6. TYPES OF FRACTIONS

Transcription

1 . TYPES OF FRACTIONS - Parts of a whole - Complementary fractions - Measuring fractions - Fractions and percentages - Parts of a group - A fraction of what? 0 - Improper fractions - Equivalent fractions - Comparing fractions 00, McMaster & Mitchelmore

2 Activity - Parts of a whole This pear has been cut into two pieces from top to bottom as shown by the dashed line. You know that each piece is a half of the pear because the two pieces are equal (i.e. the same). Now a pear will be cut into two pieces from side to side as shown by the dashed line. No. Each piece will not be a half of the pear because the two pieces will not be equal. Only the height of the pear will be halved. The length of this piece of water melon has been cut equally into three. No. Each piece of watermelon is not one third of the original slice. The diagram on the right shows division of the slice into thirds. Some oranges were cut into equal-sized pieces. No. They are not quarters because more than of them are needed to make a whole orange. 00, McMaster & Mitchelmore

3 quarters of the area of each of the shapes drawn below are shaded. There are many other ways that each shape can be divided into quarters. 00, McMaster & Mitchelmore

4 Activity - Complementary fractions ) ) ) ) ) ) ) ) ) 0) For the shapes above, the denominator of the fraction tells you the number of equal-sized pieces that the shape could be divided into. the numerator of a fraction tells you the number of these equal-sized pieces that have been shaded. 00, McMaster & Mitchelmore

5 Question number ) ) ) ) ) ) ) ) ) 0) Fraction shaded Fraction unshaded Total shaded and unshaded of this side of the noise barrier is painted. This can be seen by grouping the coloured pieces into whole rows (as shown by the arrows linking the pieces) 00, McMaster & Mitchelmore

6 Activity - Measuring fractions Fractions of a bar Fractions of a circle 00, McMaster & Mitchelmore

7 Fractions and percentages Activity - 00% 0% 0% 0% 0% 0% 0% 0% 0% 0% Fraction 0 Percentage 0% % 0% % 0% 0% 0% 0% % % % % 0% 00, McMaster & Mitchelmore

8 Activity - Parts of a group Here are some lines of counters. There are 0 counters in each line. of this line of counters has been coloured blue. of this line of counters has been coloured red. 0 of this line of counters has been coloured green. of the top line of counters has been coloured yellow. This necklace is made from dyed pasta threaded on a string in a repeating pattern. The pattern goes: yellow-orange-orange-green-green. There are 0 beads on the string. of the pasta is orange. The squares of this chess board are made from dark-coloured and lightcoloured wood. of the squares are dark. You tell without counting them because you can see that there are equal numbers of light and dark squares. 00, McMaster & Mitchelmore

9 A queue at the giant slide of the first 0 people in the queue are party guests. You tell this without colouring in the diagram because every th means out of every which is a quarter. of the first 0 people in the queue are patrons. If there are 0 people in the party, of the first 0 people in the queue are party guests. of the first 0 people in the queue are patrons. If they changed the rules and party guests merged in the ratio of patrons to party guests, this is what the queue of the first 0 people would look like. of the first 0 people in the queue are party guests. of the first 0 people in the queue are patrons. 00, McMaster & Mitchelmore

10 Activity - A fraction of what? ) Bar A Bar B is larger than because more of Bar A is shaded than Bar B. ) Bar A Bar B Bar B has the larger shaded area. Bar A has the larger fraction of its area shaded. ) Group A Group B Group B has more shaded circles. Group A has a larger fraction of its circles shaded. The fraction of all the circles (Group A and Group B) shaded is. ) Group A Group B The fraction of all the circles (Group A and Group B) shaded is. As a number of fifths, this is fifths. You know this answer without counting because if the same fraction of different groups is shaded, that is the shaded fraction of the groups when they are combined. 00, McMaster & Mitchelmore 0

11 A midnight feast Brooke had eaten a greater amount of licorice. Brooke had more licorice confiscated from her. Holly ate more pieces of chocolate. Brooke ate a greater fraction of her chocolate. Brooke s drink was sweeter because the cordial was a greater fraction of her drink. The fraction of pink marshmallows in the bag stayed the same because the fraction of white ones taken out was the same as the fraction of white ones in the bag. 00, McMaster & Mitchelmore

12 Activity - Improper fractions Abdul recorded his score one week as. 0 Israel said Abdul must have written his score down wrongly. He might have thought this because if there are only 0 questions, you can t get of them right. and are improper fractions. All improper fractions have a value greater than because the numerator is larger than the denominator. Dividing a larger number by a smaller number gives a value greater than. ) x + ) x + ) x , McMaster & Mitchelmore

13 ) ) 0 ) - ) - ) - ) ) ) , McMaster & Mitchelmore

14 Activity - Equivalent fractions 00, McMaster & Mitchelmore

15 SET A SET B x x x x x x x x x x x x No. The answers to Set B are not equivalent fractions. You know this because a different fraction of each bar is shaded. 00, McMaster & Mitchelmore

16 Halves Thirds Quarters Fifths Sixths Sevenths Eights Ninths Tenths 0 00, McMaster & Mitchelmore

17 00, McMaster & Mitchelmore

18 Activity - Comparing fractions ) Order: Reason: They are all seventeenths so the larger the numerator, the larger the fraction. ) Order: Reason: They all have the same numerator so the larger the denominator, the smaller the fraction. ) Order: Reason: The smaller a fraction s complementary fraction, the larger the fraction. ) Order: Reason: Proper fractions are less than and improper fractions are greater than. ) Order: Reason: When each fraction is written as a number of twelfths, their numerators can be compared. ) Order: Reason: When the numerator is less than half the denominator, the fraction is less than a half. When it is more than half the denominator, it is more than a half. 00, McMaster & Mitchelmore