4 6 equivalent fractions11/8/2023 using collaborative grouping so students can support each other and experience both tuakana and teina roles.encouraging sharing and discussion of students’ thinking.allowing use of scientific calculators that can process fractions.altering the complexity of the numbers involved, or the relationships between numerators and denominators.The learning opportunities in this unit can be differentiated by providing or removing support to students and by varying the task requirements. Ways to support students include: If each quarter is equally partitioned into 25 parts, those parts are called hundredths since 4 x 25 of those parts fit into one. Both 0.75 and 75% represent 75/100 which is an equivalent fraction to 3/4. Understanding equivalent fractions is critical to making sense of decimals and percentages. Therefore, each third can be divided into four twelfths. The relationship between two thirds and eight twelfths can be represented in this equality.įour times as many twelfths comprise one as thirds. Twelfths are quarter the size of thirds so four times as many twelfths fit into the same length as thirds. Sixths are half the size of thirds so twice as many sixths fit into the same length as thirds. A fraction strip (length) model of the relationships looks like this: Consider these equivalent fractions: 2/3 = 4/6 = 8/12. The symbolic expression does not explain why equivalent fractions represent the same amount. Any fraction can be expressed as an infinite number of equivalent fractions that represent the same quantity and occupy the same position on the number line.įractions are important to measurement, especially where whole units are not precise enough for the purpose. Four tenths are the same quantity of chocolate as two fifths. If the bar was made up of ten pieces then each person might be given two tenths from each bar, giving them four tenths in total. In practical terms the equal share can occur by dividing each of the two bars into fifths, then giving each person one fifth from each bar. Note that the number two fifths, is composed of two units of one fifth. The operation might be recorded as 2 ÷ 5 = 2/5. Sharing two chocolate bars equally among five people requires that the bars be cut into smaller equal parts. Division often requires equal partitioning of ones. Fractions are needed when wholes (ones) are not adequate for a task. When subtracting fractions with unlike denominators – 2/ 5 and 3/ 10 – repeat the procedure from the previous section, but subtracting, not adding in the final step:Įxpand the fractions to their equivalent fractions with a common denominator: 4/ 10 and 3/ 10.Fractions are an extension of whole numbers and integers. If you have fractions with the same denominator, subtract the numerators: If you're wondering how to subtract fractions, and you've read through the previous section How do you add fractions, we have some good news for you: it's pretty much the same! If you're still wondering how adding fractions works, maybe this visual will help? Of course, our fraction calculator deals with all of these scenarios. ➽ 13/ 5 + 3/ 2 = 26/ 10 + 15/ 10 = 41/ 10įinally, you can convert your result back into a mixed fraction: That's your new numerator – write it on top of your denominator:Īnalogically, you can find out that 1 1/ 2 = 3/ 2.ĭo the standard addition of fractions with uneven denominators: Multiply the whole number by the denominator: One solution for this kind of problem is to convert the mixed fraction to an improper fraction and sum it up as usual. You want to add two mixed fractions – e.g., 2 3/ 5 and 1 1/ 2 Now that your fractions have the same denominator, you can add them: Your second fraction already has its denominator equal to 10: So, you should multiply the fraction with the denominator equal to 5 (our 1/5) by 2 to get 10 (remember that you must multiply both top and bottom numbers): Then, you need to expand each fraction to have this common denominator as its bottom number: You can use, for example, LCM – the least common multiple to find the common number of your two denominators: LCM(5,10) = 10 Another option is to multiply your denominators and reduce the fraction later. This is a bit more of a complicated case – to add these fractions, you need to find the common denominator. The fractions have unlike denominators – e.g., 2/ 5 and 3/ 10 This is the most straightforward case all you need to do is to add numerators (top numbers) together and leave the denominator as is, e.g.: The denominator (bottom number) is the same in both fractions – e.g., 3/ 5 and 1/ 5 When it comes to adding fractions, there are three scenarios:
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