Question Video: Finding the Missing Operators in a Decimal Calculation

Insert the appropriate symbols from +, −, ×, and ÷ to make the calculation correct: 8 _ 0.5 _ 40 = 28.


Video Transcript

Insert the appropriate symbols from addition, subtraction, multiplication, and division to make the calculation correct. Eight blank 0.5 blank 40 equals 28.

We could answer this question by trial and error by substituting each combination of the four symbols in turn. An alternative method would be to initially consider the order of operations and acronym PEMDAS. Parentheses and exponents will not be relevant for this question, as we’re only allowed to use addition, subtraction, multiplication, and division. It’s important to recall that multiplication and division, along with addition and subtraction, have equal precedence. However, any multiplication or division calculation must be done prior to any addition or subtraction.

We might initially notice in our calculation that the right-hand side is equal to 28, and our first number is eight. We know that eight plus 20 equals 28. This suggests that the first missing symbol could be an addition one. 0.5 is the same as one-half, and we know that one-half of 40 is 20. This means that 0.5 multiplied by 40 is also equal to 20. This indicates that the second missing sign is a multiplication one.

We can now check to see whether eight plus 0.5 multiplied by 20 does indeed equal 28. Our first step would be to carry out the multiplication, 0.5 multiplied by 40. We know this is equal to 20. So we’re left with eight plus 20. Eight plus 20 is indeed equal to 28. The missing symbols in the calculation are addition and multiplication such that eight plus 0.5 multiplied by 40 is 28.

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