168
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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 6/48 by 7, and multiply the numerator and denominator of 11/21 by 16 so both fractions share the common base 336.
Working: 6 × 7/48 × 7 = 42/336 and 11 × 16/21 × 16 = 176/336

Step 3: Add the Numerators
Now add the numerators (42 + 176 = 218) and keep the common denominator 336 unchanged.
Working: 42 + 176/336 = 218/336

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 218 and 336, which is 2. Divide both the numerator and denominator by 2.
Working: 218 ÷ 2/336 ÷ 2 = 109/168

Step 5: Decimal & Percentage Representation
Dividing the numerator 109 by denominator 168 produces a repeating decimal (approximately 0.64881, or 64.881%).
Working: 109 ÷ 168 = 0.64881 (64.881%)

Key Values:
- Simplified Fraction: 109/168
- Mixed Number Form: 109/168
- Decimal Value: 0.64881
- Percentage: 64.881%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-6-48-plus-11-21/
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6/48 + 11/21 = 109/168

Simplified Fraction

109/168

Mixed Number

Proper (109/168)

Decimal Value

0.64881

Percentage

64.881%

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Step-by-Step Solution: 6/48 + 11/21

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 6/48 by 7, and multiply the numerator and denominator of 11/21 by 16 so both fractions share the common base 336.

6 × 7/48 × 7 = 42/336 and 11 × 16/21 × 16 = 176/336

Step 3

Add the Numerators

Now add the numerators (42 + 176 = 218) and keep the common denominator 336 unchanged.

42 + 176/336 = 218/336

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 218 and 336, which is 2. Divide both the numerator and denominator by 2.

218 ÷ 2/336 ÷ 2 = 109/168

Step 5

Decimal & Percentage Representation

Dividing the numerator 109 by denominator 168 produces a repeating decimal (approximately 0.64881, or 64.881%).

109 ÷ 168 = 0.64881 (64.881%)

Visual Representation

The diagram below illustrates 6/48 plus 11/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`109/168`
Mixed Number Form	`109/168`
Decimal Form	`0.64881`
Percentage	`64.881%`

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Frequently Asked Questions

What is 6/48 plus 11/21 as a fraction?

6/48 + 11/21 in simplest fraction form is 109/168.

What is 6/48 plus 11/21 as a decimal?

6/48 + 11/21 converted to a decimal is 0.64881.

What is 6/48 plus 11/21 as a percentage?

6/48 + 11/21 expressed as a percentage is 64.881%.

Does 6/48 plus 11/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.64881...) because the denominator contains prime factors other than 2 and 5.