Fractions with the Same Numerator

Fractions with the Same Numerator exercise

• Which fraction is bigger?

  Hints

  Look at the image of Axel and Tank's fish treat. Who has the smaller pieces?

  This treat has been broken into six pieces, the denominator is 6. Is each piece of the treat that is $\frac1 6$, larger or smaller than the pieces that are in thirds?

  The top number in a fraction is the numerator and the bottom number is the denominator.

  Solution

  When the whole is the same, a smaller number in the denominator means the fraction will be larger.

  For example, even though both $\frac1 2$ and $\frac1 3$ have the same numerator, the smaller fraction is $\mathbf{\frac{1}{3}}$.

  This is because the larger the denominator, the smaller the fraction.

• Treats for Sparky.

  Hints

  Look at the denominators. Does the larger fraction have a bigger or a smaller denominator when the numerators are the same?

  Look at the size of these fish treats and the size of the denominator. What do you notice?

  Try drawing fraction bars of identical size to compare the fractions.

  Solution

  The biggest piece will be from the food that is cut into the fewest pieces. Therefore the pieces that have been cut into three parts, where each one is $\mathbf{\frac{1}{3}}$, will be the largest.

• Comparing fractions of sandwiches.

  Hints

  Look at how many parts the sandwich has been cut into - this is the denominator. The larger the denominator, the smaller the piece.

  Look at these two sandwiches. One has been cut into thirds, one has been cut into fifths. Compare a piece of each sandwich. Which would be larger?

  Solution

  The order of the parts of the sandwiches from largest denominator to smallest:

  • The sandwich cut into eight parts: $\mathbf{\frac{1}{8}}$

  • The sandwich cut into six parts: $\mathbf{\frac{1}{6}}$

  • The sandwich cut into four parts: $\mathbf{\frac{1}{4}}$

  • The sandwich cut into three parts: $\mathbf{\frac{1}{3}}$

• Compare the fractions with the same numerator.

  Hints

  Look at the denominator. What does a larger denominator mean when the numerators are the same?

  When the numerators are the same, the larger the denominator, the smaller the part.

  Begin by finding the smallest fraction for Monday. This will be the fraction with the largest denominator.

  On Friday Sparky gets the most food, so this will be the fraction with the smallest denominator.

  Solution

  These are the correct pairs:

  Monday = $\frac3 9$

  Tuesday = $\frac3 7$

  Wednesday = $\frac3 5$

  Thursday = $\frac3 4$

  Friday = $\frac3 3$

  Each day Sparky always gets three parts (the numerator), since the numerator is the same each time, we only need to compare the denominators.

  The larger the denominator, the smaller the fraction. So we order the pieces from Monday to Friday, with the fraction that has the largest denominator first, and the fraction with the smallest denominator last, as this piece will be the biggest.

• Help Sparky choose the bigger piece.

  Hints

  Look at the denominator. When the numerators are the same, the larger the denominator, the smaller the fraction.

  In these two fractions: $\frac1 3$ and $\frac1 2$, which is the bigger fraction? Look at its denominator.

  Solution

  $\frac1 4$ is larger than $\frac1 6$. The symbol to show this is $\frac1 4$ > $\frac1 6$. When both pieces of food are broken up, the one that is broken into more pieces, means that each piece ends up smaller.

• Compare the fractions.

  Hints

  Try drawing fraction bars to compare the two fractions.

  Remember that when the numerators are the same, we only need to look at the denominators to compare the fractions.

  When the numerators are the same, the larger the denominator, the smaller the fraction.

  Solution

  • $\frac2 8$ < $\frac2 3$

  
  

  • $\frac4 9$ < $\frac4 6$

  
  

  • $\frac2 8$ > $\mathbf{\frac{2}{9}}$

  
  

  • $\frac{4}{11}$ > $\frac{4}{12}$

  
  

  • $\frac{7}{10}$ > $\mathbf{\frac{7}{12}}$

  
  

  • $\frac8 9$ < $\frac8 5$