What is 9/21 plus 21/49? (Answer: 6/7)

Exact Answer

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Problem: What is 9/21 plus 21/49?
Formula / Expression: 9/21 + 21/49
Final Answer: 6/7
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 21 and 49 share a common factor (GCD = 7). Finding their Least Common Multiple gives an LCD of 147 (which is smaller than their product 21 × 49 = 1029, keeping the calculation simpler).
Working: LCD(21, 49) = 147

Step 2: Convert to Equivalent Fractions with Common Denominator 147
Multiply the numerator and denominator of 9/21 by 7, and multiply the numerator and denominator of 21/49 by 3 so both fractions share the common base 147.
Working: 9 × 7/21 × 7 = 63/147 and 21 × 3/49 × 3 = 63/147

Step 3: Add the Numerators
Now add the numerators (63 + 63 = 126) and keep the common denominator 147 unchanged.
Working: 63 + 63/147 = 126/147

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 126 and 147, which is 21. Divide both the numerator and denominator by 21.
Working: 126 ÷ 21/147 ÷ 21 = 6/7

Step 5: Decimal & Percentage Representation
Dividing the numerator 6 by denominator 7 produces a repeating decimal (approximately 0.857143, or 85.7143%).
Working: 6 ÷ 7 = 0.857143 (85.7143%)

Key Values:
- Simplified Fraction: 6/7
- Mixed Number Form: 6/7
- Decimal Value: 0.857143
- Percentage: 85.7143%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-9-21-plus-21-49/
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9/21 + 21/49 = 6/7

Simplified Fraction

6/7

Mixed Number

Proper (6/7)

Decimal Value

0.857143

Percentage

85.7143%

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Step-by-Step Solution: 9/21 + 21/49

Step 1

Find the Least Common Denominator (LCD)

The denominators 21 and 49 share a common factor (GCD = 7). Finding their Least Common Multiple gives an LCD of 147 (which is smaller than their product 21 × 49 = 1029, keeping the calculation simpler).

LCD(21, 49) = 147

Step 2

Convert to Equivalent Fractions with Common Denominator 147

Multiply the numerator and denominator of 9/21 by 7, and multiply the numerator and denominator of 21/49 by 3 so both fractions share the common base 147.

9 × 7/21 × 7 = 63/147 and 21 × 3/49 × 3 = 63/147

Step 3

Add the Numerators

Now add the numerators (63 + 63 = 126) and keep the common denominator 147 unchanged.

63 + 63/147 = 126/147

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 126 and 147, which is 21. Divide both the numerator and denominator by 21.

126 ÷ 21/147 ÷ 21 = 6/7

Step 5

Decimal & Percentage Representation

Dividing the numerator 6 by denominator 7 produces a repeating decimal (approximately 0.857143, or 85.7143%).

6 ÷ 7 = 0.857143 (85.7143%)

Visual Representation

The diagram below illustrates 9/21 plus 21/49 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`6/7`
Mixed Number Form	`6/7`
Decimal Form	`0.857143`
Percentage	`85.7143%`

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Frequently Asked Questions

What is 9/21 plus 21/49 as a fraction?

9/21 + 21/49 in simplest fraction form is 6/7.

What is 9/21 plus 21/49 as a decimal?

9/21 + 21/49 converted to a decimal is 0.857143.

What is 9/21 plus 21/49 as a percentage?

9/21 + 21/49 expressed as a percentage is 85.7143%.

Does 9/21 plus 21/49 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.857143...) because the denominator contains prime factors other than 2 and 5.