However if you pay careful attention this logic is almost entirely reversible. Well then we are just stuck asking, "how do we extend this to non-natural numbers? Something similar happens when we want to multiply with this new formula. But what did we do last time we wanted to generalize addition to fractions? We considered the other representations of the integers. But what really makes this multiplication is the distributive rule.
If these two new definitions for addition and multiplication do not "play nice together" then we will need to fix one or the other! Well, long story short, they do. Well, it's not quite! It's a "multiplicative inverse" which means it undoes a repeated self-addition. It's the exact undoing of a repeated self-addition.
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As in earlier units of work, an emphasis is given to having students model operations with fractions, using a range of materials and record using words and symbols. There are three key understandings that underpin multiplication of fractions. The first is that multiplying two fractions involves finding the fraction of another fraction. The second is that when two fractions less than one are multiplied, the product is always less than either factor.
In multiplying whole numbers, students expect a product that is larger than either factor. Multiplying fractions requires a conceptual shift for the students who must clearly understand they are finding a part of a part. Thirdly, by understanding the commutative property, students can make problems simpler by changing the order of the factors.
The use an array model to visualise and solve problems involving finding a fraction of a fraction, by breaking an area into parts, horizontally and vertically, scaffolds the move from a whole number understanding to a fractional one.
Beginning with problems that involve working with unit parts without subdivision eg. Once this is clearly understood, working with unit parts that involve subdivision eg. Using realistic contexts for finding fractions of fractions is important. Having students respond to these, and create context of their own, will help them recognise the practical application of fraction multiplication.
Whilst the games are introduced and used within sessions to consolidate ideas, they can also be added to the class or group independent activities, or be sent home for family challenges and enjoyment. Fraction strips Material Master Refer to problem 1 from session 1. She said Is she right? Finding fractions of whole numbers. Is she correct?
Why not? Have students work in pairs to solve the problems, and pair share their results including any pictures or diagrams used. Explore fractions of fractions: Distribute think board sheets Attachment 2 to the students.
Have each student complete a think board for each of these two problems. Encourage students to use diagrams like those used for Attachment 1. Have students locate their copy of Attachment 1 Session 1, Activity 2, Step 3. Have students record written equations for each of the examples.
Have them discuss anything they notice about the numbers in these equations in which they are multiplying unit fractions. When we are multiplying whole numbers the product is larger than the factors. When we multiply fractions the product is smaller than both factors. Students play the game Multiplifraction Attachment 3 How to play Play with a partner. The winner is the person who collects the most sets of 3 cards. There are 15 sets in total. Ask students to form pairs.
Distribute cards from Attachment 4 to each pair. Have the pairs sort the cards into True and False piles. Pairs should then pair share, taking turns to read a card and talk about and justify their decision, using examples. We have been learning about multiplying fractions and would appreciate your playing a game of Multiplifraction with your child.
The cards are included in the pack. Your child will be pleased to explain the instructions for the game as it has been played in class. We hope you too will learn and enjoy. Log in or register to create plans from your planning space that include this resource. Use the resource finder. Home Resource Finder. NA Use a range of additive and simple multiplicative strategies with whole numbers, fractions, decimals, and percentages. AO elaboration and other teaching resources.
NA Know fractions and percentages in everyday use. NA Understand addition and subtraction of fractions, decimals, and integers.
Specific Learning Outcomes. Record in words, the actions and results of finding a fraction of a fraction. Record and respond to written multiplication equations.
Use arrays to model and solve multiplication equations that involve subdividing the unit. Almost all fractions being cross multiplied will have different denominators. This does not affect the process at all. Cross multiply as normal. Cross multiplying fractions to determine if one is greater than the other works because it is a shortcut for converting the fractions to a common denominator and comparing fractions. No, you cannot cross multiply when adding fractions.
Cross multiply only when you need to determine if one fraction is greater than another, or if you are trying to find a missing numerator or denominator in equivalent fractions. Cross multiply fractions with variables by multiplying opposite numerators and denominators of equivalent fractions, setting the values equal to one another, and solving for the variable. Cross multiplication can be used to answer this question. First, multiply 17 by To solve this problem, start by cross multiplying.
A man has a garden that is 6 feet wide and 9 feet long. He is planning on increasing the width to 9 feet. If he wants to increase the length proportionally, what would be the new length? To solve this problem, first set up proportional fractions.
Study Guides Flashcards Online Courses. Cross Multiplying Fractions. When cross multiplying fractions, the name sort of hints at how this is actually done. Frequently Asked Questions Q How do you cross multiply fractions?
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