Fraction skills using the calculator

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Fraction skills using 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:.

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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.

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
• ‘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 
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