Select the correct combination of mathematical signs to sequentially replace the * signs and to balance the given equation.
78 * 39 * 46 * 5 * 10 * 2
$\div$, +, =, ×, –
Balancing the Equation with Mathematical Signs
The objective is to find the correct sequence of mathematical signs to replace the asterisks (*) in the equation $78 * 39 * 46 * 5 * 10 * 2$ to make it a balanced equation.
Evaluating the Correct Sign Combination
We test the combination provided in Option A, which includes the signs: $\div$, +, =, ×, –.
Substituting these signs sequentially into the given expression results in the equation:
$78 \div 39 + 46 = 5 \times 10 - 2$
Step-by-Step Verification
We verify this equation using the standard order of operations (PEMDAS/BODMAS):
Left Hand Side (LHS) Calculation
- First, perform the division: $78 \div 39 = 2$.
- Next, perform the addition: $2 + 46 = 48$.
- The result of the LHS is 48.
Right Hand Side (RHS) Calculation
- First, perform the multiplication: $5 \times 10 = 50$.
- Next, perform the subtraction: $50 - 2 = 48$.
- The result of the RHS is 48.
Conclusion
Comparing the LHS and RHS, we find that $48 = 48$. The equation is balanced.
Thus, the correct combination of mathematical signs is $\div$, +, =, ×, –.
Important Questions from Mathematical Operations
Select the set, from the given options, in which the numbers are related in the same way as are the numbers of the following sets.
(NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into its constituent digits. E.g. 13 – Operations on 13 such as adding/subtracting/multiplying etc. to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.)
(6, 13, 78)
(5, 22, 110)
If + means -, - means ×, × means ÷, ÷ means +, then what will come in place of the question mark (?) in the following equation?
28 - 6 ÷ 4 + 14 × 14 = ?
In the following number-pairs, the second number is obtained by applying certain mathematical operations to the first number. Which numbers should replace X and Y so that the pattern followed by the two numbers on the left side of :: is the same as that on the right side of :: ?
(NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into its constituent digits. E.g. 13 Operations on 13 such as adding/subtracting /multiplying etc. to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.)
X : 649 :: 956 : Y
Which two numbers should be interchanged to make the given equation correct?
75 ÷ 5 + 15 × 4 - 17 × 3 + (60 ÷ 6) × 10 = 100
(Note: Interchange should be done of the entire number and not individual digits of a given number.)
If '+' means minus, '-' means multiplication, '÷' means plus, and 'x' means division, then solve the equation:
15 - 3 + 10 x 5 ÷ 5
