Multiplying Whole Numbers by Fractions

Date: 05/31/99 at 17:22:28
From: Lemarcus McCakk
Subject: Fractions

How do you multiply whole numbers by fractions?

Date: 06/01/99 at 12:57:53
From: Doctor Rick
Subject: Re: Fractions

Hi, Lemarcus.

I have 3 of those new quarters with Caesar Rodney on the back. If you 
have 5 times as many of them as I have, how many do you have?

  3 quarters x 5 = 15 quarters.

Let's write that in dollars: 1 quarter is 1/4 dollar, so 3 quarters = 
3/4 dollar.

  3/4 x 5 = 15/4

Do you see what I did? I just multiplied the numerator of the fraction 
(3) by the whole number (5) to get the new numerator. Then you can 
rewrite the improper fraction as a mixed fraction:

  15/4 = 3 3/4

Here is another way to think about it, if you're familiar with 
multiplying fractions. When you multiply two fractions together, you 
multiply the numerators to get the new numerator, and you multiply the 
denominators to get the new denominator. If you have a whole number 
instead of a fraction, you can rewrite it as "oneths" with a 
denominator of 1. Then you can multiply using the rule for multiplying 
fractions. For instance,

  5 = 5/1

  3         3     5    3 x 5   15
 --- x 5 = --- x --- = ----- = --
  4         4     1    4 x 1    4

- Doctor Rick, The Math Forum
  http://mathforum.org/dr.math/