SIXTHS AND TWELFTHS When anything is divided into six equal parts, we call the parts sixths. Six sixths make one whole. Circle Rectangle Hexagon 1. Show that each of these forms is divided into halves. 2. Show that each is divided into thirds; into sixths. 3. Make larger drawings of each of these forms on paper; on the blackboard. When anything is divided into twelve equal parts, we call the parts twelfths. Twelve twelfths make one whole. Circle Rectangle Hexagon 1. Show the various halves in the circle and hexagon. 2. Show thirds of each of these forms. 3. Show fourths of each. 4. Show sixths of each. 5. Make larger drawings of each of these forms on paper; on the blackboard. 6. = 1; 1= 1; 3 = 1; 4 = 1. 8 Read these facts. 7. Which is larger, or ? Why? or? Why? 8. Cut out forms to show the answers to 6 and to 7. 9. Which is larger, or ? or ?or? EQUAL PARTS OR FRACTIONS A number is always a number of ones of the same kind. A fraction is always one or more of the equal parts of some one thing. Here are four forms, A, B, C, and D. D B is divided into four parts. D is not divided. Each part of A, each part of B, and each part of C is the exact size of D. There are 5 D's in A. Count and see. There are 4 D's in B, and 2 D's in C. Each part of A is equal to every other part. The five parts are equal. Each part of B is equal to every other part. The four parts are equal. One part of Cis equal to the other part. We call equal parts fractions. Each part of A is a fraction of A. There are five parts. There are four parts. We print this, 4. are taking one part. The 4 means that there are four equal parts in B. Each part of C is a fraction of C. There are two parts. We print this, 2. 2. How many 2's are there in 6? Or, 6 contains how many 2's? Or, 6 divided by 2 is how much? What is the ratio of 2 to 6? of 6 to 2? 3. 2)16 2)8 2)12 2)14 2)10 2)18 2)20 2)4 4. How many 2's are there in 11? Five 2's and 1 that is, 11 contains five 2's and one 1. over; MULTIPLYING A FRACTION 7. If a is of S, and if b of S, a+b= 2 × of S. then a b Two halves make one whole. S SQUARE 10. John had seven apples. He gave one half of them to his sister. How many apples did she receive? PARTS Cut out of paper a square one inch on each side. Cut the square into two equal parts, one inch by inch. Do you see that the 2 parts of the square are of the rectangle? There are 5 equal parts in A. Each is of A. = a+b= 2 fractions of A= of A. a+b+c= 3 fractions of A = a b с d e A of A. = of A. = ğ of A. a+b+c+d+e= : 5 fractions of A But as there are only 5 parts in A, ğ of A = all of A This form-picture is divided into two parts, bc. b = of A. 1⁄2 c = of A. The picture of b is divided into three parts, d, e, f. d = of b. e = 3 of b. f = of b. 180 If we divide c into three parts, then A will have 6 parts. If A has 6 parts, then d = of A. d = of of A, because d is of b, which is of A. Cut and fold pieces of paper to show the answers to these six questions. RATIOS, 3, }, ±, 1, 5, 1 1. How many 3's are there in 18? How many 6's are there in of 18 = ? Sixths Thirds What is the ratio of 3 to 12? of 12 to 3? of 4 to 12? 3. How many 5's are there in 15? of 12 to 4 ? of 15=? of 15=? What is the ratio of 5 to 15? of 15 to 5? of 3 to 15? of 15 to 3? How many 3's are there in 12? What is the ratio of 4 to 12? of 12 to 4? 4. When we ask, What is the ratio of 3 to 12? we mean, What part of 12 is 3. 1 2 3 4 5 6 7 8 9 10 II 12 O OBLONG Into how many parts is the oblong divided? What part of O is 1? How many times IV is O? 5. When we ask, What is the ratio of 12 to 3? we mean, How many times does 12 contain 3? Ratio compares one thing with another. Ratio measures one thing by another. When anything is divided into equal parts, we may call the parts fractions. 6. There were 80 marbles to divide among 10 boys equally. What is the ratio of 80 to 10? |