Lesson 3: Decompose non-unit fractions and represent them as a whole number times a unit fraction using tape diagrams.

Property

A non-unit fraction $\frac{a}{b}$ can be expressed as the sum of 'a' unit fractions of $\frac{1}{b}$. This repeated addition is equivalent to multiplying the whole number 'a' by the unit fraction $\frac{1}{b}$.

Examples

Property

A fraction greater than one can be decomposed into a sum representing a whole number and a remaining fraction. For a fraction $\frac{a}{b}$ where $a > b$, it can be expressed as the sum of the parts that make one whole ($b \times \frac{1}{b}$) and the leftover fractional part. For example:

Examples

• $\frac{4}{3} = (3 \times \frac{1}{3}) + (1 \times \frac{1}{3})$
• $\frac{10}{8} = (8 \times \frac{1}{8}) + (2 \times \frac{1}{8})$
• $\frac{7}{4} = (4 \times \frac{1}{4}) + (3 \times \frac{1}{4})$

Explanation

This skill involves breaking down a fraction greater than one, also known as an improper fraction, into two parts. The first part is the group of unit fractions that make one whole. The second part is the group of remaining unit fractions. This decomposition helps to see the mixed number structure within an improper fraction, showing how many wholes it contains and what fraction is left over.