What is 4/33 plus 10/21? (Answer: 46/77)

Exact Answer

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Problem: What is 4/33 plus 10/21?
Formula / Expression: 4/33 + 10/21
Final Answer: 46/77
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 231
Multiply the numerator and denominator of 4/33 by 7, and multiply the numerator and denominator of 10/21 by 11 so both fractions share the common base 231.
Working: 4 × 7/33 × 7 = 28/231 and 10 × 11/21 × 11 = 110/231

Step 3: Add the Numerators
Now add the numerators (28 + 110 = 138) and keep the common denominator 231 unchanged.
Working: 28 + 110/231 = 138/231

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 138 and 231, which is 3. Divide both the numerator and denominator by 3.
Working: 138 ÷ 3/231 ÷ 3 = 46/77

Step 5: Decimal & Percentage Representation
Dividing the numerator 46 by denominator 77 produces a repeating decimal (approximately 0.597403, or 59.7403%).
Working: 46 ÷ 77 = 0.597403 (59.7403%)

Key Values:
- Simplified Fraction: 46/77
- Mixed Number Form: 46/77
- Decimal Value: 0.597403
- Percentage: 59.7403%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-4-33-plus-10-21/
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4/33 + 10/21 = 46/77

Simplified Fraction

46/77

Mixed Number

Proper (46/77)

Decimal Value

0.597403

Percentage

59.7403%

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Step-by-Step Solution: 4/33 + 10/21

Step 1

Find the Least Common Denominator (LCD)

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

LCD(33, 21) = 231

Step 2

Convert to Equivalent Fractions with Common Denominator 231

Multiply the numerator and denominator of 4/33 by 7, and multiply the numerator and denominator of 10/21 by 11 so both fractions share the common base 231.

4 × 7/33 × 7 = 28/231 and 10 × 11/21 × 11 = 110/231

Step 3

Add the Numerators

Now add the numerators (28 + 110 = 138) and keep the common denominator 231 unchanged.

28 + 110/231 = 138/231

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 138 and 231, which is 3. Divide both the numerator and denominator by 3.

138 ÷ 3/231 ÷ 3 = 46/77

Step 5

Decimal & Percentage Representation

Dividing the numerator 46 by denominator 77 produces a repeating decimal (approximately 0.597403, or 59.7403%).

46 ÷ 77 = 0.597403 (59.7403%)

Visual Representation

The diagram below illustrates 4/33 plus 10/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`46/77`
Mixed Number Form	`46/77`
Decimal Form	`0.597403`
Percentage	`59.7403%`

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Frequently Asked Questions

What is 4/33 plus 10/21 as a fraction?

4/33 + 10/21 in simplest fraction form is 46/77.

What is 4/33 plus 10/21 as a decimal?

4/33 + 10/21 converted to a decimal is 0.597403.

What is 4/33 plus 10/21 as a percentage?

4/33 + 10/21 expressed as a percentage is 59.7403%.

Does 4/33 plus 10/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.597403...) because the denominator contains prime factors other than 2 and 5.