Fractions in the 11+ — Questions, Worked Answers and Practice Papers

This question can be confusing at start but if you remove a few lines then an interesting pattern will emerge. {"chart":"grid","lines":[[["color","#333"], ["draw",[[2,14],[5,14],[5,12],[2,12],[2,14]]], ["draw",[[5,14],[8,14],[8,12],[5,12],[5,14]]], ["draw",[[8,14],[11,14],[11,12],[8,12],[8,14]]], ["draw",[[11,14],[14,14],[14,12],[11,12],[11,14]]], ["draw",[[11,12],[14,12],[14,10],[11,10],[11,12]]], ["draw",[[8,10],[8,12],[11,12],[11,10],[8,10]]], ["draw",[[8,10],[5,10],[5,12],[8,12],[8,10]]], ["draw",[[5,10],[2,10],[2,12],[5,12],[5,10]]], ["draw",[[2,9],[5,9],[5,5],[2,5],[2,9]]], ["draw",[[11,9],[14,9],[14,7],[11,7],[11,9]]], ["draw",[[8,5],[8,7],[11,7],[11,5],[8,5]]], ["draw",[[8,5],[5,5],[5,7],[8,7],[8,5]]], ["draw",[[11,7],[14,7],[14,5],[11,5],[11,7]]], ["draw",[[2,4],[5,4],[5,2],[2,2],[2,4]]], ["draw",[[5,4],[8,4],[8,2],[5,2],[5,4]]], ["draw",[[8,4],[11,4],[11,2],[8,2],[8,4]]], ["draw",[[11,4],[14,4],[14,2],[11,2],[11,4]]], ["draw",[[11,2],[14,2],[14,0],[11,0],[11,2]]], ["draw",[[8,0],[8,2],[11,2],[11,0],[8,0]]], ["draw",[[8,0],[5,0],[5,2],[8,2],[8,0]]], ["draw",[[5,0],[2,0],[2,2],[5,2],[5,0]]] ]],"shapes":["C,black F,lightblue 2,10 5,14 11,12 14,14 2,14 2,10", "C,black F,lightblue 2,5 5,9 11,7 14,9 2,9 2,5","C,black F,lightblue 2,2 8,2 8,4 2,4 2,2","C,black F,lightblue 11,2 14,4 11,4 11,2"],"textplot":[[3,13,"1"],[6,13,"2"],[9,13,"3"],[12,13,"4"],[3,11,"5"],[6,11,"6"],[9,11,"7"],[12,11,"8"],[3,8,"1"],[6,8,"2"],[9,8,"3"],[12,8,"4"],[3,6,"5"],[6,6,"6"],[9,6,"7"],[12,6,"8"],[3,3,"1"],[6,3,"2"],[9,3,"3"],[12,3,"4"],[3,1,"5"],[6,1,"6"],[9,1,"7"],[12,1,"8"]], "color":"multi","xalign":"bottom","yalign":"left","xaxis":[0,14],"yaxis":[0,14],"hideGrid":true} There are a total of 8 rectangles. Rectangle (1,5) when combined together forms a bigger rectangle which is half shaded. Which means 1 out of 2 rectangles are shaded. So we can redraw the rectangles as in the third diagram.  Rectangle (2,3) also when combined together forms a bigger rectangle which is half shaded. Which means 1 out of 2 rectangles are shaded. So we can redraw the rectangles as in the third diagram.  Rectangle (4) is half shaded so we do not need to do anything.  From the third diagram, 2 and half out of 8 rectangles are shaded. {"math":"formula","eq":"Shaded part= 2| 1/2"} {"math":"formula","eq":"Shaded part= 5/2"} {"math":"formula","eq":"Shaded fraction= 5/2 | out of 8"} {"math":"formula","eq":"Shaded fraction= 5/2 x 8"} {"math":"formula","eq":"Shaded fraction= 5/16"}