Question

Translate to an equation and solve. \(98 \%\) of \(60 \frac{1}{4}\) is what number?

Short answer

Answer: 59.1

Step-by-step solution

Convert the mixed number to a fraction

We are given the mixed number \(60\frac{1}{4}\), and we need to convert it to a fraction in order to find its percentage. To do this, we multiply the whole number by the denominator and add the numerator: $$60\frac{1}{4} = \frac{60*4+1}{4}= \frac{241}{4}$$

Set up the equation

Now, we need to find \(98\%\) of this fraction, which can be written as an equation. We want to find a number \(x\) which represents \(98\%\) of \(60 \frac{1}{4}\). Equivalently, we want to find \(x\) such that: $$x = 0.98 * \frac{241}{4}$$

Solve the equation

To solve for \(x\), multiply \(0.98\) by \(\frac{241}{4}\): $$x = \frac{0.98 * 241}{4}$$

Simplify the expression

Now, calculate the product and simplify the expression: $$x = \frac{236.38}{4}$$

Calculate the final value

Finally, divide the numerator by the denominator to get the value of \(x\): $$x = 59.095$$ So, \(98\%\) of \(60\frac{1}{4}\) is approximately \(59.1\).

Key concepts

Mixed Numbers

A mixed number consists of a whole number and a fraction combined. It is often used to represent quantities that are not whole. For example, when you have "two and a half," you write it as the mixed number \(2\frac{1}{2}\). Dealing with mixed numbers can be confusing if you're not familiar with how to convert them into fractions.
Converting a mixed number to an improper fraction involves:

• Multiplying the whole number by the denominator of the fraction part.
• Adding the numerator to this result.
• Writing the total as the numerator over the original denominator.

This allows us to perform further calculations easily, such as multiplication or division.

Fractions

Fractions represent parts of a whole number, with a numerator on top and a denominator on the bottom. They are written as \(\frac{a}{b}\), where "a" is the numerator and "b" is the denominator.
Converting between mixed numbers and improper fractions helps when performing arithmetic operations like addition, subtraction, and multiplication.

• A proper fraction has a numerator smaller than the denominator (e.g., \(\frac{3}{4}\)).
• An improper fraction has a numerator larger or equal to the denominator (e.g., \(\frac{5}{3}\)).

Understanding fractions is crucial in solving equations and calculating percentages, as they provide a versatile way to handle non-whole numbers.

Equations

Equations are mathematical statements that express the equality between two expressions. In an equation, you often solve for an unknown variable. This involves finding the value of the variable that makes the equation true.
When dealing with percentages, equations help us determine what a certain percentage of a number is. For example, to find \(98\%\) of \(60\frac{1}{4}\), you first convert the percentage to a decimal \(0.98\) and then set up an equation like \(x = 0.98 \times\frac{241}{4}\).
Solving this equation involves performing the multiplication and then simplifying the results.

Decimal Multiplication

Decimal multiplication is a method to perform arithmetic operations on numbers that have a decimal point. It becomes particularly useful when dealing with percentages, which are typically converted to decimals before performing calculations. To multiply a decimal by a fraction:

• Multiply the decimal by the numerator of the fraction.
• Then, divide the result by the denominator.

For instance, multiplying \(0.98\) by \(\frac{241}{4}\) involves calculating \(0.98 \times 241\), giving \(236.38\), and then dividing by \(4\) to get the final result \(59.095\).
Mastering decimal multiplication is key for solving real-world problems that involve percentages and fractional values.