Question

Find each quantity. \(\frac{7}{9}\) of 54

Short answer

42

Step-by-step solution

Understand the Problem

You need to find \(\frac{7}{9}\) of the number 54. This means you need to multiply 54 by \(\frac{7}{9} \).

Set Up the Multiplication

Write the expression for the multiplication you need to perform: \(\frac{7}{9} \times 54 \).

Perform the Multiplication

Multiply 54 by \(\frac{7}{9} \). To do this, you can first divide 54 by 9, and then multiply the result by 7. \(\frac{54}{9} = 6 \) and \(6 \times 7 = 42 \).

State the Final Answer

After performing the multiplication, the result is 42. Therefore, \(\frac{7}{9}\) of 54 is 42.

Key concepts

fraction multiplication

Fraction multiplication is a key concept in mathematics. It involves multiplying two fractions with each other. This is done by multiplying the numerators together and the denominators together. For instance, to multiply \(\frac{a}{b}\) by \(\frac{c}{d}\), you would perform the operation \(\frac{a \times c}{b \times d}\). In our exercise, we were multiplying a fraction by a whole number. We converted the whole number into a fraction (\(54\) becomes \(\frac{54}{1}\)) before multiplying. To make things easier, you can simplify fractions before multiplying. Simplifying can help prevent large numbers and reduce errors.

algebraic fractions

Algebraic fractions are fractions where the numerators or denominators (or both) contain algebraic expressions (like variables). Working with algebraic fractions follows similar rules as numerical fractions. When you multiply algebraic fractions, simplify where possible and use the same rules for multiplying numerators and denominators. For example, multiplying \(\frac{x}{y}\) by \(\frac{a}{b}\) would result in \(\frac{ax}{by}\). Just like with numerical fractions, you can cancel factors that appear in both the numerator and the denominator before multiplying, which simplifies your work.

fraction of a number

Finding a fraction of a number means determining what part of that number corresponds to a given fraction. This involves multiplication. For example, finding \(\frac{7}{9}\) of 54 means you multiply 54 by \(\frac{7}{9}\). Here's how it works step by step:

• Convert the whole number to a fraction. (\(54\) becomes \(\frac{54}{1}\)).
• Set up the multiplication: \(\frac{7}{9} \times \frac{54}{1}\).
• Simplify if possible (Here, \(54\div9=6\))
• Multiply the results: \(\frac{7 \times 6}{1} = 42\).
• Therefore, \(\frac{7}{9}\) of 54 is 42.

By understanding these steps, you can solve similar problems more easily.