What is 4/21 plus 7/36? (Answer: 97/252)

Exact Answer

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Problem: What is 4/21 plus 7/36?
Formula / Expression: 4/21 + 7/36
Final Answer: 97/252
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 21 and 36 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 252 (which is smaller than their product 21 × 36 = 756, keeping the calculation simpler).
Working: LCD(21, 36) = 252

Step 2: Convert to Equivalent Fractions with Common Denominator 252
Multiply the numerator and denominator of 4/21 by 12, and multiply the numerator and denominator of 7/36 by 7 so both fractions share the common base 252.
Working: 4 × 12/21 × 12 = 48/252 and 7 × 7/36 × 7 = 49/252

Step 3: Add the Numerators
Now add the numerators (48 + 49 = 97) and keep the common denominator 252 unchanged.
Working: 48 + 49/252 = 97/252

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 97 and 252 is 1, confirming that 97/252 cannot be reduced further—it is already in its simplest irreducible form.
Working: 97/252

Step 5: Decimal & Percentage Representation
Dividing the numerator 97 by denominator 252 produces a repeating decimal (approximately 0.384921, or 38.4921%).
Working: 97 ÷ 252 = 0.384921 (38.4921%)

Key Values:
- Simplified Fraction: 97/252
- Mixed Number Form: 97/252
- Decimal Value: 0.384921
- Percentage: 38.4921%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-4-21-plus-7-36/
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4/21 + 7/36 = 97/252

Simplified Fraction

97/252

Mixed Number

Proper (97/252)

Decimal Value

0.384921

Percentage

38.4921%

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Step-by-Step Solution: 4/21 + 7/36

Step 1

Find the Least Common Denominator (LCD)

The denominators 21 and 36 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 252 (which is smaller than their product 21 × 36 = 756, keeping the calculation simpler).

LCD(21, 36) = 252

Step 2

Convert to Equivalent Fractions with Common Denominator 252

Multiply the numerator and denominator of 4/21 by 12, and multiply the numerator and denominator of 7/36 by 7 so both fractions share the common base 252.

4 × 12/21 × 12 = 48/252 and 7 × 7/36 × 7 = 49/252

Step 3

Add the Numerators

Now add the numerators (48 + 49 = 97) and keep the common denominator 252 unchanged.

48 + 49/252 = 97/252

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 97 and 252 is 1, confirming that 97/252 cannot be reduced further—it is already in its simplest irreducible form.

97/252

Step 5

Decimal & Percentage Representation

Dividing the numerator 97 by denominator 252 produces a repeating decimal (approximately 0.384921, or 38.4921%).

97 ÷ 252 = 0.384921 (38.4921%)

Visual Representation

The diagram below illustrates 4/21 plus 7/36 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`97/252`
Mixed Number Form	`97/252`
Decimal Form	`0.384921`
Percentage	`38.4921%`

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Frequently Asked Questions

What is 4/21 plus 7/36 as a fraction?

4/21 + 7/36 in simplest fraction form is 97/252.

What is 4/21 plus 7/36 as a decimal?

4/21 + 7/36 converted to a decimal is 0.384921.

What is 4/21 plus 7/36 as a percentage?

4/21 + 7/36 expressed as a percentage is 38.4921%.

Does 4/21 plus 7/36 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.384921...) because the denominator contains prime factors other than 2 and 5.