Fractions Operations: Multiplication and Division Literature Review
Multiplication. 38. Division. 39. Effective teaching includes multiple and carefully selected representations for multiplying and dividing fractions.
THINKING IN PATTERNS TO SOLVE MULTIPLICATION DIVISION
MULTIPLICATION DIVISION
gemh102.pdf
We shall now learn multiplication and division of fractions as well as of decimals. 2.3.1 Multiplication of a Fraction by a Whole Number.
Mathematics programmes of study: key stages 1 and 2 - GOV.UK
Pupils connect multiplication by a fraction to using fractions as operators (fractions of) and to division
Grade 5 Math Unit Assessment Multiplication and Division of
What fraction of a gallon of Gatorade did Nico drink? 12. Janna needs help multiplying fractions. She is working on the following problem: 4. × 1.
Fraction Multiplication and Division Models: A Practitioner
27 Dec 2016 Fraction multiplication and division models: A practitioner reference paper. International Journal of Research in Education and Science (IJRES) ...
Fractions Packet - CNM
denominator. If the answer to an addition subtraction
MULTIPLICATION ET DIVISION DE FRACTIONS
! Je peux simplifier une fraction uniquement lorsqu'il n'y a QUE des multiplications. 2. Calculer une fraction d'un nombre
00 Grade 5 Multiplication and Division of Fractions Unit Conceptual
Grade 5 Multiplication and Division of Fractions – Conceptual Lessons/Unit Outline. Page 1 of 9. SUGGESTED TIME FRAME: 5 Weeks. Time. Lesson Title.
An Examination of Meanings and Error Types Associated with Pre
TEACHERS' POSED PROBLEMS FOR THE MULTIPLICATION AND DIVISION OF FRACTIONS. European Journal of Education Studies - Volume 6 ? Issue 4 ? 2019.
[PDF] Multiplication et division de fraction
Pour multiplier deux fractions on multiplie les numérateurs entre eux et les dénominateurs entre eux Rappel : Pour multiplier une fraction par un nombre m :
[PDF] MULTIPLICATION ET DIVISION DE FRACTIONS
Pour multiplier deux fractions on multiplie les numérateurs entre eux et les dénominateurs entre eux Ex1 : A = 7 4 × 3 5 B = -5
[PDF] Contrôle n°4: Multiplication et division de fractions
Contrôle n°4: Multiplication et division de fractions 4 ème Exercice 1 : 2 points Calculer et donner le résultat sous forme irréductible : A =
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Multiplication et division de fractions I) Multiplication de fractions Il suffit de multiplier les numérateurs entre eux et les dénominateurs
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Chapitre 3: Multiplication division des fractions MULTIPLICATION DIVISION DES FRACTIONS CORRECTION DES EXERCICES Exercice 1 :
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Quatrième/Fractions: multiplication et division 1 Multiplications et simplifications : Exercice 4666 Parmi les transformations suivantes
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Page 6 sur 7 6 Règle de division de deux fractions La règle permet donc de transformer une division de fraction en une multiplication Exemple
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Divisions de fractions 2 1 Inverse d'un nombre Deux nombres sont inverses l'un de l'autre si leur produit est égal à 1 Exemples : 4 et 025 sont inverses
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Combien a coûté le cadeau de son frère ? Page 2 Exercices – Divisions de fractions Exercice 9 : Effectuer les calculs suivants :
[PDF] ; ; ; NO Calculs avec les fractions : multiplication et division
NO Calculs avec les fractions : multiplication et division Pour multiplier deux fractions on multiplie les numérateurs entre eux et les dénominateurs
Comment multiplier et diviser des fractions ?
Pour diviser une fraction par une fraction on la multiplie par la fraction inverse. Et pour multiplier deux fractions on multiplie les numérateurs entre eux et les dénominateurs entre eux.- Les multiplications et divisions sont effectuées de gauche à droite: Si une multiplication est à gauche d'une division, on effectue d'abord la multiplication. Si une division est à gauche d'une multiplication, on effectue d'abord la division.
MATHEMATICS20
2.1 MULTIPLICATION OF FRACTIONS
You know how to find the area of a rectangle. It is equal to length × breadth. If the length and breadth of a rectangle are 7 cm and 4 cm respectively, then what will be its area? Its area would be 7 × 4 = 28 cm 2. What will be the area of the rectangle if its length and breadth are 712 cm and
312 cm respectively? You will say it will be 71
2 × 31
2 = 15
2 × 7
2 cm2. The numbers 15
2and 72 are fractions. To calculate the area of the given rectangle, we need to know how to
multiply fractions. We shall learn that now.2.1.1 Multiplication of a Fraction by a Whole Number
Observe the pictures at the left (Fig 2.1). Each shaded part is 14part of a circle. How much will the two shaded parts represent together?
They will represent
1 14 4+ = 12×4.
Combining the two shaded parts, we get Fig 2.2 . What part of a circle does the shaded part in Fig 2.2 represent? It represents 24 part of a circle .Fig 2.1
Fig 2.2
Chapter 2
Fractions and
Decimals
Rationalised 2023-24
FRACTIONS AND DECIMALS21The shaded portions in Fig 2.1 taken together are the same as the shaded portion inFig 2.2, i.e., we get Fig 2.3.
Fig 2.3
or12×4 =2
4 . Can you now tell what this picture will represent? (Fig 2.4)Fig 2.4
And this? (Fig 2.5)
Fig 2.5
Let us now find
13×2.
We have
13×2 =
1 1 1 3
2 2 2 2+ + =We also have
1 1 1 1+1+1 3×1 3+ + = = =2 2 2 2 2 2So
13×2 =3×1
2 = 32Similarly
2×53 =2×5
3 = ?Can you tell
23×7 =?
34× ?5=The fractions that we considered till now, i.e.,
1 2 2 3, , ,2 3 7 5 and 3
5 were proper fractions.=
=Rationalised 2023-24MATHEMATICS22
For improper fractions also we have,
52×3 =2×5
3 = 10
3Try,83×7 =?74×5 = ?
Thus, to multiply a whole number with a proper or an improper fraction, we multiply the whole number with the numerator of the fraction, keeping the denominator same1.Find: (a)
2×37 (b) 967×(c) 13×8(d) 13×611 If the product is an improper fraction express it as a mixed fr
action.2.Represent pictorially :
2 42×5 5=To multiply a mixed fraction to a whole number, first convert the
mixed fraction to an improper fraction and then multiply.Therefore,
53 27× =1937× = 57
7 = 187.
Similarly,
22 45× =2225× = ?
Fraction as an operator 'of'
Observe these figures (Fig 2.6)
The two squares are exactly similar.
Each shaded portion represents
12 of 1.
So, both the shaded portions together will represent 12 of 2.
Combine the 2 shaded
12 parts. It represents 1.
So, we say
12 of 2 is 1. We can also get it as 1
2 × 2 = 1.
Thus, 12 of 2 = 1
2 × 2 = 1TRY THESETRY THESE
Find: (i)
35×27 (ii)
41 ×69Fig 2.6
Rationalised 2023-24
FRACTIONS AND DECIMALS23Also, look at these similar squares (Fig 2.7).Each shaded portion represents
12 of 1.
So, the three shaded portions represent
12 of 3.
Combine the 3 shaded parts.
It represents 1
12 i.e., 3
2. So, 12 of 3 is 3
2. Also, 1
2 × 3 = 3
2. Thus, 12 of 3 = 1
2 × 3 = 3
2.So we see that 'of' represents multiplication.
Farida has 20 marbles. Reshma has
1th5of the number of marbles what
Farida has. How many marbles Reshma has? As, 'of' indicates multiplication, so, Reshma has1×205 = 4 marbles.
Similarly, we have
12of 16 is 1×162 = 16
2 = 8.
Can you tell, what is (i)
12of 10?, (ii) 1
4of 16?, (iii) 2
5 of 25?
EXAMPLE 1 In a class of 40 students
15 of the total number of studetns like to study
English,
25 of the total number like to study Mathematics and the remaining
students like to study Science. (i)How many students like to study English? (ii)How many students like to study Mathematics? (iii)What fraction of the total number of students like to study Science? SOLUTIONTotal number of students in the class = 40. (i)Of these 15 of the total number of students like to study English.Fig 2.7
TRY THESERationalised 2023-24
MATHEMATICS24
Thus, the number of students who like to study English = 15 of 40 = 1405× = 8.
(ii)Try yourself. (iii)The number of students who like English and Mathematics = 8 + 16 = 24. T hus, the number of students who like Science = 40 - 24 = 16.Thus, the required fraction is
16 40.EXERCISE 2.1
1.Which of the drawings (a) to (d) show :
(i) (c)(d)2.Some pictures (a) to (c) are given below. Tell which of them show:
(i)1 335 5× =(ii)1 223 3× =(iii)33
4214× =(a)(b)
(c)3.Multiply and reduce to lowest form and convert into a mixed fraction:
(i)375×(ii)143×(iii)627×(iv)259×(v)243× (vi)
=Rationalised 2023-24FRACTIONS AND DECIMALS254.Shade:(i)
12 of the circles in box (a)(ii)2
3 of the triangles in box (b)
(iii) 35 of the squares in box (c).
(a)(b)(c)5.Find:
(a) 12 of (i) 24(ii) 46(b) 2
3 of(i) 18(ii) 27
(c) 34 of (i) 16(ii) 36(d) 4
5 of(i) 20(ii) 35
6.Multiply and express as a mixed fraction :
(a) 3 515×(b) 35 64×(c) 17 24×(d)
14 63×(e) 13 64×(f) 23 85×7.Find: (a)
12 of (i) 324 (ii) 249 (b) 5
8 of (i) 536 (ii) 2938.Vidya and Pratap went for a picnic. Their mother gave them a water bottle that
contained 5 litres of water. Vidya consumed 25 of the water. Pratap consumed the
remaining water. (i)How much water did Vidya drink? (ii)What fraction of the total quantity of water did Pratap drink?2.1.2 Multiplication of a Fraction by a Fraction
Farida had a 9 cm long strip of ribbon. She cut this strip into four equ al parts. How did she do it? She folded the strip twice. What fraction of the total length wil l each part represent?Each part will be
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