Different Shapes, Same Fractions

Different Shapes, Same Fractions exercise

• Can you find the shapes with the same shaded fractions?

  Hints

  Can you work out what fraction of each shape is shaded before finding a matching one? Look at the total number of parts to help.

  In this example, $\frac{1}{2}$ of the shape is shaded as 1 of 2 equal parts is shaded.

  Solution

  • The square and the rectangle both had $\frac{1}{4}$ shaded.
  • The circle and the triangle both had $\frac{1}{3}$ shaded.
  • The star and the pentagon both had $\frac{1}{5}$ shaded.
  • The heart and the hexagon both had $\frac{1}{2}$ shaded.

• Can you assign the shape to the matching fraction?

  Hints

  How many parts has each shape been split into? That is the denominator.

  How many parts are shaded in? That is the numerator.

  For example, this circle has been split into three equal parts and one part is shaded, so it would be assigned to $\frac{1}{3}$.

  Solution

  • Find the number of equal parts the shape has been split into; this is the denominator.
  • Find the number of parts that have been shaded; this is the numerator.

• Which is the correct shape?

  Hints

  How many parts is the shape split into? This should be the same as the denominator.

  How many parts are shaded? This should be the same as the numerator.

  Remember:

  • the top number is the numerator.
  • the bottom number is the denominator.

  Solution

  The shapes that should have been highlighted are:

  • $\frac{1}{6}$ - the circle, as it is split into six equal parts and one is shaded in.
  • $\frac{3}{5}$ - the star, as it is split into five equal parts and three are shaded in.
  • $\frac{4}{7}$ - the hepatgon, as it is split into seven equal parts and four are shaded in.
  • $\frac{3}{5}$ - the rectangle, as it is split into ten equal parts and seven are shaded in.

  These shapes were incorrect because:

  • The hexagon had only 2 parts shaded.
  • The pentagon had only 2 parts shaded.
  • The rectangle on the third row was only split into 6 equal parts.
  • The square was only split into 8 equal parts.

• Which fractions are being represented?

  Hints

  Find out how many equal parts the shape has been split into and how many parts are shaded.

  Remember:

  • the numerator (top number) represents the shaded parts.
  • the denominator (bottom number) represents the total number of equal parts.

  Solution

  Here are the correct fractions:

  Circle

  • The circle has 7 equal parts and 3 are shaded.
  • The matching fraction is $\frac{3}{7}$.

  Rectangle (top row)

  • The rectangle has 9 equal parts and 5 are shaded.
  • The matching fraction is $\frac{5}{9}$.

  Hexagon

  • The hexagon has 6 equal parts and 2 are shaded.
  • The matching fraction is $\frac{2}{6}$.

  Square

  • The square has 4 equal parts and 2 are shaded.
  • The matching fraction is $\frac{2}{4}$.

  Rhombus

  • The rhombus has 8 equal parts and 6 are shaded.
  • The matching fraction is $\frac{6}{8}$.

  Rectangle (bottom row)

  • The rectangle has 8 equal parts and 2 are shaded.
  • The matching fraction is $\frac{2}{8}$.

• Which shapes are $\frac{1}{3}$ shaded?

  Hints

  $\frac{1}{3}$ has a numerator of 1, so you are looking for shapes that only have 1 part shaded.

  $\frac{1}{3}$ has a denominator of 3, so you are looking for shapes that are split into 3 equal parts.

  Solution

  This circle and triangle both have $\frac{1}{3}$ shaded.

  They are both split into 3 equal parts and both have 1 part shaded.

• Find the pairs.

  Hints

  Create a fraction for each shape by finding how many equal parts the shape is split into and how many are shaded.

  Remember:

  • the shaded parts represent the numerator (top number)
  • the total number of equal parts represent the denominator (bottom number)

  Can this fraction be simplified? To simplify a fraction we look for a factor that both the numerator and denominator share.

  For example, we could simplify $\frac{2}{4}$ to $\frac{1}{2}$ by dividing both the numerator and the denominator by 2.

  $\frac{6}{8}$ of the circle is shaded. If we divide both the numerator and denominator by 2, what do we get?

  Solution

  $\frac{3}{4}$

  • The circle and the rhombus should have been highlighted in green.
  • The circle has $\frac{6}{8}$ shaded which can be simplified to $\frac{3}{4}$ by dividing the numerator and denominator by 2.
  • The rhombus has $\frac{9}{12}$ shaded which can also be simplified to $\frac{3}{4}$ by dividing the numerator and denominator by 3.

  $\frac{1}{3}$

  • The triangle and the tall rectangle should have been highlighted in blue.
  • The triangle has $\frac{1}{3}$ shaded which cannot be simplified further.
  • The tall rectangle has $\frac{3}{9}$ shaded which can be simplified to $\frac{1}{3}$ by dividing the numerator and denominator by 3.

  $\frac{1}{5}$

  • The star and the wide rectangle should have been highlighted in violet.
  • The star has $\frac{1}{5}$ shaded which cannot be simplified further.
  • The wide rectangle has $\frac{3}{15}$ shaded which can be simplified to $\frac{1}{5}$ by dividing the numerator and denominator by 3.

  $\frac{2}{3}$

  • The square and the hexagon should have been highlighted in yellow.
  • The square has $\frac{6}{9}$ shaded which can be simplified to $\frac{2}{3}$ by dividing the numerator and the denominator by 3.
  • The hexagon has $\frac{4}{6}$ shaded which can also be simplified to $\frac{2}{3}$ by dividing the numerator and denominator by 2.