Problem 113 - Fundamentals of Mathematics

Question

There are 48 plants per flat. How many plants are there in \(\frac{1}{3}\) of a flat?

Step-by-Step Solution

Answer

There are 16 plants in one-third of a flat.

Step 1: Understanding the Problem

We need to find out how many plants are there in one-third of a flat that contains 48 plants.

Step 2: Setting Up the Calculation

Since we want to find out how many plants are in \(\frac{1}{3}\) of a flat, we need to multiply the total number of plants per flat by \(\frac{1}{3}\). The total number of plants per flat is 48.

Step 3: Perform the Multiplication

Multiply 48 by \(\frac{1}{3}\). This can be expressed as:\[\frac{48}{1} \times \frac{1}{3} = \frac{48 \times 1}{3} = \frac{48}{3}\]

Step 4: Simplifying the Fraction

We now simplify the fraction \(\frac{48}{3}\). Divide 48 by 3:\[48 \div 3 = 16\]

Step 5: Conclusion

Thus, \(\frac{1}{3}\) of a flat contains 16 plants.

Key Concepts

Division

Division is a fundamental arithmetic operation that helps us split a larger quantity into smaller, equal parts. In real-life scenarios, division allows us to divide items into groups or portions.

• When you divide a number by another number, you are finding out how many times the divisor fits into the dividend.


• For example, in the exercise, the division operation helps determine how many plants are in one-third of the flat.


• In our example, we took 48 plants (dividend) and divided by 3 to find out how many plants fit into one flat (divisor), giving us 16 plants.

Understanding division is crucial as it enables us to work with fractions, ratios, and more advanced mathematical concepts.

Fractions

Fractions represent parts of a whole. They consist of two numbers: the numerator (top part) and the denominator (bottom part).

• The numerator represents how many parts we have.


• The denominator tells us how many equal parts the whole is divided into.

In our exercise, the fraction \(\frac{1}{3}\) signifies that we are considering one part out of three equal parts of a flat.
Fractions can also help us compare different quantities. Knowing how to manipulate fractions through multiplication, division, and more, allows you to solve real-life problems easily.

Arithmetic Operations

Arithmetic operations are the basic mathematical operations we use daily: addition, subtraction, multiplication, and division. These operations help us to perform various calculations.

• Multiplication is used for finding a product by combining groups of equal sizes.


• Division, on the other hand, helps to break things down into smaller units, as we've seen in the exercise.


• In this exercise, multiplication and division are interconnected: we firstly multiplied by a fraction, and then simplified the fraction by dividing.

Arithmetic operations are the foundation of mathematics, making it possible to handle numbers and solve problems effectively.