Question

Change the following mixed numbers to improper fractions. \(8 \frac{3}{5}=\) ______

Short answer

The improper fraction is \(\frac{43}{5}\).

Step-by-step solution

Understand the Problem

We need to convert the mixed number \(8 \frac{3}{5}\) into an improper fraction. A mixed number consists of a whole number and a proper fraction.

Multiply the Whole Number by the Denominator

To begin, multiply the whole number \(8\) by the denominator of the fraction part, which is \(5\). Therefore, \(8 \times 5 = 40\). This step helps us convert the whole part of the mixed number into a fractional form.

Add the Numerator

Next, add the numerator of the fractional part, which is \(3\), to the result obtained in Step 2. Add \(3\) to \(40\) to get \(40 + 3 = 43\). This results in the total numerator of the improper fraction.

Form the Improper Fraction

Finally, place the result from Step 3 over the original denominator of the fraction. This gives us an improper fraction of \(\frac{43}{5}\).

Key concepts

mixed numbers

Mixed numbers are a combination of a whole number and a proper fraction. They look like numbers that haven’t fully made up their mind—they hang between whole and fractional values! For example, in the mixed number \(8 \frac{3}{5}\), the whole number is \(8\) and the fractional part is \(\frac{3}{5}\).

These numbers are useful when you want to express quantities that are more than one, but not entire numbers, like when you have 8 whole pizzas and 3/5 of another. Mixed numbers provide an easy way to visualise fractions because they directly show how much of a whole we have, plus a bit more.

• The whole number tells how many entire wholes there are.
• The fraction indicates how parts of another whole are present.

Understanding mixed numbers is essential because they frequently appear in everyday scenarios, such as in measurements and recipes.

improper fractions

Unlike mixed numbers, improper fractions have numerators that are equal to or greater than their denominators. This makes them look somewhat top-heavy. In mathematical terms, an improper fraction appears as \(\frac{43}{5}\), where \(43\) is the numerator and \(5\) is the denominator.

Improper fractions might seem unusual when compared to proper fractions, but they serve an important purpose in mathematical calculations. They express the same value as mixed numbers but do so by showing all the parts as fractions.

• They're useful for multiplication and division of fractions.
• They simplify algebraic manipulation.

Converting mixed numbers to improper fractions helps maintain consistency and simplicity in various math operations.

numerator and denominator

When dealing with fractions, the terms numerator and denominator come up frequently. Understanding these is crucial to mastering fractions. The numerator is the top number of a fraction, indicating how many parts are being considered. In \(\frac{43}{5}\), \(43\) is the numerator.

The denominator is the bottom number, showing the total number of equal parts into which the whole is divided. In the same fraction, \(5\) is the denominator.

• The numerator tells you the count of parts you have.
• The denominator tells you how many parts make up a whole.

In our example, \(\frac{43}{5}\), the numerator 43 refers to the number of parts, and the denominator 5 shows these parts make up a whole. A good way to remember is: numerator ‘numerates’ the parts, denominator ‘denotes’ the divisors.

fraction conversion steps

Converting mixed numbers to improper fractions involves specific steps. It may seem complex at first, but it's simple when broken down.

1. **Multiply the Whole Number by the Denominator:** This is your first step. If your fraction part is \(\frac{3}{5}\) in the mixed number \(8 \frac{3}{5}\), multiply the whole \(8\) by \(5\) to get \(40\). This step converts the whole number part into a fractional equivalent.

• Calculation: \(8 \times 5 = 40\)

2. **Add the Numerator to the Result:** Next, add the numerator (3) to your result from the previous step (40) to get \(43\).

• Calculation: \(40 + 3 = 43\)

3. **Construct the Improper Fraction:** Finally, take \(43\), your result, as the new numerator. Place \(5\), the original denominator, below to form \(\frac{43}{5}\).Following these steps ensures a smooth conversion from mixed numbers to improper fractions, making handling fractions in calculations much easier!