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

You are watching: What fraction is between 2/5 and 3/5


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Number structure LinksTo effort these activities successfully, students will must be making use of multiplicative strategies. Therefore, lock will must be using advanced additive strategies (stage 6) or greater for multiplication and also division.


Students often struggle to discover a fraction between 2 fractions if the fractions room close in size but have various denominators. That is an important idea that between any two fractions over there is one infinite number of other fractions. Because that example:

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The students require to have the ability to create equivalent fractions the have different denominators native the original portion in bespeak to uncover fractions between two fractions. For example, to uncover a fraction between 3/4 and also 4/5, both fountain rememberingsomer.comuld be rememberingsomer.comnverted to indistinguishable fractions v the exact same denominator.4 x 5 = 20 is the obvious selection because 3/4 = 15/20 and 4/5 = 16/20.The college student are most likely to use the part–whole biscuit diagrams together a overview in recognize the fountain in between. For example, to discover a fraction between 2/3 and 1/20, the student might notice that one fraction is 8/12 that a biscuit and also the other is 6/12. Therefore 7/12 is in between.

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On pages 18–19, Charu’s method of detect a portion between two fractions entails rememberingsomer.comnverting both fountain to decimals. This is similar to the equivalent fractions technique in that each portion is rememberingsomer.comnverted come a rememberingsomer.commmon base. V decimals, the rememberingsomer.commmon bases space tenths, hundredths, thousandths, and so on. Fractions can also be rememberingsomer.comnverted come percentages, whereby the rememberingsomer.commmon basic is hundredths. The is important that students have actually experience in rememberingsomer.comnverting fractions to decimals and percentages and vice versa due to the fact that this ability is an extremely important in solving an ext rememberingsomer.commplex operations. Percentages are often used to make rememberingsomer.commparisons whereby the bases room different, forexample, rememberingsomer.commparing basketball shooters who take various numbers the shots.Both Chris and also Hannah use identical fractions. In one of two people case, the fractions can be expressed together twelfths. In between 8/12 and also 9/12, there exists an infinite variety of hypothetical fractions favor (8 1/4)/12, (8 1/2)/12 , (8 3/4)/12 , and so on, and also these deserve to be rememberingsomer.comnverted into tantamount fractions such together 33/48, 17/24, 35/48, and also so on.Hannah’s method also supplies averages. Both Hannah and also Chris find the midpoints that the numerators, yet Hannah go this by including the fractions and also then dividing by 2.

The students can inspect that Vaitoa’s technique works through trying lots of possibilities. The an approach can additionally be confirmed algebraically, however not by students at this level. Vaitoa’s technique is based upon finding the midpoints (averages) of the numerators and the denominators. To discover a fraction between 2/3 and also 5/6, he would uncover the midpoint in between 2 and also 5 (that is, 3 1/2) and between 3 and also 6 (that is, 4 1/2).The fraction (3 1/2) / (4 1/2) = 7/9 will certainly lie in between 2/3 and 5/6.Question 3 is helpful for assessing even if it is the students room able to apply the techniques to discover fractions between fractions. Look for the students to readjust 2 3/4 and 2 7/8 right into improper fractions or to simply operate on 3/4 and also 7/8, discovering that the fraction between will likewise be between 2 and also 3.

Extension

rememberingsomer.comnnect the rememberingsomer.comncept of “betweenness” of fountain to enhancement and individually problems. For example: “ 1/2 is included to a fraction. The answer is in between 2/3 and 3/4. What can the portion be?” The students must use reverse thinking to realise the the fraction must be in between 1/6 and 1/4, and they require to know that an infinite number of fractions will certainly work. Mathematically, this information deserve to be stood for using 2 inequalities: 1/6 fraction.

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Answers to Activities

Activity One1. Any fraction between 1/2 and 3/4 is rememberingsomer.comrrect, yet Kylie is probably searching for a portion as close come halfway in between 1/2 and also 3/4 together possible. The shrimp biscuits are separated into twelfths. 1/2 is 6/12, and 3/4 is 9/12, so a “close come halfway” fractionis 7/12 or 8/12.2. The fountain given below are close come halfway in between the two fractions Kylie has tried in every scenario. They are based on twelfths because that is exactly how the shrimp biscuits are presented on the page. Various other fractions close to the halfway suggest are additionally 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, therefore 7/12 must work.c. 5/6 is 10/12 and also 2/3 is 8/12, for this reason 9/12 have to work. 9/12 is 3/4.d. 1 1/3 is 1 1/4, and also 1 1/2 is 1 6/12 , therefore 1 5/12 should work.3. Strategies might vary. First, you need to divide the biscuit right into parts so that each fraction can it is in shown. The strategy used above is to revolve the fractions into twelfths and also find the halfway suggest of the numerators (the optimal numbers). One more strategy is come halve the parts of the shrimp biscuit until you can discover an “in-between” fraction.

Activity Two1. A. The biscuit would should be divided 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 need to divide the numerator by 2, yet the denominator continues to be the same. (8 1/2)/ 12 is the exact same as 17/24.d. Yes, 5/7 is in between 2/3 and 3/4 . Using indistinguishable fractions, 2/3 = 56/84, 5/7 = 60/84, and also 3/4 = 63/84. (84 is the lowest rememberingsomer.commmon denominator because that 3, 7, and also 4.) 60 is between 56 and also 63.2. Answers may vary. Chris and also Hannah have comparable strategies because they both find the worth halfway in between the 2 fractions.3. A.• Decimals technique (Charu):5/4 = 1.25, 6/4 = 1.5. Any portion that rememberingsomer.comnverts come a decimal in between 1.25 and1.5 will certainly do. Because that example, 1 (1.3333) or 1 4/10 (1.4).•Halfway method (Chris):(5 1/2)/ 4, which 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 between denominators and 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 type of decimal in 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 method (Chris):2 3/4 = 2 6/8, so 2 (6 1/2)/8 is midway between the 2 numbers, that is, 2 13/16.•Averaging technique (Hannah):2 3/4 + 2 7/8 = 2 6/8 + 2 7/8= 4 13/8Half the 4 13/8 = 2 wholes and (6 1/2)/8, that is, 2 13/16.•Halfway between denominators and also numerators method (Vaitoa):2 3/4 = 11/4, 2 7/8 = 23/8. The typical (mid value) that 11 and also 23 is 17; the median of 4 and also 8 is 6. 17/6 = 2 5/6