Problem 25 - Basic College Mathematics

Question

Multiply. $$ \frac{1}{4} \times \frac{1}{10} $$

Step-by-Step Solution

Answer

The product is \(\frac{1}{40}\).

Step 1: Understand the problem

We need to multiply two fractions, \(\frac{1}{4}\) and \(\frac{1}{10}\). The product of two fractions can be found by multiplying their numerators and their denominators.

Step 2: Multiply the numerators

Multiply the numerators of the fractions: \(1 \times 1 = 1\).

Step 3: Multiply the denominators

Next, multiply the denominators of the fractions: \(4 \times 10 = 40\).

Step 4: Form the new fraction

The product of \(\frac{1}{4} \times \frac{1}{10}\) is \(\frac{1}{40}\).

Key Concepts

fraction multiplication

Multiplying fractions might seem a bit tricky at first, but it's quite simple! To multiply fractions, you just follow a few easy steps. You don’t need to find a common denominator like you do in addition or subtraction. Instead, just focus on the numerators and the denominators.
Always remember, when multiplying two fractions, multiply the numerators together and the denominators together. This will give you a new fraction which is the product of the two original fractions.

numerators

Numerators are the top numbers of fractions. They tell us how many parts we have. For example, in the fraction \(\frac{1}{4}\), 1 is the numerator. When multiplying fractions, you multiply the numerators to get the numerator of the product. So, in the problem \(\frac{1}{4} \times \frac{1}{10}\), you multiply 1 (from the first numerator) by 1 (from the second numerator) to get 1. This is why the numerator of the answer is 1.

denominators

Denominators are the bottom numbers of fractions. They tell us the total number of equal parts. For instance, in the fraction \(\frac{1}{10}\), 10 is the denominator. Just like with the numerators, when you multiply fractions, you also multiply the denominators. So in \(\frac{1}{4}\) and \(\frac{1}{10}\), \(4 \times 10 = 40\). The denominator of the new fraction, which is the product, is 40.

product of fractions

The product of two fractions is the result you get after multiplying them. From our example, multiplying \(\frac{1}{4}\) and \(\frac{1}{10}\), we get the new fraction \(\frac{1}{40}\). In general, if you multiply \(\frac{a}{b}\) by \(\frac{c}{d}\), the product will be \(\frac{ac}{bd}\). It’s a straightforward process: just multiply the numerators to get the new numerator, and the denominators to get the new denominator. The resulting fraction, or the product of the fractions, tells you the new portion you have when combining these two fractions.