What is 7/49 plus 5/21? (Answer: 8/21)

Exact Answer

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Problem: What is 7/49 plus 5/21?
Formula / Expression: 7/49 + 5/21
Final Answer: 8/21
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 49 and 21 share a common factor (GCD = 7). Finding their Least Common Multiple gives an LCD of 147 (which is smaller than their product 49 × 21 = 1029, keeping the calculation simpler).
Working: LCD(49, 21) = 147

Step 2: Convert to Equivalent Fractions with Common Denominator 147
Multiply the numerator and denominator of 7/49 by 3, and multiply the numerator and denominator of 5/21 by 7 so both fractions share the common base 147.
Working: 7 × 3/49 × 3 = 21/147 and 5 × 7/21 × 7 = 35/147

Step 3: Add the Numerators
Now add the numerators (21 + 35 = 56) and keep the common denominator 147 unchanged.
Working: 21 + 35/147 = 56/147

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 56 and 147, which is 7. Divide both the numerator and denominator by 7.
Working: 56 ÷ 7/147 ÷ 7 = 8/21

Step 5: Decimal & Percentage Representation
Dividing the numerator 8 by denominator 21 produces a repeating decimal (approximately 0.380952, or 38.0952%).
Working: 8 ÷ 21 = 0.380952 (38.0952%)

Key Values:
- Simplified Fraction: 8/21
- Mixed Number Form: 8/21
- Decimal Value: 0.380952
- Percentage: 38.0952%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-7-49-plus-5-21/
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7/49 + 5/21 = 8/21

Simplified Fraction

8/21

Mixed Number

Proper (8/21)

Decimal Value

0.380952

Percentage

38.0952%

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Step-by-Step Solution: 7/49 + 5/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 49 and 21 share a common factor (GCD = 7). Finding their Least Common Multiple gives an LCD of 147 (which is smaller than their product 49 × 21 = 1029, keeping the calculation simpler).

LCD(49, 21) = 147

Step 2

Convert to Equivalent Fractions with Common Denominator 147

Multiply the numerator and denominator of 7/49 by 3, and multiply the numerator and denominator of 5/21 by 7 so both fractions share the common base 147.

7 × 3/49 × 3 = 21/147 and 5 × 7/21 × 7 = 35/147

Step 3

Add the Numerators

Now add the numerators (21 + 35 = 56) and keep the common denominator 147 unchanged.

21 + 35/147 = 56/147

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 56 and 147, which is 7. Divide both the numerator and denominator by 7.

56 ÷ 7/147 ÷ 7 = 8/21

Step 5

Decimal & Percentage Representation

Dividing the numerator 8 by denominator 21 produces a repeating decimal (approximately 0.380952, or 38.0952%).

8 ÷ 21 = 0.380952 (38.0952%)

Visual Representation

The diagram below illustrates 7/49 plus 5/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`8/21`
Mixed Number Form	`8/21`
Decimal Form	`0.380952`
Percentage	`38.0952%`

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Frequently Asked Questions

What is 7/49 plus 5/21 as a fraction?

7/49 + 5/21 in simplest fraction form is 8/21.

What is 7/49 plus 5/21 as a decimal?

7/49 + 5/21 converted to a decimal is 0.380952.

What is 7/49 plus 5/21 as a percentage?

7/49 + 5/21 expressed as a percentage is 38.0952%.

Does 7/49 plus 5/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.380952...) because the denominator contains prime factors other than 2 and 5.