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:


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.
Extensiongimpppa.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.
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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