Date: 08/13/97 at 09:56:20 From: Maria Angelica P. Bocade Subject: fractions 1 3 Sally ate - of a cake and her sister ate - of it. 8 8 What fraction did they eat altogether? I've tried so hard to solve this question! Thanks, Angel
Date: 08/13/97 at 11:23:04 From: Doctor Mike Subject: Re: Fractions Hello Angel, It's nice you are starting to learn about fractions. Usually fractions are introduced by talking about dividing something up into a certain number of equal sized pieces, and then focusing on just a PART of the whole, consisting of some of those pieces. I want to draw a picture to help you understand. Most cakes are round, and that's hard to draw well with a keyboard, so I'll draw a long thin cake here, and show it divided up into 8 equal parts: _________________________________________________ | | | | | | | | | | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | |_____|_____|_____|_____|_____|_____|_____|_____| One eighth of the cake is 1 of those 8 equal parts. Three eighths of the cake is 3 of those 8 equal parts. Let's re-draw the cake to show what Sally and her sister ate : _________________________________________________ | | | | | | | |Sally| Sally's sister | 5 | 6 | 7 | 8 | |_____|_________________|_____|_____|_____|_____| As you can see, exactly 4 of the 8 pieces have been eaten by the two sisters. This is half of the cake. When the cake is divided up into 8 pieces, half of the cake corresponds to 4/8 of the cake. Let's explore some other ways to divide up the cake. If you make only 2 pieces by cutting it right down the center you get : _________________________________________________ | | | | 1 | 2 | |_______________________|_______________________| In this cake, a half of it would be just one of the 2 big pieces. So, 1 of the 2 big pieces is the same part of the cake as 4 of the smaller pieces. Writing this with fractions it looks like : 1 4 ----- = ----- 2 8 and we often write that as 1/2 = 4/8 to save space. If you divide the cake into 52 pieces, then half of the cake would be 26 pieces : 1 26 ----- = ------ 2 52 So, finally, the answer to your question is that the sisters ate 4/8 of the cake, which is the same as 1/2 of the cake. And as we saw there are many other equivalent ways to write that fraction. I hope this helps. Enjoy fractions! -Doctor Mike, The Math Forum Check out our web site! http://mathforum.org/dr.math/
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