Question

Find each quantity. $$\frac{3}{10} \text { of } 15$$

Short answer

4.5

Step-by-step solution

Identify the values

The problem is asking for \( \frac{3}{10} \) of 15. This means we need to find what \( \frac{3}{10} \) of 15 is.

Set up the equation

To find \( \frac{3}{10} \) of 15, you can set up the equation: \[ \frac{3}{10} \times 15 \]

Perform the multiplication

Multiply \( \frac{3}{10} \) by 15: \[ \frac{3 \times 15}{10} = \frac{45}{10} \]

Simplify the result

Simplify the fraction \( \frac{45}{10} \): \[ \frac{45}{10} = 4.5 \]

Key concepts

fraction multiplication

To multiply fractions, you can follow a straightforward process. First, if you have a whole number like in the exercise, convert it to a fraction by placing it over 1. For example, 15 becomes \(\frac{15}{1}\).
Then, multiply the numerators (the top numbers) together, and do the same for the denominators (the bottom numbers). In our case, multiplying \(\frac{3}{10}\) by 15 is the same as performing:

• Numerator: 3 \( 3 \times 15 = 45 \)
• Denominator: 10 \( 10 \times 1 = 10 \)

This results in the fraction \(\frac{45}{10}\). Multiplying fractions is quite simple when you break it down step by step. Just ensure to handle both the top and bottom parts separately before combining them back into a single fraction.

simplifying fractions

Simplifying fractions means reducing them to their simplest form where the numerator and denominator are as small as possible, and they no longer have any common factors other than 1. In our example, we ended up with \(\frac{45}{10}\). Both numbers can be divided by their greatest common divisor (GCD), which is 5 in this case:

• Numerator: \( 45 \div 5 = 9 \)
• Denominator: \( 10 \div 5 = 2 \)

So, \(\frac{45}{10}\) becomes \(\frac{9}{2}\). If a fraction can't be simplified any further, we say it's in its simplest form. Simplifying fractions can help make equations easier to understand and compare.
In other words, the fraction is cleaner and simpler. In some cases, fractions can also be converted to mixed numbers or decimals for simpler interpretation.

algebraic expressions

An algebraic expression is a mathematical phrase that involves numbers, variables, and operation symbols. In our context, identifying the fraction and setting up the equation are part of handling algebraic expressions.
When dealing with the question asking for \(\frac{3}{10}\) of 15, we essentially set up the expression \[ \frac{3}{10} \times 15 \]. This is an example of combining a fraction with a whole number.
Such expressions can become complex, especially when multiple operations or variables are involved. Understanding the basic rules of arithmetic operations on fractions, like multiplication, is crucial.By systematically breaking down the equation, we manage to solve the problem step by step effectively. In more complicated cases, different algebraic techniques might be needed, but the core concept remains the same: handle each part of the expression according to the rules.