Question

Find a decimal equivalent for each fraction or mixed number. \(\frac{33}{24}\)

Short answer

1.375

Step-by-step solution

- Simplify the Fraction

First, simplify the fraction \(\frac{33}{24}\). Find the greatest common divisor (GCD) of both the numerator and denominator. The GCD of 33 and 24 is 3. Therefore, \(\frac{33}{24} = \frac{33 \div 3}{24 \div 3} = \frac{11}{8}\).

- Divide the Numerator by the Denominator

To convert the simplified fraction \( \frac{11}{8} \) to a decimal, divide 11 by 8. \( 11 \div 8 = 1.375 \).

Key concepts

Fraction Simplification

Simplifying a fraction is the process of reducing the fraction to its simplest form. This means making the numerator and denominator as small as possible, while still keeping the same value for the fraction. In our example, \(\frac{33}{24}\), we first need to find a common factor for both 33 and 24. When both numerator and denominator are divided by their greatest common divisor (GCD), the fraction is in its simplest form.

For instance, if you have \(\frac{33}{24}\), you should look for the biggest number that divides both numbers exactly. Simplifying a fraction really helps in making mathematical calculations easier!

Greatest Common Divisor (GCD)

The greatest common divisor (GCD) of two numbers is the largest number that can divide both of them without leaving a remainder. To determine the GCD of 33 and 24, you need to list all the factors of both numbers.

For 33, the factors are 1, 3, 11, and 33. For 24, the factors are 1, 2, 3, 4, 6, 8, 12, and 24. The largest number that appears in both lists is 3, so the GCD of 33 and 24 is 3.

Once you identify the GCD, you can simplify the fraction by dividing both the numerator and the denominator by this number. This makes your fraction simpler and easier to work with.

Long Division

Long division is a method used to divide larger numbers. For example, to convert the simplified fraction \(\frac{11}{8}\) into a decimal, you would use long division to divide 11 by 8.

Here’s how it works: \(\begin{array}{r|l} 8 & 11.000 \ &\begin{array}{r} 1.375 \ \end{array}\begin{array}{r} -\frac{8}{8} \ \end{array}\begin{array}{r} 30 \ \end{array}8 \ \end{array}\) First, you see how many times 8 can fit into 11, which is 1. You then write 1 above the 11. Next, multiply 1 by 8 to get 8, and subtract it from 11 to get 3. Then, bring down a 0 to make 30.

8 goes into 30 three times. Write 3 above the next digit, multiply 3 by 8 to get 24, and subtract it from 30 to get 6. Bring down another 0 to make 60. 8 will fit into 60 seven times. Write 7 above, multiply 7 by 8 to get 56, and subtract that from 60 to get 4.

Bring down another 0 to make 40, and 8 fits into 40 five times exactly. The result of 11 divided by 8 is 1.375. This is how you convert a fraction into a decimal using long division!