What is 4/49 plus 2/21? (Answer: 26/147)

Exact Answer

==================================================
Problem: What is 4/49 plus 2/21?
Formula / Expression: 4/49 + 2/21
Final Answer: 26/147
==================================================

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 4/49 by 3, and multiply the numerator and denominator of 2/21 by 7 so both fractions share the common base 147.
Working: 4 × 3/49 × 3 = 12/147 and 2 × 7/21 × 7 = 14/147

Step 3: Add the Numerators
Now add the numerators (12 + 14 = 26) and keep the common denominator 147 unchanged.
Working: 12 + 14/147 = 26/147

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 26 and 147 is 1, confirming that 26/147 cannot be reduced further—it is already in its simplest irreducible form.
Working: 26/147

Step 5: Decimal & Percentage Representation
Dividing the numerator 26 by denominator 147 produces a repeating decimal (approximately 0.176871, or 17.6871%).
Working: 26 ÷ 147 = 0.176871 (17.6871%)

Key Values:
- Simplified Fraction: 26/147
- Mixed Number Form: 26/147
- Decimal Value: 0.176871
- Percentage: 17.6871%

--------------------------------------------------
Solved with FractionsCalc:
https://fractionscalc.com/what-is-4-49-plus-2-21/
==================================================

4/49 + 2/21 = 26/147

Simplified Fraction

26/147

Mixed Number

Proper (26/147)

Decimal Value

0.176871

Percentage

17.6871%

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: 4/49 + 2/21

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 4/49 by 3, and multiply the numerator and denominator of 2/21 by 7 so both fractions share the common base 147.

4 × 3/49 × 3 = 12/147 and 2 × 7/21 × 7 = 14/147

Step 3

Add the Numerators

Now add the numerators (12 + 14 = 26) and keep the common denominator 147 unchanged.

12 + 14/147 = 26/147

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 26 and 147 is 1, confirming that 26/147 cannot be reduced further—it is already in its simplest irreducible form.

26/147

Step 5

Decimal & Percentage Representation

Dividing the numerator 26 by denominator 147 produces a repeating decimal (approximately 0.176871, or 17.6871%).

26 ÷ 147 = 0.176871 (17.6871%)

Visual Representation

The diagram below illustrates 4/49 plus 2/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`26/147`
Mixed Number Form	`26/147`
Decimal Form	`0.176871`
Percentage	`17.6871%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

What is 4/49 plus 2/21 as a fraction?

4/49 + 2/21 in simplest fraction form is 26/147.

What is 4/49 plus 2/21 as a decimal?

4/49 + 2/21 converted to a decimal is 0.176871.

What is 4/49 plus 2/21 as a percentage?

4/49 + 2/21 expressed as a percentage is 17.6871%.

Does 4/49 plus 2/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.176871...) because the denominator contains prime factors other than 2 and 5.