Adding and subtracting fractions

Hello, and welcome to Myriora Maths! What is two sevenths add three sevenths? And what is one half add one third? Adding fractions is easy, once the pieces are the same size. Let's see how!

Two sevenths add three sevenths. The pieces are all sevenths, the same size. Two pieces add three pieces is five pieces: five sevenths. The bottom number stays the same, because the pieces don't change size!

Taking away works the same way. Five eighths take away two eighths: five pieces, take away two pieces, leaves three pieces. Three eighths!

Now one half add one third. Halves and thirds are different sizes, so we can't just count the pieces. Cut both into sixths, because six is in the two and the three times tables. One half is three sixths, and one third is two sixths. Three sixths add two sixths is five sixths!

Taking away works the same. Three quarters take away one half. Change the half into quarters: two quarters. Three quarters take away two quarters is one quarter.

Let's try one together. What is one quarter add one half? Say it out loud!

Change the half into quarters: two quarters. One quarter add two quarters is three quarters!

Here's a question that catches lots of people. What is one half add one third? Some people add the tops and add the bottoms, and get two fifths. But two fifths is less than one half! Make the pieces the same size, and it's five sixths.

Your turn! What is two thirds add one quarter? Pick the right card. You've got twenty seconds, or pause the video. Go!

Time's up! Twelve is in the three and the four times tables. Two thirds is eight twelfths, and one quarter is three twelfths. Eight add three is eleven: eleven twelfths!

Quick review. When the bottoms are the same, add or take away the tops. The bottom stays the same, because the pieces don't change size. When the bottoms are different, change them to the same first. And never add the bottoms! See you next time!