What is 1/28 plus 6/21? (Answer: 9/28)

Exact Answer

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Problem: What is 1/28 plus 6/21?
Formula / Expression: 1/28 + 6/21
Final Answer: 9/28
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 28 and 21 share a common factor (GCD = 7). Finding their Least Common Multiple gives an LCD of 84 (which is smaller than their product 28 × 21 = 588, keeping the calculation simpler).
Working: LCD(28, 21) = 84

Step 2: Convert to Equivalent Fractions with Common Denominator 84
Multiply the numerator and denominator of 1/28 by 3, and multiply the numerator and denominator of 6/21 by 4 so both fractions share the common base 84.
Working: 1 × 3/28 × 3 = 3/84 and 6 × 4/21 × 4 = 24/84

Step 3: Add the Numerators
Now add the numerators (3 + 24 = 27) and keep the common denominator 84 unchanged.
Working: 3 + 24/84 = 27/84

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 27 and 84, which is 3. Divide both the numerator and denominator by 3.
Working: 27 ÷ 3/84 ÷ 3 = 9/28

Step 5: Decimal & Percentage Representation
Dividing the numerator 9 by denominator 28 produces a repeating decimal (approximately 0.321429, or 32.1429%).
Working: 9 ÷ 28 = 0.321429 (32.1429%)

Key Values:
- Simplified Fraction: 9/28
- Mixed Number Form: 9/28
- Decimal Value: 0.321429
- Percentage: 32.1429%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-1-28-plus-6-21/
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1/28 + 6/21 = 9/28

Simplified Fraction

9/28

Mixed Number

Proper (9/28)

Decimal Value

0.321429

Percentage

32.1429%

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Step-by-Step Solution: 1/28 + 6/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 28 and 21 share a common factor (GCD = 7). Finding their Least Common Multiple gives an LCD of 84 (which is smaller than their product 28 × 21 = 588, keeping the calculation simpler).

LCD(28, 21) = 84

Step 2

Convert to Equivalent Fractions with Common Denominator 84

Multiply the numerator and denominator of 1/28 by 3, and multiply the numerator and denominator of 6/21 by 4 so both fractions share the common base 84.

1 × 3/28 × 3 = 3/84 and 6 × 4/21 × 4 = 24/84

Step 3

Add the Numerators

Now add the numerators (3 + 24 = 27) and keep the common denominator 84 unchanged.

3 + 24/84 = 27/84

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 27 and 84, which is 3. Divide both the numerator and denominator by 3.

27 ÷ 3/84 ÷ 3 = 9/28

Step 5

Decimal & Percentage Representation

Dividing the numerator 9 by denominator 28 produces a repeating decimal (approximately 0.321429, or 32.1429%).

9 ÷ 28 = 0.321429 (32.1429%)

Visual Representation

The diagram below illustrates 1/28 plus 6/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`9/28`
Mixed Number Form	`9/28`
Decimal Form	`0.321429`
Percentage	`32.1429%`

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Frequently Asked Questions

What is 1/28 plus 6/21 as a fraction?

1/28 + 6/21 in simplest fraction form is 9/28.

What is 1/28 plus 6/21 as a decimal?

1/28 + 6/21 converted to a decimal is 0.321429.

What is 1/28 plus 6/21 as a percentage?

1/28 + 6/21 expressed as a percentage is 32.1429%.

Does 1/28 plus 6/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.321429...) because the denominator contains prime factors other than 2 and 5.