About

Multiplying a whole number by a fraction often confuses students who struggle to visualize the integer as a fraction with a denominator of 1. This tool converts the integer I into I1, performs the multiplication across numerators and denominators, and reduces the result to its simplest form. It also handles mixed number conversion automatically.

Correct calculation is essential in carpentry, cooking scaling, and material estimation where partial units are multiplied by quantities. A rounding error here propagates through subsequent project steps. This calculator provides exact fractional values rather than decimal approximations to ensure precision.

Formulas

To multiply an integer n by a fraction ab, rewrite n as a fraction over 1:

n × ab = n1 × ab = n × a1 × b = nab

After multiplication, find the Greatest Common Divisor (GCD) of the numerator and denominator to simplify. If na > b, convert to a mixed number.

Reference Data

Expression	Step 1 (Setup)	Step 2 (Multiply)	Result (Simplified)
5 × 23	51 × 23	103	3 13
4 × 38	41 × 38	128	32 = 1.5
10 × 15	101 × 15	105	2
6 × 27	61 × 27	127	1 57
3 × 49	31 × 49	129	43 = 1.33…
0 × 56	01 × 56	06	0
-2 × 14	-21 × 14	-24	−12
7 × 310	71 × 310	2110	2.1

Frequently Asked Questions

Placing an integer over 1 changes its format to a fraction without changing its value. This aligns the numerators and denominators visually, reducing errors when multiplying across.

Yes. The sign rules of multiplication apply. If the integer is negative and the fraction is positive, the result is negative.

No. You multiply the integer only by the numerator. Multiplying by the denominator would be equivalent to division.

The filled slices represent the fractional parts. If the result is greater than 1, you will see multiple full circles plus a partial circle representing the remainder.