topic badge
New Zealand
Level 6 - NCEA Level 1

Adding and Subtracting Fractions


Chris, a farmer, would like to know how much land he owns in total. Given that he has one piece of land that is $\frac{1}{3}$13 acres and another that is $\frac{2}{5}$25 acres, how much land is that altogether? To find out, he has to add the two fractions. Adding fractions is something you'll often have to do in your daily life. For example, suppose you ate half of that cake you baked the other day for lunch and ate another quarter for dinner. How much of the cake have you eaten altogether? To find out you'd have to add up the two fractions.

But it is important to keep in mind that adding fractions is different to adding whole numbers. For example, Chris' total land is not $\frac{1}{3}+\frac{2}{5}\ne\frac{1+2}{3+5}$13+251+23+5 acres.

This interactive will help you to visualise adding and subtracting fractions, including getting a common denominator.  

So adding or subtracting fractions uses our skills of finding Lowest Common Multiples, and Equivalent Fractions.  


Question 1

Evaluate: $\frac{3}{4}+\frac{2}{5}$34+25

Think: Find the LCM between $4$4 and $5$5 and find equivalent fractions.  Then we will be able to add them.

Do: The LCM between $4$4 and $5$5 is $20$20

$\frac{3}{4}+\frac{2}{5}$34+25 $=$= $\frac{15}{20}+\frac{8}{20}$1520+820
  $=$= $\frac{23}{20}$2320



Question 2

Evaluate: $\frac{7}{8}-\frac{3}{5}$7835

Think: Before we can add fractions I have to have a common denominator, so I need the lowest common multiple between $8$8 and $5$5.  After some investigation I can see that$40$40, is the lowest common multiple.  I will need to make both fractions with denominators of $40$40.


$\frac{7}{8}-\frac{3}{5}$7835 $=$= $\frac{7\times5}{8\times5}-\frac{3\times8}{8\times5}$7×58×53×88×5  
  $=$= $\frac{35}{40}-\frac{24}{40}$35402440  
  $=$= $\frac{11}{40}$1140  



Question 3

Evaluate $\frac{4}{5}-\frac{4}{7}$4547.

Write your answer in its simplest form.

Question 4

Evaluate $\frac{2}{3}+\frac{4}{5}-\frac{1}{2}$23+4512.

Write your answer in the simplest form possible.





Generalise the properties of operations with rational numbers, including the properties of exponents


Apply algebraic procedures in solving problems

What is Mathspace

About Mathspace