What is 4/25 plus 7/21? (Answer: 37/75)

Exact Answer

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Problem: What is 4/25 plus 7/21?
Formula / Expression: 4/25 + 7/21
Final Answer: 37/75
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 25 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 25 × 21 = 525.
Working: LCD(25, 21) = 525

Step 2: Convert to Equivalent Fractions with Common Denominator 525
Multiply the numerator and denominator of 4/25 by 21, and multiply the numerator and denominator of 7/21 by 25 so both fractions share the common base 525.
Working: 4 × 21/25 × 21 = 84/525 and 7 × 25/21 × 25 = 175/525

Step 3: Add the Numerators
Now add the numerators (84 + 175 = 259) and keep the common denominator 525 unchanged.
Working: 84 + 175/525 = 259/525

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 259 and 525, which is 7. Divide both the numerator and denominator by 7.
Working: 259 ÷ 7/525 ÷ 7 = 37/75

Step 5: Decimal & Percentage Representation
Dividing the numerator 37 by denominator 75 produces a repeating decimal (approximately 0.493333, or 49.3333%).
Working: 37 ÷ 75 = 0.493333 (49.3333%)

Key Values:
- Simplified Fraction: 37/75
- Mixed Number Form: 37/75
- Decimal Value: 0.493333
- Percentage: 49.3333%

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Solved with FractionsCalc:
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4/25 + 7/21 = 37/75

Simplified Fraction

37/75

Mixed Number

Proper (37/75)

Decimal Value

0.493333

Percentage

49.3333%

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Step-by-Step Solution: 4/25 + 7/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 25 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 25 × 21 = 525.

LCD(25, 21) = 525

Step 2

Convert to Equivalent Fractions with Common Denominator 525

Multiply the numerator and denominator of 4/25 by 21, and multiply the numerator and denominator of 7/21 by 25 so both fractions share the common base 525.

4 × 21/25 × 21 = 84/525 and 7 × 25/21 × 25 = 175/525

Step 3

Add the Numerators

Now add the numerators (84 + 175 = 259) and keep the common denominator 525 unchanged.

84 + 175/525 = 259/525

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 259 and 525, which is 7. Divide both the numerator and denominator by 7.

259 ÷ 7/525 ÷ 7 = 37/75

Step 5

Decimal & Percentage Representation

Dividing the numerator 37 by denominator 75 produces a repeating decimal (approximately 0.493333, or 49.3333%).

37 ÷ 75 = 0.493333 (49.3333%)

Visual Representation

The diagram below illustrates 4/25 plus 7/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`37/75`
Mixed Number Form	`37/75`
Decimal Form	`0.493333`
Percentage	`49.3333%`

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Frequently Asked Questions

What is 4/25 plus 7/21 as a fraction?

4/25 + 7/21 in simplest fraction form is 37/75.

What is 4/25 plus 7/21 as a decimal?

4/25 + 7/21 converted to a decimal is 0.493333.

What is 4/25 plus 7/21 as a percentage?

4/25 + 7/21 expressed as a percentage is 49.3333%.

Does 4/25 plus 7/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.493333...) because the denominator contains prime factors other than 2 and 5.