80
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:
[tex]\boxed{ \ 32 = 40 \% \times N \ }[/tex]
Which can be rewritten to be
[tex]\boxed{ \ 40 \% \times N = 32 \ }[/tex]
All we have to do to get the N value is a division operation.
[tex]\boxed{ \ If \ a \times b = c, \ then \ a = c \div b \ or \ b = c \div a \ }[/tex]
[tex]\boxed{ \ If \ a \times b = c \ then \ a = \frac{c}{b} \ or \ b = \frac{c}{a} \ }[/tex]
[tex]\boxed{ \ 40 \% \times N = 32 \ }[/tex]
[tex]\boxed{ \ N = 32 \div 40 \% \ }[/tex]
Recall that [tex]\boxed{ \ 40 \% = \frac{40}{100} \ }[/tex]
[tex]\boxed{ \ N = 32 \div \frac{40}{100} \ }[/tex] ... Equation-1
Recall that [tex]\boxed{ \ a \div \frac{b}{c} \rightarrow a \times \frac{c}{b} \ }[/tex]
[tex]\boxed{ \ N = 32 \times \frac{100}{40} \ }[/tex] ... Equation-2
Both 100 and 40 divided by 10 to make it simpler.
[tex]\boxed{ \ N = 32 \times \frac{10}{4} \ }[/tex]
32 is crossed out with 4, in other words dividing each other.
[tex]\boxed{ \ N = 8 \times 10 \ }[/tex]
Thus, the result is [tex]\boxed{\boxed{ \ N = 80 \ }}[/tex]
Alternative-1:
Recall that [tex]\boxed{ \ \frac{40}{100} = 0.40 = 0.4 \ }[/tex]
From Equation-1 above, we rearrange it into
[tex]\boxed{ \ N = \frac{32}{0.4} \ }[/tex]
Both the numerator and denominator are multiplied by 10.
[tex]\boxed{ \ N = \frac{320}{4} \ }[/tex]
Thus, the result is [tex]\boxed{\boxed{ \ N = 80 \ }}[/tex]
Alternative-2:
From Equation-2 above, both 100 and 40 are divided by 20.
[tex]\boxed{ \ N = 32 \times \frac{5}{2} \ }[/tex]
32 is crossed out with 2, in other words dividing each other.
[tex]\boxed{ \ N = 16 \times 5 \ }[/tex]
Thus, the result is [tex]\boxed{\boxed{ \ N = 80 \ }}[/tex]
Alternative-3:
[tex]\boxed{ \ 40 \% \times N = 32 \ }[/tex]
Both sides are multiplied by [tex]\boxed{ \ \frac{100}{40} \ }[/tex]
[tex]\boxed{ \ N = 32 \times \frac{100}{40} \ }[/tex]
[tex]\boxed{ \ N = 32 \times \frac{10}{4} \ }[/tex]
[tex]\boxed{ \ N = 32 \times \frac{5}{2} \ }[/tex]
[tex]\boxed{ \ N = 16 \times 5 \ }[/tex]
Thus, the result is [tex]\boxed{\boxed{ \ N = 80 \ }}[/tex]
Keywords: 32 is 40 percent of what number, a division operation, fraction, multiply, 80, decimals, alternative steps, the mathematical equation
