What are Improper Fractions?
An improper fraction is a type of fraction where the numerator (the number on top) is larger than or equal to the denominator (the number at the bottom). This means the fraction represents a value greater than or equal to 1.
Examples of Improper Fractions
$\frac{4}{3}$, $\frac{5}{2}$, $\frac{12}{7}$
In each example, the numerator is greater than the denominator, making them improper fractions.
What are Mixed Numbers?
A mixed number is a combination of a whole number and a proper fraction (where the numerator is smaller than the denominator). Mixed numbers make it easier to visualize quantities that are greater than 1.
Examples of Mixed Numbers
2$\frac{1}{3}$, 3$\frac{2}{5}$, 1$\frac{3}{8}$
Where are they used?
- Measurements – Recipes often use mixed numbers like 1$\frac{1}{2}$ cups of flour.
- Time – Mixed numbers like 1$\frac{1}{4}$ hours (1 hour and 15 minutes) are common.
- Construction and Crafting – Measurements like 2$\frac{3}{8}$ inches or 51$\frac{1}{2}$ feet are frequently used.
Visualizing Improper Fractions and Mixed Numbers
To help understand the relationship between improper fractions and mixed numbers, imagine you have a pizza:
- Improper fraction: If you cut a pizza into 4 slices and eat 9 slices, you ate more than 1 pizza (that’s $\frac{9}{4}$).
- Mixed number: This can be written as 2 pizzas and 1 slice, or 2$\frac{1}{4}$.
Converting Improper Fractions to Mixed Numbers
To convert an improper fraction to a mixed number:
- Divide the numerator by the denominator. The quotient becomes the whole number.
- The remainder becomes the numerator of the fraction, while the denominator stays the same. Hence, the fraction part is the remainder by the divisor.
The mixed number is Q$\frac{R}{D}$.
Example 1
Convert $\frac{7}{3}$ to a mixed number.
Divide 7 by 3, which equals 2 with a remainder of 1.
So, $\frac{7}{3}$ = 2$\frac{1}{3}$
Example 2
Convert $\frac{13}{4}$ to a mixed number.
Divide 13 by 4, which equals 3 with a remainder of 1.
So, $\frac{13}{4}$ = 3$\frac{1}{4}$
Converting Mixed Numbers to Improper Fractions
To convert a mixed number to an improper fraction:
- Multiply the whole number by the denominator.
- Add the result to the numerator of the fraction.
- Keep the denominator the same.
Example 1:
Convert 4$\frac{3}{5}$ to an improper fraction.
Multiply 4 (whole number) by 5 (denominator). 4 x 5 = 20
Add the numerator. 20 + 3 = 23
So, 4$\frac{3}{5}$ becomes $\frac{23}{5}$.
Example 2:
Convert 6$\frac{1}{4}$ to an improper fraction.
Multiply 6 (whole number) by 4 (denominator). 6 x 4 = 24
Add the numerator. 24 + 1 = 25
So, 6$\frac{1}{4}$ becomes $\frac{25}{4}$.
- Mixed Numbers are easier to interpret visually, especially when dealing with quantities greater than one.
- When adding or subtracting fractions, it’s common to first convert mixed numbers into improper fractions for ease of calculation.
- Improper fractions are also used in multiplication and division because they simplify calculations. They are easier to work with than mixed numbers in such cases.
FAQs on Improper and Mixed Fractions
- Divide the numerator by the denominator to get the whole number. The remainder becomes the numerator, with the same denominator. We can easily remember by the expression Q R/D, where Q is the quotient, R is the remainder and D is the divisor.