80
Further explanation
Given:
32 is 40 percent of what number?
The Process:
Let N as the number asked.
The mathematical equation of the question sentence represents as follows:
\(\boxed{ \ 32 = 40 \% \times N \ }\)
Which can be rewritten to be
\(\boxed{ \ 40 \% \times N = 32 \ }\)
All we have to do to get the N value is a division operation.
\(\boxed{ \ If \ a \times b = c, \ then \ a = c \div b \ or \ b = c \div a \ }\)
\(\boxed{ \ If \ a \times b = c \ then \ a = \frac{c}{b} \ or \ b = \frac{c}{a} \ }\)
\(\boxed{ \ 40 \% \times N = 32 \ }\)
\(\boxed{ \ N = 32 \div 40 \% \ }\)
Recall that \(\boxed{ \ 40 \% = \frac{40}{100} \ }\)
\(\boxed{ \ N = 32 \div \frac{40}{100} \ }\) ... Equation-1
Recall that \(\boxed{ \ a \div \frac{b}{c} \rightarrow a \times \frac{c}{b} \ }\)
\(\boxed{ \ N = 32 \times \frac{100}{40} \ }\) ... Equation-2
Both 100 and 40 divided by 10 to make it simpler.
\(\boxed{ \ N = 32 \times \frac{10}{4} \ }\)
32 is crossed out with 4, in other words dividing each other.
\(\boxed{ \ N = 8 \times 10 \ }\)
Thus, the result is \(\boxed{\boxed{ \ N = 80 \ }}\)
Alternative-1:
Recall that \(\boxed{ \ \frac{40}{100} = 0.40 = 0.4 \ }\)
From Equation-1 above, we rearrange it into
\(\boxed{ \ N = \frac{32}{0.4} \ }\)
Both the numerator and denominator are multiplied by 10.
\(\boxed{ \ N = \frac{320}{4} \ }\)
Thus, the result is \(\boxed{\boxed{ \ N = 80 \ }}\)
Alternative-2:
From Equation-2 above, both 100 and 40 are divided by 20.
\(\boxed{ \ N = 32 \times \frac{5}{2} \ }\)
32 is crossed out with 2, in other words dividing each other.
\(\boxed{ \ N = 16 \times 5 \ }\)
Thus, the result is \(\boxed{\boxed{ \ N = 80 \ }}\)
Alternative-3:
\(\boxed{ \ 40 \% \times N = 32 \ }\)
Both sides are multiplied by \(\boxed{ \ \frac{100}{40} \ }\)
\(\boxed{ \ N = 32 \times \frac{100}{40} \ }\)
\(\boxed{ \ N = 32 \times \frac{10}{4} \ }\)
\(\boxed{ \ N = 32 \times \frac{5}{2} \ }\)
\(\boxed{ \ N = 16 \times 5 \ }\)
Thus, the result is \(\boxed{\boxed{ \ N = 80 \ }}\)
Learn more
- 100 is ¹/₁₀ of what? brainly.com/question/96535
- 4 times as much as 3 is https://brainly.com/question/573729
- 68.32 divided by 2.8 is divisible https://brainly.com/question/5022643#
Keywords: 32 is 40 percent of what number, a division operation, fraction, multiply, 80, decimals, alternative steps, the mathematical equation
