Which of the following is the same as $40\div 15$? a)$5(10\div 3)$ b)$(30\div 15)3$ c)$5\div 5\times 8$ d)$40\div (5\times 3)$
ANSWER
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Hint: In this question, we should find out the expression given in the question. We should also find out the value of the expressions given in the options and check which of them match the value given in the question. The option whose value matches the value obtained in the question will be the correct answer to this question. We should use the BODMAS rule while solving the expressions.
Complete step-by-step answer: In this question, we have to use the BODMAS rule, that is in an expression, we should evaluate the terms in brackets, followed by the orders (power or square root), then division, multiplication, addition and subtraction respectively. The expression given in the question is $40\div 15$. We can divide 40 by 15 in the following way $\dfrac{40}{15}=\dfrac{30+10}{15}=\dfrac{30}{15}+\dfrac{10}{15}=2+\dfrac{2}{3}=2+0.66=2.66......................(1.1)$ Now, we should check the values obtained from the expressions given in the options The value of the expression in option (a) is: $5(10\div 3)=5\times \dfrac{10}{3}=\dfrac{50}{3}=16.66$ Which is not equal to the value given in the question (equation 1.1). The value of the expression in option (b) is: $(30\div 15)3=\dfrac{30}{15}\times 3=2\times 3=6$ Which is not equal to the value given in the question (equation 1.1). The value of the expression in option (c) is: $5\div 5\times 8=\dfrac{5}{5}\times 8=1\times 8=8$ Which is not equal to the value given in the question (equation 1.1).
The value of the expression in option (c) is: $40\div (5\times 3)=\dfrac{40}{5\times 3}=\dfrac{40}{15}=40\div 15$ Which is the same expression as given in the question (equation 1.1). Therefore, the correct option to this question should be option (d) which is the expression $40\div (5\times 3)$.
Note: We should be very careful to use the BODMAS rule. For example, in option (d), if we perform the division operation first without considering the brackets, then the obtained value (24) would be different from the actual value which matches the expression in the question.