What is 5/28 plus 12/21? (Answer: 3/4)

Exact Answer

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Problem: What is 5/28 plus 12/21?
Formula / Expression: 5/28 + 12/21
Final Answer: 3/4
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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 5/28 by 3, and multiply the numerator and denominator of 12/21 by 4 so both fractions share the common base 84.
Working: 5 × 3/28 × 3 = 15/84 and 12 × 4/21 × 4 = 48/84

Step 3: Add the Numerators
Now add the numerators (15 + 48 = 63) and keep the common denominator 84 unchanged.
Working: 15 + 48/84 = 63/84

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 63 and 84, which is 21. Divide both the numerator and denominator by 21.
Working: 63 ÷ 21/84 ÷ 21 = 3/4

Step 5: Decimal & Percentage Representation
Dividing the numerator 3 by denominator 4 yields an exact terminating decimal of 0.75 (or 75%).
Working: 3 ÷ 4 = 0.75 (75%)

Key Values:
- Simplified Fraction: 3/4
- Mixed Number Form: 3/4
- Decimal Value: 0.75
- Percentage: 75%

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Solved with FractionsCalc:
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5/28 + 12/21 = 3/4

Simplified Fraction

3/4

Mixed Number

Proper (3/4)

Decimal Value

0.75

Percentage

75%

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Step-by-Step Solution: 5/28 + 12/21

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 5/28 by 3, and multiply the numerator and denominator of 12/21 by 4 so both fractions share the common base 84.

5 × 3/28 × 3 = 15/84 and 12 × 4/21 × 4 = 48/84

Step 3

Add the Numerators

Now add the numerators (15 + 48 = 63) and keep the common denominator 84 unchanged.

15 + 48/84 = 63/84

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 63 and 84, which is 21. Divide both the numerator and denominator by 21.

63 ÷ 21/84 ÷ 21 = 3/4

Step 5

Decimal & Percentage Representation

Dividing the numerator 3 by denominator 4 yields an exact terminating decimal of 0.75 (or 75%).

3 ÷ 4 = 0.75 (75%)

Visual Representation

The diagram below illustrates 5/28 plus 12/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`3/4`
Mixed Number Form	`3/4`
Decimal Form	`0.75`
Percentage	`75%`

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Frequently Asked Questions

What is 5/28 plus 12/21 as a fraction?

5/28 + 12/21 in simplest fraction form is 3/4.

What is 5/28 plus 12/21 as a decimal?

5/28 + 12/21 converted to a decimal is 0.75.

What is 5/28 plus 12/21 as a percentage?

5/28 + 12/21 expressed as a percentage is 75%.

Does 5/28 plus 12/21 result in a terminating or repeating decimal?

It results in an exact terminating decimal (0.75) because the denominator in simplest terms contains only prime factors 2 and/or 5.