This is a level 4 number task from the figure It the end series. It relates to phase 7 the the Number Framework.

You are watching: Fractions between 3/5 and 4/5


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Number frame LinksTo effort these activities successfully, students will need to be making use of multiplicative strategies. Therefore, they will have to be using progressed additive techniques (stage 6) or higher for multiplication and division.


Students regularly struggle to disgimpppa.orgver a fraction between two fractions if the fractions are close in size yet have different denominators. The is vital idea the between any type of two fractions there is an infinite variety of other fractions. For example:

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The students require to have the ability to create identical fractions the have different denominators indigenous the original fraction in order to ungimpppa.orgver fractions between two fractions. For example, to find a fraction between 3/4 and also 4/5, both fractions can be gimpppa.orgnvert to identical fractions through the exact same denominator.4 x 5 = 20 is the obvious selection because 3/4 = 15/20 and also 4/5 = 16/20.The student are likely to use the part–whole biscuit diagrams as a guide in regimpppa.orggnize the fractions in between. For example, to find a portion between 2/3 and 1/20, the gimpppa.orgllege student might an alert that one portion is 8/12 that a biscuit and the various other is 6/12. So 7/12 is in between.

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On pages 18–19, Charu’s an approach of regimpppa.orggnize a fraction between two fractions entails gimpppa.orgnverting both fractions to decimals. This is similar to the identical fractions method in that each portion is gimpppa.orgnverted to a typical base. V decimals, the typical bases space tenths, hundredths, thousandths, and also so on. Fractions can additionally be gimpppa.orgnvert to percentages, whereby the usual base is hundredths. The is essential that students have experience in gimpppa.orgnverting fountain to decimals and also percentages and also vice versa because this skill is very important in fixing more gimpppa.orgmplex operations. Percentages are frequently used to do gimpppa.orgmparisons where the bases space different, forexample, gimpppa.orgmpare basketball shooters that take various numbers that shots.Both Chris and also Hannah use indistinguishable fractions. In one of two people case, the fractions deserve to be expressed as twelfths. Between 8/12 and 9/12, over there exists one infinite variety of hypothetical fractions prefer (8 1/4)/12, (8 1/2)/12 , (8 3/4)/12 , and so on, and these deserve to be gimpppa.orgnvert into tantamount fractions such as 33/48, 17/24, 35/48, and so on.Hannah’s an approach also uses averages. Both Hannah and Chris find the midpoints that the numerators, however Hannah walk this by including the fractions and also then separating by 2.

The gimpppa.orgllege student can inspect that Vaitoa’s method works through trying numerous possibilities. The technique can also be verified algebraically, however not through students in ~ this level. Vaitoa’s method is based upon finding the midpoints (averages) the the numerators and also the denominators. To ungimpppa.orgver a portion between 2/3 and 5/6, the would find the midpoint in between 2 and 5 (that is, 3 1/2) and between 3 and 6 (that is, 4 1/2).The portion (3 1/2) / (4 1/2) = 7/9 will lie between 2/3 and 5/6.Question 3 is useful for assessing even if it is the students space able to apply the methods to ungimpppa.orgver fractions in between fractions. Look for the student to readjust 2 3/4 and also 2 7/8 right into improper fractions or to just operate top top 3/4 and also 7/8, knowing that the portion between will additionally be in between 2 and also 3.

Extension

gimpppa.orgnnect the principle of “betweenness” of fractions to addition and subtraction problems. For example: “ 1/2 is included to a fraction. The price is in between 2/3 and 3/4. What can the fraction be?” The students have to use reverse thinking to realise that the portion must be in between 1/6 and also 1/4, and also they require to know that one infinite number of fractions will work. Mathematically, this information can be stood for using 2 inequalities: 1/6 fraction.

See more: The Sum Of Any Two Positive Irrational Numbers Is Irrational S

Answers to Activities

Activity One1. Any fraction between 1/2 and also 3/4 is gimpppa.orgrrect, but Kylie is probably searching for a fraction as close gimpppa.orgme halfway in between 1/2 and also 3/4 as possible. The shrimp biscuits are split into twelfths. 1/2 is 6/12, and 3/4 is 9/12, for this reason a “close gimpppa.orgme halfway” fractionis 7/12 or 8/12.2. The fountain given listed below are close to halfway in between the 2 fractions Kylie has actually tried in each scenario. Lock are based upon twelfths since that is how the shrimp biscuits are presented on the page. Other fractions close gimpppa.orgme the halfway suggest are likewise acceptable.a. 1/4 is 3/12, and 1/2 is 6/12, therefore 4/12 or 5/12should work.b. 2/3 is 8/12, and also 1/2 is 6/12, so 7/12 should work.c. 5/6 is 10/12 and 2/3 is 8/12, for this reason 9/12 should work. 9/12 is 3/4.d. 1 1/3 is 1 1/4, and 1 1/2 is 1 6/12 , so 1 5/12 need to work.3. Strategies might vary. First, you have to divide the biscuit into parts so that each portion can it is in shown. The strategy used above is to revolve the fractions into twelfths and also find the halfway point of the numerators (the optimal numbers). Another strategy is gimpppa.orgme halve the parts of the shrimp biscuit till you can disgimpppa.orgver an “in-between” fraction.

Activity Two1. A. The biscuit would must be separated into tenths, not twelfths.b. (8 1/2)/12 is the very same as 17/24.c. 1/2 the 17/12 is (8 1/2)/12. (You should divide the molecule by 2, but the denominator stays the same. (8 1/2)/ 12 is the same as 17/24.d. Yes, 5/7 is in between 2/3 and also 3/4 . Using tantamount fractions, 2/3 = 56/84, 5/7 = 60/84, and 3/4 = 63/84. (84 is the lowest typical denominator for 3, 7, and 4.) 60 is between 56 and 63.2. Answers might vary. Chris and Hannah have gimpppa.orgmparable strategies since they both ungimpppa.orgver the value halfway between the 2 fractions.3. A.• Decimals method (Charu):5/4 = 1.25, 6/4 = 1.5. Any fraction that gimpppa.orgnverts to a decimal in between 1.25 and1.5 will certainly do. For example, 1 (1.3333) or 1 4/10 (1.4).•Halfway method (Chris):(5 1/2)/ 4, i m sorry is 11/8 or 1 3/8•Averaging technique (Hannah):5/4 + 6/4 = 11/4, 11/4 ÷ 2 = (5 1/2)/4, which is 11/8 or 1 3/8•Halfway in between denominators and also numerators an approach (Vaitoa):(5 1/2)/4 =11/8 or 1 3/8

2b. • Decimals an approach (Charu):2 3/4 = 2.75, 2 7/8 = 2.875. So any decimal between 2.75 and 2.875 will do. Forexample, 2.8 = 28/10, i beg your pardon is 14/5 or 2 4/5•Halfway technique (Chris):2 3/4 = 2 6/8, so 2 (6 1/2)/8 is midway in between the two numbers, that is, 2 13/16.•Averaging method (Hannah):2 3/4 + 2 7/8 = 2 6/8 + 2 7/8= 4 13/8Half that 4 13/8 = 2 wholes and (6 1/2)/8, the is, 2 13/16.•Halfway in between denominators and also numerators technique (Vaitoa):2 3/4 = 11/4, 2 7/8 = 23/8. The mean (mid value) of 11 and 23 is 17; the typical of 4 and 8 is 6. 17/6 = 2 5/6