How can you find 40% of 150 using mental math? Explain.
The Correct Answer and Explanation is:
To find 40% of 150 using mental math, follow these steps:
Step 1: Understand the problem
The task is to calculate 40% of 150. The term “percent” means “per hundred,” so 40% can be written as a fraction:
[
40\% = \frac{40}{100} = 0.40
]
Thus, the problem becomes finding 0.40 of 150, or simply multiplying 150 by 0.40.
Step 2: Break down the calculation
Rather than multiplying 150 directly by 0.40, you can break it down into simpler parts:
[
150 \times 0.40 = 150 \times \left(\frac{40}{100}\right)
]
This can be rewritten as:
[
150 \times \frac{40}{100} = \frac{150 \times 40}{100}
]
Now, you need to calculate ( 150 \times 40 ) first, which is easier to do:
[
150 \times 40 = 6000
]
Step 3: Simplify the result
Now that we have ( 150 \times 40 = 6000 ), divide this by 100 to get the final result:
[
\frac{6000}{100} = 60
]
Step 4: Check the calculation
You can also verify your answer by using another method. You know that 10% of 150 is 15 (because ( \frac{10}{100} \times 150 = 15 )). To find 40%, you can multiply 10% by 4:
[
15 \times 4 = 60
]
Thus, 40% of 150 is 60.
Final Answer:
The correct answer is 60.
Explanation:
In this process, we simplified the multiplication by breaking it into manageable parts: calculating ( 150 \times 40 = 6000 ) and dividing by 100. We also verified the result by considering that 10% of 150 is 15, and multiplying this by 4 gives the same result, 60. This mental math method allows for quick and accurate calculations without the need for a calculator.