What is 1/49 plus 5/21? (Answer: 38/147)

Exact Answer

==================================================
Problem: What is 1/49 plus 5/21?
Formula / Expression: 1/49 + 5/21
Final Answer: 38/147
==================================================

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 1/49 by 3, and multiply the numerator and denominator of 5/21 by 7 so both fractions share the common base 147.
Working: 1 × 3/49 × 3 = 3/147 and 5 × 7/21 × 7 = 35/147

Step 3: Add the Numerators
Now add the numerators (3 + 35 = 38) and keep the common denominator 147 unchanged.
Working: 3 + 35/147 = 38/147

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 38 and 147 is 1, confirming that 38/147 cannot be reduced further—it is already in its simplest irreducible form.
Working: 38/147

Step 5: Decimal & Percentage Representation
Dividing the numerator 38 by denominator 147 produces a repeating decimal (approximately 0.258503, or 25.8503%).
Working: 38 ÷ 147 = 0.258503 (25.8503%)

Key Values:
- Simplified Fraction: 38/147
- Mixed Number Form: 38/147
- Decimal Value: 0.258503
- Percentage: 25.8503%

--------------------------------------------------
Solved with FractionsCalc:
https://fractionscalc.com/what-is-1-49-plus-5-21/
==================================================

1/49 + 5/21 = 38/147

Simplified Fraction

38/147

Mixed Number

Proper (38/147)

Decimal Value

0.258503

Percentage

25.8503%

Reduce / Convert Fraction:

Convert Fraction:

Enter Decimal Number:

Enter Percentage: %

What is % of

From Value: To Value:

Simplify Ratio: :

Switch to Proportion / Missing X Solver (A/B = C/D) →

Enter 3 known numbers and leave 1 empty (or type x) to solve:

← Switch to Ratio Simplifier (A:B)

Provide any 2 values below to calculate the remaining:

Price before discount

Discount

Price after discount

You saved

+ Add Sales Tax & Extra Coupon (Optional)

Sales Tax: % Extra Off: %

Provide any 2 values below to calculate the remaining:

Cost

Markup

REVENUE

Gross Profit

Profit Margin

Bill Subtotal

Tip Percentage

Split (People)

👥

Quick Tip:

Total Bill

Split Between

👥

Tip % (Optional)

Include Tip:

Total Price

Quantity

Unit of Measure

← Discount & Sales Tax • Ratio Simplifier (A:B) →

First Number: Second Number:

Find All Factors of:

Dividend: ÷ Divisor:

Number to Round: To Nearest:

Method: Standard (5+ ↑) Always Up (Ceil) Always Down (Floor)

Presets:

√ Square Root of: OR Power (x^y): ^{^}

x² + x + = 0

Number (n! & log):

Circle Radius (r):

Side a: Side b:

Angle (Degrees): °

Numbers (comma separated):

Total Items (n): Choose (r):

Decimal Number:

Number (1–3999):

Step-by-Step Solution: 1/49 + 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 1/49 by 3, and multiply the numerator and denominator of 5/21 by 7 so both fractions share the common base 147.

1 × 3/49 × 3 = 3/147 and 5 × 7/21 × 7 = 35/147

Step 3

Add the Numerators

Now add the numerators (3 + 35 = 38) and keep the common denominator 147 unchanged.

3 + 35/147 = 38/147

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 38 and 147 is 1, confirming that 38/147 cannot be reduced further—it is already in its simplest irreducible form.

38/147

Step 5

Decimal & Percentage Representation

Dividing the numerator 38 by denominator 147 produces a repeating decimal (approximately 0.258503, or 25.8503%).

38 ÷ 147 = 0.258503 (25.8503%)

Visual Representation

The diagram below illustrates 1/49 plus 5/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`38/147`
Mixed Number Form	`38/147`
Decimal Form	`0.258503`
Percentage	`25.8503%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

What is 1/49 plus 5/21 as a fraction?

1/49 + 5/21 in simplest fraction form is 38/147.

What is 1/49 plus 5/21 as a decimal?

1/49 + 5/21 converted to a decimal is 0.258503.

What is 1/49 plus 5/21 as a percentage?

1/49 + 5/21 expressed as a percentage is 25.8503%.

Does 1/49 plus 5/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.258503...) because the denominator contains prime factors other than 2 and 5.