Equivalent and comparing fractions (grade 3) · lesson

Same amount, new name

💡 Cutting each piece into smaller equal pieces gives more pieces but the same amount.

Shade 1/4 of a bar. Now cut each fourth in half. The bar has 8 parts, and 2 are shaded. So 1/4 = 2/8.

This works backward too. 2 eighths join to make 1 fourth.

A fraction is half when its top is half of its bottom, like 4/8.

🧠 Let's work it out

Find the missing top: 1/4 = ?/8.

What do you think comes next?

💡 One whole is all its parts, so a whole number can be written as a fraction.

When the top and bottom match, you have all the parts. So 5/5 = 1.

Two wholes cut in halves make 4 halves. So 2 = 4/2. For more wholes, times the number of wholes by the parts in each.

4/1 is not 1 whole. Each whole has just 1 part, so 4/1 is 4 wholes.

🧠 Let's work it out

Find the missing top: 4 = ?/2.

What do you think comes next?

💡 When two fractions have the same bottom, the one with more pieces is bigger.

Fractions with the same bottom number have pieces of the same size.

So just compare the tops. More pieces of the same size is more.

🧠 Let's work it out

Which is greater, 3/6 or 4/6?

What do you think comes next?

💡 When two fractions have the same top, the one with the smaller bottom has bigger pieces, so it is bigger.

A bigger bottom number means the whole is cut into more pieces. More pieces means each piece is smaller.

So 2/3 is more than 2/8. Both have 2 pieces, but thirds are much bigger than eighths.

🧠 Let's work it out

Which is less, 1/2 or 1/8?

What do you think comes next?