Understanding the Calculation: 1/0.24 of 1.44

The question asks for the value of a mathematical expression involving decimals. The phrase "of" in mathematics often indicates multiplication. So, "1/0.24 of 1.44" can be interpreted as multiplying 1.44 by the fraction 1/0.24.

This means we need to calculate:

$\frac{1}{0.24} \times 1.44$

This is equivalent to dividing 1.44 by 0.24.

$\frac{1.44}{0.24}$

Step-by-Step Calculation

To perform the division $\frac{1.44}{0.24}$, it is often easier to remove the decimals. We can do this by multiplying both the numerator and the denominator by a power of 10 that shifts the decimal point to the right until both numbers are integers. In this case, both 1.44 and 0.24 have two digits after the decimal point, so we multiply by $10^2 = 100$.

$\frac{1.44 \times 100}{0.24 \times 100} = \frac{144}{24}$

Now, we need to calculate $\frac{144}{24}$. We can perform long division or recognize that 144 is a multiple of 24.

Let's perform the division:

Alternatively, you can check multiples of 24:

• $24 \times 1 = 24$
• $24 \times 2 = 48$
• $24 \times 3 = 72$
• $24 \times 4 = 96$
• $24 \times 5 = 120$
• $24 \times 6 = 144$

So, $\frac{144}{24} = 6$.

Therefore, the value of 1/0.24 of 1.44 is 6.

Result Verification

Let's double-check the original expression using the calculated value:

• First, calculate $\frac{1}{0.24}$.
• $\frac{1}{0.24} = \frac{1}{\frac{24}{100}} = 1 \times \frac{100}{24} = \frac{100}{24}$
• Now multiply this by 1.44:
• $\frac{100}{24} \times 1.44 = \frac{100}{24} \times \frac{144}{100}$
• Cancel out the 100 in the numerator and denominator:
• $\frac{1}{24} \times 144 = \frac{144}{24}$
• $\frac{144}{24} = 6$

The calculation is consistent. The value of 1/0.24 of 1.44 is indeed 6.

Revision Table: Key Concepts

Additional Information: Working with Fractions and Decimals

Working with fractions and decimals is a fundamental skill in arithmetic. Understanding how to convert between them and perform operations like multiplication and division is crucial.

• Decimal to Fraction Conversion: A decimal like 0.ab can be written as $\frac{ab}{100}$, 0.abc as $\frac{abc}{1000}$, and so on. The denominator is $10^n$ where $n$ is the number of digits after the decimal point.
• Fraction to Decimal Conversion: Divide the numerator by the denominator. For example, $\frac{3}{4} = 0.75$.
• Multiplication: When multiplying decimals, multiply the numbers as if they were integers, then place the decimal point in the product so that the number of decimal places equals the sum of the decimal places in the numbers being multiplied.
• Division: When dividing by a decimal, shift the decimal point in both the divisor and the dividend by the same number of places so that the divisor becomes an integer. Then perform standard long division.