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9. [Fractions] Skill 9.1 MMYellow 1 1 2 2 3 3 4 4 MMRed 1 1 2 2 3 3 4 4 Illustrating proper fractions as part of one whole. numerator - how many parts count 3 5 Q. Shade in denominator - how many equal parts in one whole 5 (five sixths) 6 ⇒ A. of this hexagon. 5 6 Q. What fraction of this A. circle is shaded? 3 4 The hexagon is divided into 6 equal parts. The numerator tells us to shade 5 parts. The circle is divided into 4 equal parts, so the denominator of the fraction is 4. Only 3 parts of the circle are shaded so the numerator is 3. The fraction of the circle that is shaded is three fourths or 3 . 4 a) 5 Shade in 9 (five nineths) of this square. d) What fraction of this pentagon is shaded? g) Shade in square. page 49 1 of this 4 b) Shade in 1 (one quarter) 4 Shade in 7 (four sevenths) of this rectangle. f) What fraction of this circle is shaded? i) Shade in of this 3 parallelogram. of this triangle. e) What fraction of this rectangle is shaded? h) Shade in hexagon. 1 of this 2 www.mathsmate.net 4 c) 2 © Math’s Mate Yellow/Red Skill Builder 9 Skill 9.2 MMYellow 1 1 2 2 3 3 4 4 MMRed 1 1 2 2 3 3 4 4 Illustrating proper fractions as part of a group. numerator - how many identical circles in the group count 3 5 denominator - how many identical circles in the group all together group of identical circles Hint: 3 can read as “three out of five”, which means three objects out of a total of five are counted. 5 Q. Shade in 7 of this group 10 A. ⇒ of apples. Q. What fraction of this A. group of sunglasses is shaded? 7 10 The group has 10 identical apples. The numerator shows to shade 7 apples. 3 4 There are 4 sunglasses in the group all together, so the denominator of the fraction is 4. Only 3 sunglasses are shaded so the numerator is 3. The fraction of the group of sunglasses that is shaded is three fourths or 3 . 4 a) 5 Shade in 6 of this group of butterflies. d) What fraction of this group of balloons is shaded? page 50 b) Shade in 2 of this group 5 Shade in 3 of this group of ginger bread men. f) What fraction of this group of lemons is shaded? of houses. e) What fraction of this group of stars is shaded? www.mathsmate.net 2 c) © Math’s Mate Yellow/Red Skill Builder 9 Skill 9.3 MMYellow 1 1 2 2 3 3 4 4 MMRed 1 1 2 2 3 3 4 4 Writing 1 as a fraction. 1 whole circle shaded 1 1 2 2 = 3 3 = 4 4 = 5 5 = = numerator = denominator Q. Which of the following fractions = 1 A. A and D fractions equal 1? 3 A) 3 4 B) 3 2 C) 3 cake was eaten, what fraction of the cake remains? Which of the following fractions equal 1? A) 3 3 B) 1 8 C) 8 8 D) 3 8 A) c) to 1 that has a denominator of 8. g) Luke has spent one sixth 5 2 B) 2 2 C) 1 2 D) 5 5 Write a fraction equal to 1 that has a denominator of 5. h) If three fifths of the show is over, what fraction of the performance is left? www.mathsmate.net Which of the following fractions equal 1? A) and e) 4 Three thirds make the whole cake. If one third was eaten, there are two thirds left. fractions equal 1? d) Write a fraction equal page 51 2 3 b) Which of the following and of his pocket money. What fraction of the money is left? The only fractions in which the numerator is the same as the denominator are 3 and 4 . 3 3 = 1 (three thirds make a whole) 3 4 = 1 (four fourths or quarters make a whole) 4 4 D) 4 Q. If one third of the birthday A. a) 1 1 7 B) 7 7 C) 1 1 D) 7 1 and f) Write a fraction equal to 1 that has a denominator of 12. i) Three quarters of the students are girls. What fraction of the students are boys? © Math’s Mate Yellow/Red Skill Builder 9 Skill 9.4 • • • • Illustrating and converting mixed numbers to improper fractions. Consider the mixed number as two bits: A whole number. A fraction. Draw and shade both bits. Count the total parts shaded. Write this total over the same denominator. 1 2 1 3 5 1 3 = 8 IMPROPER FRACTION 5 5 fraction denominator - 5 equal parts in one whole Q. Name the mixed number A. 3 represented by these shaded rectangles. Q. Shade these circles to 2 Name the mixed number represented by these shaded squares. 1 + 1 + 1 2 2 to show that 3 = page 52 15 5 Three whole rectangles are shaded and one sixth of another rectangle is shaded. The total number of rectangles shaded is three 1 and one sixth, or 3 6 . 1 = 1 3 + 1 + 1 3 3 7 = 3 3 + 3 3 + 1 3 b) Name the mixed number Shade two whole circles and a third of the remaining circle. In total 7 thirds have been shaded. This shows that 2 1 = 7 3 1 + e) 3 c) Name the mixed number represented by these shaded hexagons. f) Shade these rectangles 3 8 to show that 1 = 5 5 represented by these shaded triangles. 1 2 d) Shade these pentagons 1 6 A. 1 7 show that 2 = 3 3 a) 8 numerator - 8 parts count MIXED NUMBER whole number 3 6 7 5 4 MMYellow 1 1 2 2 3 3 4 4 MMRed 1 1 2 2 3 3 4 4 3 4 Shade these circles 2 8 to show that 2 = 3 3 www.mathsmate.net © Math’s Mate Yellow/Red Skill Builder 9 Skill 9.5 • • MMYellow 1 1 2 2 3 3 4 4 MMRed 1 1 2 2 3 3 4 4 Comparing fractions. First illustrate each fraction by shading the appropriate proportion of the identical shapes. Then compare the size of the shaded areas to decide which is largest or smallest. Hint: 3 6 < same numerator largest numerator = largest fraction 5 6 BUT 1 7 same denominator Q. Which fraction is larger? 1 or 1 3 4 A. 1 3 3 Q. Shade this diagram to 2 5 compare and . 3 9 A. 2 3 2 3 5 9 Which fraction is larger? Which fraction is larger? 2 3 or 5 5 2 5 3 5 4 Shade two thirds of the first rectangle. Shade five ninths of the second rectangle. The fractions are close in value however 2 is slightly greater than 5 . b) Which fraction is larger? 3 3 or 4 5 3 c) 9 Which fraction is larger? 4 4 or 7 9 3 5 d) Which fraction is smaller? e) 1 3 or 6 6 g) Shade this diagram to 2 1 compare and . 5 3 Which fraction is smaller? page 53 smallest denominator = largest fraction The shaded area corresponding to 1 is 3 bigger than the area shaded for 1 , 4 which means that 1 is larger than 1 . 1 3 1 4 a) 1 4 < Which fraction is smaller? f) 2 2 or 5 7 h) Shade this diagram to 2 7 compare and . 5 8 Which fraction is larger? www.mathsmate.net i) Which fraction is smaller? 2 2 or 3 5 Shade this diagram to 3 5 compare and . 4 6 Which fraction is smaller? © Math’s Mate Yellow/Red Skill Builder 9 Skill 9.6 MMYellow 1 1 2 2 3 3 4 4 MMRed 1 1 2 2 3 3 4 4 Illustrating and finding equivalent fractions. same area shaded 1 2 = 2 4 3 6 = 4 8 = different fraction names equal value (equivalent fractions) Q. Shade this diagram to A. Shade three fourths inside the first square. Shade six eighths inside the second square. The same area of each square has been shaded. This shows that 3 = 6 = show the equivalent 3 6 fractions: = 4 8 = 4 Q. Complete to form A. equivalent fractions: 1 3 = 4 12 The rectangle on the left has 4 equal parts. Shade one part. The rectangle on the right has 12 equal parts. Shade the same area as in the first rectangle. Three out of twelve parts have been shaded. One fourth is the same as three twelfths. 1 3 are equivalent fractions. = = 1 = 4 12 4 a) Shade this diagram to show the equivalent 2 4 fractions: = 3 6 b) Shade this diagram to c) equivalent fractions: e) Complete to form equivalent fractions: g) Complete to form equivalent fractions: 2 6 = 3 f) Complete to form equivalent fractions: 4 16 = 5 i) Complete to form equivalent fractions: 3 9 = 10 6 = 2 12 1 = 3 9 h) Complete to form equivalent fractions: 2 1 = 8 www.mathsmate.net Shade this diagram to show the equivalent fractions: 3 = 12 4 16 = = d) Complete to form page 54 12 show the equivalent fractions: 4 = 8 5 10 = 8 © Math’s Mate Yellow/Red Skill Builder 9 Skill 9.7 • Adding and subtracting fractions with the same denominators. MMYellow 1 1 2 2 3 3 4 4 MMRed 1 1 2 2 3 3 4 4 Add or subtract the numerators (top numbers of the fractions). Don’t add or subtract the denominators (bottom numbers of the fractions). Q. 1 + 3 = 9 A. 9 4 9 Add the fractions: One ninth plus three ninths is four ninths. Add only the top numbers. + = one ninth + three ninths = four ninths 1 9 Q. 4 − 2 = 7 A. 7 2 7 + 3 9 = 4 9 Subtract the fractions: Four sevenths minus two sevenths is two sevenths. Subtract only the top numbers. four sevenths − two sevenths = two sevenths 4 7 a) 1+1 = 3 3 + 2 3 − 2 7 b) 2+3 = 7 7 c) 2+2 = 5 5 2 7 = d) 3+2 = 8 8 e) 3 + 4 = 10 10 f) 5 + 6 = 12 12 g) 2−1 = 3 3 h) 4−1= 5 5 i) 6−2 = 9 9 j) 3−2 = 5 5 k) 9 − 6 = 10 10 l) 8 − 3 = 12 12 m) 1+4 = 6 6 n) 6−3 = 7 7 o) 7 − 2 = 11 11 page 55 = www.mathsmate.net © Math’s Mate Yellow/Red Skill Builder 9 Skill 9.8 • MMYellow 1 1 2 2 3 3 4 4 MMRed 1 1 2 2 3 3 4 4 Simplifying fractions. Decide if the fraction can be simplified. If both numbers, top (numerator) and bottom (denominator), can be divided by the same number then the fraction can be simplified. Hint: If the numbers are both even then you can start with dividing by 2. 6 8 • numerator (even) denominator (even) Always divide both the numerator and the denominator by the same number. 6 8 ÷2 ÷2 = 3 4 Q. Simplify: 6 10 A. Simplify: 12 18 b) Simplify: ÷2 ÷3 a) 6 = 10 6 ÷2 3 = = 10 ÷ 2 5 12 =6 = 18 9 ÷3 ÷2 .................................................... 2 3 4 20 d) Simplify: Both 6 and 10 are even numbers. They can be divided by 2. The fraction can be simplified. 4 6 c) .................................................... e) .................................................... 10 25 Simplify: 9 12 Simplify: f) .................................................... .................................................... g) Which of the following h) Which of the following 20 70 Simplify: .................................................... fractions cannot be simplified? A) 3 B) 4 C) 5 D) 13 fractions cannot be simplified? A) 5 B) 6 C) 7 D) 9 Which of the following fractions cannot be simplified? A) 7 B) 9 C) 12 D) 17 ...................................................................... ...................................................................... ...................................................................... 15 15 15 15 B and D page 56 10 10 10 and www.mathsmate.net 10 i) 18 18 18 18 and © Math’s Mate Yellow/Red Skill Builder 9 Skill 9.9 • • MMYellow 1 1 2 2 3 3 4 4 MMRed 1 1 2 2 3 3 4 4 Adding and subtracting mixed numbers. Add or subtract the whole numbers first. Hint: For subtractions you may need to convert 1 whole number to an equivalent fraction. 5 Example: 1 = one whole equals five fifths 5 Then add or subtract the numerators (top numbers of the fractions). Don’t add or subtract the denominators (bottom numbers of the fractions). Q. 1 1 2 +2 = 4 4 A. 3 3 4 Add the whole numbers first: 1 + 2 = 3 Add the fractions: One fourth plus two fourths is three fourths. Add only the top numbers. + 11 4 Q. 2 − 5 = 6 A. 1 1 6 = 22 4 + 33 4 = The two can be seen as one whole and six sixths. Six sixths minus five sixths is one sixth. 6 5 1 − = 6 6 6 2− a) 3 3 2 +3 = 7 7 d) 4 1 4 +1 = 6 6 5 6 7 2 5 +1 = 8 8 c) 2 2 1 3 +1 = 5 5 f) 2 3 2 +4 = 9 9 b) 2 e) 5 = 11 6 6 3 4 +2 = 10 10 g) 2 − 1 = 3 h) 4 − 1 = 2 i) 3− 2 = 7 2− 1 = 4 k) 4− 2 = 3 l) 9− 5 = 9 m) 1 − 3 = 5 n) 5 − 3 = 4 o) 6 − 5 = 6 j) page 57 www.mathsmate.net © Math’s Mate Yellow/Red Skill Builder 9 Skill 9.10 • • MMYellow 1 1 2 2 3 3 4 4 MMRed 1 1 2 2 3 3 4 4 Finding a fraction of a number. First find one fraction of the number by dividing by the denominator. Then multiply the number of fractions you need by the result. Example: Three fifths of 10? First find one fifth of 10 by dividing 10 by 5. 10 ÷ 5 = 2 Then find three fifths of 10 by multiplying 3 by 2. 2+2+2=3×2=6 So three fifths of 10 is 6. Q. Eric kicked two thirds of A. 8 his team’s 12 goals. How many goals did he kick? a) Three fourths of the 28 students in the class are boys. How many boys are in the class? b) Two fifths of the 50 children at the day care had the flu. How many children were ill? one fourth of 28 = 28 ÷ 4 = 7 .................................................................................................................... three fourths of 28 = 3 × 7 = .............................................................................................. c) one fifth of 50 = .................................................................................................................... 21 Ian scored five eighths of the 40 points on the test. How many points did he score? two fifths of 50 = .............................................................................................. d) Of the 24 students in a class, one third are chosen for the school play. How many students are chosen for the play? one eighth of 40 = .................................................................................................................... one third of 24 = .............................................................................................. five eighths of 40 = .............................................................................................. e) Find one third of 12 ⇒ divide 12 by 3 12 ÷ 3 = 4 Find two thirds of 12 ⇒ multiply 2 by 4 2×4=8 Of the 100 cakes at a party, seven tenths were eaten in the first hour. How many cakes were eaten in the first hour? f) Five sixths of the 30 horses in the race jumped over the first hurdle. How many horses passed the first hurdle? .................................................................................................................... .................................................................................................................... .............................................................................................. .............................................................................................. page 58 www.mathsmate.net © Math’s Mate Yellow/Red Skill Builder 9