What is 10/28 plus 9/21? (Answer: 11/14)

Exact Answer

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Problem: What is 10/28 plus 9/21?
Formula / Expression: 10/28 + 9/21
Final Answer: 11/14
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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 10/28 by 3, and multiply the numerator and denominator of 9/21 by 4 so both fractions share the common base 84.
Working: 10 × 3/28 × 3 = 30/84 and 9 × 4/21 × 4 = 36/84

Step 3: Add the Numerators
Now add the numerators (30 + 36 = 66) and keep the common denominator 84 unchanged.
Working: 30 + 36/84 = 66/84

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 66 and 84, which is 6. Divide both the numerator and denominator by 6.
Working: 66 ÷ 6/84 ÷ 6 = 11/14

Step 5: Decimal & Percentage Representation
Dividing the numerator 11 by denominator 14 produces a repeating decimal (approximately 0.785714, or 78.5714%).
Working: 11 ÷ 14 = 0.785714 (78.5714%)

Key Values:
- Simplified Fraction: 11/14
- Mixed Number Form: 11/14
- Decimal Value: 0.785714
- Percentage: 78.5714%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-10-28-plus-9-21/
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10/28 + 9/21 = 11/14

Simplified Fraction

11/14

Mixed Number

Proper (11/14)

Decimal Value

0.785714

Percentage

78.5714%

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Step-by-Step Solution: 10/28 + 9/21

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 10/28 by 3, and multiply the numerator and denominator of 9/21 by 4 so both fractions share the common base 84.

10 × 3/28 × 3 = 30/84 and 9 × 4/21 × 4 = 36/84

Step 3

Add the Numerators

Now add the numerators (30 + 36 = 66) and keep the common denominator 84 unchanged.

30 + 36/84 = 66/84

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 66 and 84, which is 6. Divide both the numerator and denominator by 6.

66 ÷ 6/84 ÷ 6 = 11/14

Step 5

Decimal & Percentage Representation

Dividing the numerator 11 by denominator 14 produces a repeating decimal (approximately 0.785714, or 78.5714%).

11 ÷ 14 = 0.785714 (78.5714%)

Visual Representation

The diagram below illustrates 10/28 plus 9/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`11/14`
Mixed Number Form	`11/14`
Decimal Form	`0.785714`
Percentage	`78.5714%`

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Frequently Asked Questions

What is 10/28 plus 9/21 as a fraction?

10/28 + 9/21 in simplest fraction form is 11/14.

What is 10/28 plus 9/21 as a decimal?

10/28 + 9/21 converted to a decimal is 0.785714.

What is 10/28 plus 9/21 as a percentage?

10/28 + 9/21 expressed as a percentage is 78.5714%.

Does 10/28 plus 9/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.785714...) because the denominator contains prime factors other than 2 and 5.