What is 4/21 plus 7/33? (Answer: 31/77)

Exact Answer

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Problem: What is 4/21 plus 7/33?
Formula / Expression: 4/21 + 7/33
Final Answer: 31/77
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 21 and 33 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 231 (which is smaller than their product 21 × 33 = 693, keeping the calculation simpler).
Working: LCD(21, 33) = 231

Step 2: Convert to Equivalent Fractions with Common Denominator 231
Multiply the numerator and denominator of 4/21 by 11, and multiply the numerator and denominator of 7/33 by 7 so both fractions share the common base 231.
Working: 4 × 11/21 × 11 = 44/231 and 7 × 7/33 × 7 = 49/231

Step 3: Add the Numerators
Now add the numerators (44 + 49 = 93) and keep the common denominator 231 unchanged.
Working: 44 + 49/231 = 93/231

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 93 and 231, which is 3. Divide both the numerator and denominator by 3.
Working: 93 ÷ 3/231 ÷ 3 = 31/77

Step 5: Decimal & Percentage Representation
Dividing the numerator 31 by denominator 77 produces a repeating decimal (approximately 0.402597, or 40.2597%).
Working: 31 ÷ 77 = 0.402597 (40.2597%)

Key Values:
- Simplified Fraction: 31/77
- Mixed Number Form: 31/77
- Decimal Value: 0.402597
- Percentage: 40.2597%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-4-21-plus-7-33/
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4/21 + 7/33 = 31/77

Simplified Fraction

31/77

Mixed Number

Proper (31/77)

Decimal Value

0.402597

Percentage

40.2597%

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Step-by-Step Solution: 4/21 + 7/33

Step 1

Find the Least Common Denominator (LCD)

The denominators 21 and 33 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 231 (which is smaller than their product 21 × 33 = 693, keeping the calculation simpler).

LCD(21, 33) = 231

Step 2

Convert to Equivalent Fractions with Common Denominator 231

Multiply the numerator and denominator of 4/21 by 11, and multiply the numerator and denominator of 7/33 by 7 so both fractions share the common base 231.

4 × 11/21 × 11 = 44/231 and 7 × 7/33 × 7 = 49/231

Step 3

Add the Numerators

Now add the numerators (44 + 49 = 93) and keep the common denominator 231 unchanged.

44 + 49/231 = 93/231

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 93 and 231, which is 3. Divide both the numerator and denominator by 3.

93 ÷ 3/231 ÷ 3 = 31/77

Step 5

Decimal & Percentage Representation

Dividing the numerator 31 by denominator 77 produces a repeating decimal (approximately 0.402597, or 40.2597%).

31 ÷ 77 = 0.402597 (40.2597%)

Visual Representation

The diagram below illustrates 4/21 plus 7/33 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`31/77`
Mixed Number Form	`31/77`
Decimal Form	`0.402597`
Percentage	`40.2597%`

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Frequently Asked Questions

What is 4/21 plus 7/33 as a fraction?

4/21 + 7/33 in simplest fraction form is 31/77.

What is 4/21 plus 7/33 as a decimal?

4/21 + 7/33 converted to a decimal is 0.402597.

What is 4/21 plus 7/33 as a percentage?

4/21 + 7/33 expressed as a percentage is 40.2597%.

Does 4/21 plus 7/33 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.402597...) because the denominator contains prime factors other than 2 and 5.