What is 7/21 plus 17/50? (Answer: 101/150)

Exact Answer

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Problem: What is 7/21 plus 17/50?
Formula / Expression: 7/21 + 17/50
Final Answer: 101/150
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 21 and 50 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 21 × 50 = 1050.
Working: LCD(21, 50) = 1050

Step 2: Convert to Equivalent Fractions with Common Denominator 1050
Multiply the numerator and denominator of 7/21 by 50, and multiply the numerator and denominator of 17/50 by 21 so both fractions share the common base 1050.
Working: 7 × 50/21 × 50 = 350/1050 and 17 × 21/50 × 21 = 357/1050

Step 3: Add the Numerators
Now add the numerators (350 + 357 = 707) and keep the common denominator 1050 unchanged.
Working: 350 + 357/1050 = 707/1050

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 707 and 1050, which is 7. Divide both the numerator and denominator by 7.
Working: 707 ÷ 7/1050 ÷ 7 = 101/150

Step 5: Decimal & Percentage Representation
Dividing the numerator 101 by denominator 150 produces a repeating decimal (approximately 0.673333, or 67.3333%).
Working: 101 ÷ 150 = 0.673333 (67.3333%)

Key Values:
- Simplified Fraction: 101/150
- Mixed Number Form: 101/150
- Decimal Value: 0.673333
- Percentage: 67.3333%

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Solved with FractionsCalc:
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7/21 + 17/50 = 101/150

Simplified Fraction

101/150

Mixed Number

Proper (101/150)

Decimal Value

0.673333

Percentage

67.3333%

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Step-by-Step Solution: 7/21 + 17/50

Step 1

Find the Least Common Denominator (LCD)

The denominators 21 and 50 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 21 × 50 = 1050.

LCD(21, 50) = 1050

Step 2

Convert to Equivalent Fractions with Common Denominator 1050

Multiply the numerator and denominator of 7/21 by 50, and multiply the numerator and denominator of 17/50 by 21 so both fractions share the common base 1050.

7 × 50/21 × 50 = 350/1050 and 17 × 21/50 × 21 = 357/1050

Step 3

Add the Numerators

Now add the numerators (350 + 357 = 707) and keep the common denominator 1050 unchanged.

350 + 357/1050 = 707/1050

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 707 and 1050, which is 7. Divide both the numerator and denominator by 7.

707 ÷ 7/1050 ÷ 7 = 101/150

Step 5

Decimal & Percentage Representation

Dividing the numerator 101 by denominator 150 produces a repeating decimal (approximately 0.673333, or 67.3333%).

101 ÷ 150 = 0.673333 (67.3333%)

Visual Representation

The diagram below illustrates 7/21 plus 17/50 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`101/150`
Mixed Number Form	`101/150`
Decimal Form	`0.673333`
Percentage	`67.3333%`

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Frequently Asked Questions

What is 7/21 plus 17/50 as a fraction?

7/21 + 17/50 in simplest fraction form is 101/150.

What is 7/21 plus 17/50 as a decimal?

7/21 + 17/50 converted to a decimal is 0.673333.

What is 7/21 plus 17/50 as a percentage?

7/21 + 17/50 expressed as a percentage is 67.3333%.

Does 7/21 plus 17/50 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.673333...) because the denominator contains prime factors other than 2 and 5.