Lesson 25: Writing Division Answers as Mixed Numbers

New Concept

Instead of using remainders, division answers can be written as mixed numbers. The remainder becomes the numerator, and the divisor becomes the denominator.

What’s next

Next, you will apply this skill through worked examples, solving word problems and converting improper fractions into their mixed number equivalents.

Property

When dividing, the answer can be written as a mixed number where the remainder is the numerator and the divisor is the denominator. For example, in $15 \div 4$, the result is $3\frac{3}{4}$.

Examples

• A 15-inch length of ribbon cut into 4 equal lengths results in pieces that are $3\frac{3}{4}$ inches long.
• Dividing 100 percent into 3 equal parts gives you $33\frac{1}{3}$ percent for each part.
• If 10 cookies are shared equally among 3 people, each person receives $3\frac{1}{3}$ cookies.

Explanation

Some problems need more than just a remainder! Imagine sharing 15 inches of ribbon among 4 friends. You can't have a 'remainder' of ribbon. Instead, you get practical, real-world answers. By turning the remainder into a fraction, we can describe exactly how big that leftover piece is, making division useful for everyday situations.

Property

We find multiples of a number by multiplying the number by 1, 2, 3, 4, 5, 6, and so on.

Examples

The first four multiples of 9 are: $9, 18, 27, 36$.
The tenth multiple of 6 is $10 \times 6 = 60$.
The first five multiples of 11 are $11, 22, 33, 44, 55$.

Explanation

Think of multiples as the 'greatest hits' from a number's multiplication table! They are all the answers you get when you multiply your number by any whole number, starting with one. It is like skip-counting, but on a super-powered level. Knowing multiples helps you spot patterns and is a key skill for division and finding common denominators.

Property

The fraction bar in an improper fraction like $\frac{a}{b}$ serves as a division symbol. To convert it to a mixed number, you divide the numerator ($a$) by the denominator ($b$).

Examples

To convert $\frac{27}{5}$: $27 \div 5 = 5$ with a remainder of 2, so the mixed number is $5\frac{2}{5}$.
To convert $\frac{19}{4}$: $19 \div 4 = 4$ with a remainder of 3, so the mixed number is $4\frac{3}{4}$.
To convert $\frac{31}{7}$: $31 \div 7 = 4$ with a remainder of 3, so the mixed number is $4\frac{3}{7}$.

Explanation

An improper fraction is like a top-heavy suitcase—the number on top is bigger! To make it easier to handle, you repack it. Just divide the top number by the bottom one. The whole number result is how many full bags you have, and the remainder becomes the small fraction left over. It is just a neater way to write the same value.