What is 1/48 plus 8/21? (Answer: 45/112)

Exact Answer

==================================================
Problem: What is 1/48 plus 8/21?
Formula / Expression: 1/48 + 8/21
Final Answer: 45/112
==================================================

Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 48 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 336 (which is smaller than their product 48 × 21 = 1008, keeping the calculation simpler).
Working: LCD(48, 21) = 336

Step 2: Convert to Equivalent Fractions with Common Denominator 336
Multiply the numerator and denominator of 1/48 by 7, and multiply the numerator and denominator of 8/21 by 16 so both fractions share the common base 336.
Working: 1 × 7/48 × 7 = 7/336 and 8 × 16/21 × 16 = 128/336

Step 3: Add the Numerators
Now add the numerators (7 + 128 = 135) and keep the common denominator 336 unchanged.
Working: 7 + 128/336 = 135/336

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 135 and 336, which is 3. Divide both the numerator and denominator by 3.
Working: 135 ÷ 3/336 ÷ 3 = 45/112

Step 5: Decimal & Percentage Representation
Dividing the numerator 45 by denominator 112 produces a repeating decimal (approximately 0.401786, or 40.1786%).
Working: 45 ÷ 112 = 0.401786 (40.1786%)

Key Values:
- Simplified Fraction: 45/112
- Mixed Number Form: 45/112
- Decimal Value: 0.401786
- Percentage: 40.1786%

--------------------------------------------------
Solved with FractionsCalc:
https://fractionscalc.com/what-is-1-48-plus-8-21/
==================================================

1/48 + 8/21 = 45/112

Simplified Fraction

45/112

Mixed Number

Proper (45/112)

Decimal Value

0.401786

Percentage

40.1786%

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: 1/48 + 8/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 48 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 336 (which is smaller than their product 48 × 21 = 1008, keeping the calculation simpler).

LCD(48, 21) = 336

Step 2

Convert to Equivalent Fractions with Common Denominator 336

Multiply the numerator and denominator of 1/48 by 7, and multiply the numerator and denominator of 8/21 by 16 so both fractions share the common base 336.

1 × 7/48 × 7 = 7/336 and 8 × 16/21 × 16 = 128/336

Step 3

Add the Numerators

Now add the numerators (7 + 128 = 135) and keep the common denominator 336 unchanged.

7 + 128/336 = 135/336

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 135 and 336, which is 3. Divide both the numerator and denominator by 3.

135 ÷ 3/336 ÷ 3 = 45/112

Step 5

Decimal & Percentage Representation

Dividing the numerator 45 by denominator 112 produces a repeating decimal (approximately 0.401786, or 40.1786%).

45 ÷ 112 = 0.401786 (40.1786%)

Visual Representation

The diagram below illustrates 1/48 plus 8/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`45/112`
Mixed Number Form	`45/112`
Decimal Form	`0.401786`
Percentage	`40.1786%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

What is 1/48 plus 8/21 as a fraction?

1/48 + 8/21 in simplest fraction form is 45/112.

What is 1/48 plus 8/21 as a decimal?

1/48 + 8/21 converted to a decimal is 0.401786.

What is 1/48 plus 8/21 as a percentage?

1/48 + 8/21 expressed as a percentage is 40.1786%.

Does 1/48 plus 8/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.401786...) because the denominator contains prime factors other than 2 and 5.