What is 6/48 plus 10/21? (Answer: 101/168)

Exact Answer

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Problem: What is 6/48 plus 10/21?
Formula / Expression: 6/48 + 10/21
Final Answer: 101/168
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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 10/21 by 16 so both fractions share the common base 336.
Working: 6 × 7/48 × 7 = 42/336 and 10 × 16/21 × 16 = 160/336

Step 3: Add the Numerators
Now add the numerators (42 + 160 = 202) and keep the common denominator 336 unchanged.
Working: 42 + 160/336 = 202/336

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 202 and 336, which is 2. Divide both the numerator and denominator by 2.
Working: 202 ÷ 2/336 ÷ 2 = 101/168

Step 5: Decimal & Percentage Representation
Dividing the numerator 101 by denominator 168 produces a repeating decimal (approximately 0.60119, or 60.119%).
Working: 101 ÷ 168 = 0.60119 (60.119%)

Key Values:
- Simplified Fraction: 101/168
- Mixed Number Form: 101/168
- Decimal Value: 0.60119
- Percentage: 60.119%

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Solved with FractionsCalc:
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6/48 + 10/21 = 101/168

Simplified Fraction

101/168

Mixed Number

Proper (101/168)

Decimal Value

0.60119

Percentage

60.119%

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Step-by-Step Solution: 6/48 + 10/21

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 10/21 by 16 so both fractions share the common base 336.

6 × 7/48 × 7 = 42/336 and 10 × 16/21 × 16 = 160/336

Step 3

Add the Numerators

Now add the numerators (42 + 160 = 202) and keep the common denominator 336 unchanged.

42 + 160/336 = 202/336

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 202 and 336, which is 2. Divide both the numerator and denominator by 2.

202 ÷ 2/336 ÷ 2 = 101/168

Step 5

Decimal & Percentage Representation

Dividing the numerator 101 by denominator 168 produces a repeating decimal (approximately 0.60119, or 60.119%).

101 ÷ 168 = 0.60119 (60.119%)

Visual Representation

The diagram below illustrates 6/48 plus 10/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`101/168`
Mixed Number Form	`101/168`
Decimal Form	`0.60119`
Percentage	`60.119%`

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Frequently Asked Questions

What is 6/48 plus 10/21 as a fraction?

6/48 + 10/21 in simplest fraction form is 101/168.

What is 6/48 plus 10/21 as a decimal?

6/48 + 10/21 converted to a decimal is 0.60119.

What is 6/48 plus 10/21 as a percentage?

6/48 + 10/21 expressed as a percentage is 60.119%.

Does 6/48 plus 10/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.60119...) because the denominator contains prime factors other than 2 and 5.