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Fractions

Definitions


Hugo is very hungry after playing soccer. His dad baked two identical cakes.
Hugo eats one whole cake:
Then, Hugo is still hungry, so he eats half of the second cake:
How much cake does Hugo eat in total? Write your answer as a fraction.

  • Hugo eats one whole cake and half of another cake.
  • The numerator (top number) shows how many parts Hugo eats: \(3\).
  • The denominator (bottom number) shows how many equal parts make one cake: \(2\).
  • So Hugo eats \(\dfrac{3}{2}\) cakes in total.


Definition Fraction
A fraction includes two numbers: the numerator and the denominator, separated by a bar.

On the number line


  • Hugo is walking along a path.
  • He stops and asks himself, "Where am I?"
  • His father says, "You are at half of the way that is \(\dfrac{1}{2}\)."

Method Representing a Fraction on the Number Line
To represent the fraction \(\dfrac{\textcolor{colordef}{2}}{\textcolor{colorprop}{3}}\) on a number line.
  1. Draw a straight line and mark the points 0 and 1.
  2. Divide the line between 0 and 1 into \(\textcolor{colorprop}{3}\) equal parts.
  3. Count \(\textcolor{colordef}{2}\) parts from 0 and mark the point.

Equivalent Fractions


Mr. Tariel has a cake that he cuts into 3 equal parts. He plans to give 1 part to his son, Louis.
Louis says, "I want 2 pieces!"
His dad replies, "Alright," and cuts each of the 3 parts in half, making 6 smaller equal parts. He then gives Louis 2 of these smaller pieces.
Louis looks at his plate and feels disappointed.
Why is Louis still not happy?

Even though Louis got 2 pieces instead of 1, the total amount of cake he received is the same as before. His dad just cut the cake into smaller pieces.
\(\quad =\quad \)
In fractions: $$\frac{1}{3} = \frac{2}{6}$$


Definition Equivalent Fractions
When you multiply the numerator and the denominator by the same number, the fractions are equals.

Addition and Subtraction


Hugo eats \(\dfrac{2}{4}\) of a cake: and Louis eats \(\dfrac{1}{4}\) of the same cake:
Which fraction of the cake have Hugo and Louis eaten together?

So Hugo and Louis eat \(\dfrac{3}{4}\) of the cake together:


Definition Addition of Fractions with Common Denominators
When we add fractions with common denominators, we keep the denominator the same and add the numerators:
Definition Subtraction of Fractions with Common Denominators
When we subtract fractions with common denominators, we keep the denominator the same and subtract the numerators: