Answer :
Sure, let's walk through the solution step-by-step.
The problem tells us that 45% of a number is 83. We need to find out which statement about this situation is not true.
To do this, we begin by setting up an equation to find the original number. We know that:
[tex]\[ 0.45 \times x = 83 \][/tex]
To find [tex]\( x \)[/tex], we should divide 83 by 0.45:
[tex]\[ x = \frac{83}{0.45} \][/tex]
Now, let's evaluate the given statements to determine which one is not correct:
1. Evaluate the expression [tex]\( 83 \div \frac{9}{20} \)[/tex]:
- The fraction [tex]\(\frac{9}{20}\)[/tex] is equivalent to 0.45, so dividing by [tex]\(\frac{9}{20}\)[/tex] is equivalent to dividing by 0.45. This statement is true because this division correctly calculates the original number.
2. Evaluate the expression [tex]\( 83 \times 0.45 \)[/tex]:
- This statement suggests multiplying 83 by 0.45. However, to find the original number, we need to divide by 0.45, not multiply. This statement is not true because it doesn't help in finding the original number; it calculates 45% of an incorrect number instead.
3. The problem asks, "45% of what number equals 83?":
- This statement simply restates the problem correctly. Therefore, it is true.
4. Evaluate the expression [tex]\( 83 \div 0.45 \)[/tex]:
- This division directly calculates the original number, as we've set up at the start. This statement is a correct method for solving the problem.
Based on these evaluations, the statement that is not true is the one suggesting to evaluate [tex]\( 83 \times 0.45 \)[/tex]. This calculation doesn't help in finding the original number, which makes it the incorrect approach for solving the problem.
The problem tells us that 45% of a number is 83. We need to find out which statement about this situation is not true.
To do this, we begin by setting up an equation to find the original number. We know that:
[tex]\[ 0.45 \times x = 83 \][/tex]
To find [tex]\( x \)[/tex], we should divide 83 by 0.45:
[tex]\[ x = \frac{83}{0.45} \][/tex]
Now, let's evaluate the given statements to determine which one is not correct:
1. Evaluate the expression [tex]\( 83 \div \frac{9}{20} \)[/tex]:
- The fraction [tex]\(\frac{9}{20}\)[/tex] is equivalent to 0.45, so dividing by [tex]\(\frac{9}{20}\)[/tex] is equivalent to dividing by 0.45. This statement is true because this division correctly calculates the original number.
2. Evaluate the expression [tex]\( 83 \times 0.45 \)[/tex]:
- This statement suggests multiplying 83 by 0.45. However, to find the original number, we need to divide by 0.45, not multiply. This statement is not true because it doesn't help in finding the original number; it calculates 45% of an incorrect number instead.
3. The problem asks, "45% of what number equals 83?":
- This statement simply restates the problem correctly. Therefore, it is true.
4. Evaluate the expression [tex]\( 83 \div 0.45 \)[/tex]:
- This division directly calculates the original number, as we've set up at the start. This statement is a correct method for solving the problem.
Based on these evaluations, the statement that is not true is the one suggesting to evaluate [tex]\( 83 \times 0.45 \)[/tex]. This calculation doesn't help in finding the original number, which makes it the incorrect approach for solving the problem.
