Illustrating Addition and Subtraction of Proper Fractions
- Lew W.S.
Aim of Applet This applet illustrate the addition and subtraction of proper fractions of different denominatiors. The need to make up equivalent fractions with same denominators before we can add the numerators and get the resulting fraction is visually demonstrated. The resulting fraction may also need to be reduced to the lowest term where necessary Interactive elements (checkboxes and sliders) Use the 1. Subtract Fraction checkbox to activate the operation of subtraction of proper fractions in the applet.
2. numerator & denominator sliders to change the values of the two proper fractions.
3. FractionSlider checkbox to show the numerator & denominator sliders for the two fractions to be added/subtracted.
4. EquivalentFraction checkbox to reveal more diagrams and illustrate concept of creating equivalent fractions for adding subtracting fractions with a common denominator.
5. Evaluate Result checkbox to show the arithmetic operations of the equivalent fractions and the resulting fraction in its lowest terms.
2. Enter the numerators and denominators into the input boxes below (beige colored boxes)
3. Click on the "Next Step" button (green) to go through the process of forming equivalent fractions,
combining into a single fraction and adding numerators for fractions with common denominators
4. When the "<= Move Pie =>" slider appears, you can use it to shift the blue fraction pie towards or away
from the red fraction pie.
6. ShiftCircleLeftRight slider to shift blue circle towards red circle on the right!
7. MixedNumberResult slider to show the resulting fraction in mixed number format.
5. DetachPie slider to show visually the resulting fractions from
(i) addition of proper fractions resulting in proper fractions, improper fraction or mixed numbers.
(ii) subtraction of proper fractions resulting in remaining proper fractions or negative fractions.
6. The "Next Step" button changes to "Start over with New Inputs" and input boxes reappear to allow
for new inputs.
Prior knowledge of pupils
1 Pupils know the terms fraction, proper fractions, improper fractions, whole and mixed numbers
2. Pupils know addition and subtraction of whole numbers and proper fractions of same denominator
3. Pupils know idea of equivalent fractions
4. Pupils may or may not know the idea of lowest common multiple, but are be able to grasp the visual idea of having fraction parts of the same size and hence the concept of equivalent fractions of the same/common denominator
See also https://www.geogebra.org/material/show/id/qwjhd8kx
on comparing fractions by converting to equivalent fractions using common denominators or common numerators!
Questions for Learner : 1. How do we add two fractions of the same/common denominator ? 2. Explain the idea of equivalent fractions 3. How do we add two fractions with different denominators ? 4. How do we find the "right" number of parts to split, so that the parts in both fractions are of the same size ? (From this we get the same/common denominator for both fractions)