Fraction skills using the calculator

1
Fraction skillsusing the calculator
2
Interpreting fractions

• (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)

• 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)

3
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

4
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.
• 9a b/c4 2 ? 1 ? 4
• Note that 2 ? 1 ? 4 is a calculator output
  meaning 2¼

5
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
• 9a b/c4 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

6
Mixed numbers Top heavy fraction

• 2 ? 1 ? 4 is a mixed number
• To convert it to a top heavy fraction, use the
  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

7
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 ?

8
Adding Fractions Pen and Paper approach
9
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

10
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

11
Fractions and the x2 key

• 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

12
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

13
The Separate approach! (contd)

• 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