Fraction skills using the calculator

Fraction skillsusing the calculator

(b) How many bundles of 4 in 9? 9  4 = 2.25 There are two whole bundles of 4 plus another quarter of a bundle (i.e. 2.25 bars) What concrete real-world situations are modelled for example, by the fraction ? Two possible situations: Interpreting fractions • 9 ‘Lion Bars’ are divided between 4 students. • 9  4 = 2.25 • Each student receives two bars as well as an extra quarter bar (i.e. 2.25 bars)

‘Pen and Paper vs. Calculator When introducing the concept of a fraction as division and the resultant ‘answer’ as a decimal, students should be encouraged to carry out pen and paper calculations before using the calculator, for example: ‘Pen and Paper: = 9.00  4 = 2.25 ‘Calculator’: key in 9 [] 4 to get 2.25

Use of [] and [a b/c] keys • As already shown, can be keyed in using the [] key and the answer is given in decimal format. 9  4 = 2.25 • can also be keyed in using the [a b/c] key and here the answer is given in mixed-number or ‘fraction format’. • 9[a b/c]4 = 2  1  4 Note that 2  1  4 is a calculator output meaning 2¼

Changing fractions to decimals and back again The calculator has been programmed to perform ‘fraction to decimal’ or ‘decimal to fraction’ conversions automatically. We already had: 9[a b/c]4 = 2  1  4 2  1  4 Pressing the [a b/c] key coverts this output to 2.25 Pressing the [a b/c] key again and it is coverted back to 2  1  4

Mixed numbers Top heavy fraction • 2  1  4 is a mixed number • To convert it to a top heavy fraction, usethe[d/c] button which is [shift] [a b/c] i.e.2  1  4 [shift] [a b/c] produces 9 4 • Use [shift] [a b/c] repeatedly to alternate between mixed number output and top-heavy fraction output

Adding fractions • ‘Pen and paper’ approach is essential for: (a) mathematical understanding and (b) developing approaches to operating on algebraic fractions. • Have a look at the next slide 

Adding Fractions: ‘Pen and Paper’ approach

Operating on fractions using a calculator • Use calculator to add: +Key sequence 1 [a b/c] 2 [+] 2 [a b/c] 3 produces output 1  1  6 • Use calculator to subtract: - Key sequence 2 [a b/c] 3 [-] 1 [a b/c] 2 produces output 1  6

Operating on fractions using a calculator • Use calculator to multiply: xKey sequence 1 [a b/c] 2 [x] 2 [a b/c] 3 produces output 1  3 • Use calculator to divide:Key sequence 1 [a b/c] 2 [] 2 [a b/c] 3 produces output 3  4

Fractions and the x2key • Evaluate: • ‘Key as you see’ approach incorrectly produces 20 • ‘Separate approach’ (separate top, separate bottom) is safer at this level of complexity as you will see on the next slide

The ‘Separate’ approach! Evaluate: Top: Key sequence 4 [(] 1 [+] 2 [)] [x2] Numerator output is: 36 Bottom: Key sequence 3 [x2] [+] 4 [x2] Denominator output is: 25

The ‘Separate’ approach! (cont’d) Once numerator and denominator have been calculated, a student has the choice of using [] key or [a b/c] key i.e. 36  25 = 1.44decimal format 36 [a b/c] 25 = 1  11  25fraction format

Fraction skills using the calculator