Fractions GCSE lesson: add, subtract, multiply and divide fractions and mixed numbers

Fractions: estimate first

Don't work it out exactly: put it where you think it goes.

1. Without working it out exactly, drag the marker to where 2/3 + 1/4 is on the number line.They drag a marker on a number line from 0 to 2.

Fractions: practice

Estimate first, then work it out. Give fractions in their simplest form. Show your working on paper. The stretch is optional.

Diagnostic question: choose and explain

1. Work out 3/4 ÷ 2/3.
   1. 8/9
   2. 9/8
   3. 1/2
   4. 2

Practice questions

1. 2/5 + 1/3 = ___
2. Work out 3 1/5 − 1 2/3. Type the answer as a fraction or a mixed number, such as 7/4 or 1 3/4.
3. The bar is cut into 12 equal parts. Shade 3/4 of 2/3 of the bar.They shade parts of a bar cut into 12 equal parts.
4. Drag the marker to the answer of 2 ÷ 4/5 on the number line. (How many four-fifths fit in 2?)They drag a marker on a number line from 0 to 4.
5. Work out 5/6 ÷ 2/3, a line at a time. Start each line with x =, and simplify until the last line is x = the answer in its simplest form (a mixed number such as 1 1/4 is fine, written with a space).They solve x = 5/6 / 2/3 line by line, each line checked as they write it.
6. Work out 2 1/2 × 1 1/5, a line at a time. Start each line with x =, make the mixed numbers improper fractions first, and end with x = the answer in its simplest form.They solve x = 2 1/2 × 1 1/5 line by line, each line checked as they write it.
7. Which method does each calculation need? Sort them.They sort 7 items into Same-size parts first and Multiply tops and bottoms and Flip the second, then multiply.
8. Without working it out: is 5/8 ÷ 1/4 more or less than 5/8?
   1. More than 5/8
   2. Less than 5/8
   3. Exactly 5/8
9. A ribbon is 3 3/4 m long. It is cut into pieces each 5/8 m long. How many pieces are there?
10. Ben spends 1/4 of his money on a ticket, then 2/5 of what is left on food. What fraction of his money is left? ___
11. Stretch: 3/4 × ___ = 5/6. Give the missing fraction.

Support: For dividing: keep the first fraction, flip the second, multiply. Then check the size: dividing by a fraction less than 1 gives more than you started with.

Fractions: exit

A picture and a sentence are enough.

1. Use a picture to explain why 1/2 + 1/3 is not 2/5, and give the right answer.

Exit check

A picture and a sentence show who knows why the parts must match.

Students draw two bars of the same length, one in halves and one in thirds, then cut both into the same parts and count.

Fractions: all four operations

Estimate each answer first. Give fractions in their simplest form, as a mixed number where the answer is more than 1. Show your working.