What is 3/45 plus 7/21? (Answer: 2/5)

Exact Answer

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Problem: What is 3/45 plus 7/21?
Formula / Expression: 3/45 + 7/21
Final Answer: 2/5
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 45 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 315 (which is smaller than their product 45 × 21 = 945, keeping the calculation simpler).
Working: LCD(45, 21) = 315

Step 2: Convert to Equivalent Fractions with Common Denominator 315
Multiply the numerator and denominator of 3/45 by 7, and multiply the numerator and denominator of 7/21 by 15 so both fractions share the common base 315.
Working: 3 × 7/45 × 7 = 21/315 and 7 × 15/21 × 15 = 105/315

Step 3: Add the Numerators
Now add the numerators (21 + 105 = 126) and keep the common denominator 315 unchanged.
Working: 21 + 105/315 = 126/315

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 126 and 315, which is 63. Divide both the numerator and denominator by 63.
Working: 126 ÷ 63/315 ÷ 63 = 2/5

Step 5: Decimal & Percentage Representation
Dividing the numerator 2 by denominator 5 yields an exact terminating decimal of 0.4 (or 40%).
Working: 2 ÷ 5 = 0.4 (40%)

Key Values:
- Simplified Fraction: 2/5
- Mixed Number Form: 2/5
- Decimal Value: 0.4
- Percentage: 40%

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Solved with FractionsCalc:
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3/45 + 7/21 = 2/5

Simplified Fraction

2/5

Mixed Number

Proper (2/5)

Decimal Value

0.4

Percentage

40%

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Step-by-Step Solution: 3/45 + 7/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 45 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 315 (which is smaller than their product 45 × 21 = 945, keeping the calculation simpler).

LCD(45, 21) = 315

Step 2

Convert to Equivalent Fractions with Common Denominator 315

Multiply the numerator and denominator of 3/45 by 7, and multiply the numerator and denominator of 7/21 by 15 so both fractions share the common base 315.

3 × 7/45 × 7 = 21/315 and 7 × 15/21 × 15 = 105/315

Step 3

Add the Numerators

Now add the numerators (21 + 105 = 126) and keep the common denominator 315 unchanged.

21 + 105/315 = 126/315

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 126 and 315, which is 63. Divide both the numerator and denominator by 63.

126 ÷ 63/315 ÷ 63 = 2/5

Step 5

Decimal & Percentage Representation

Dividing the numerator 2 by denominator 5 yields an exact terminating decimal of 0.4 (or 40%).

2 ÷ 5 = 0.4 (40%)

Visual Representation

The diagram below illustrates 3/45 plus 7/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`2/5`
Mixed Number Form	`2/5`
Decimal Form	`0.4`
Percentage	`40%`

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Frequently Asked Questions

What is 3/45 plus 7/21 as a fraction?

3/45 + 7/21 in simplest fraction form is 2/5.

What is 3/45 plus 7/21 as a decimal?

3/45 + 7/21 converted to a decimal is 0.4.

What is 3/45 plus 7/21 as a percentage?

3/45 + 7/21 expressed as a percentage is 40%.

Does 3/45 plus 7/21 result in a terminating or repeating decimal?

It results in an exact terminating decimal (0.4) because the denominator in simplest terms contains only prime factors 2 and/or 5.