SOLUTION: how to write algebraic expression? ex; 7 less than 4 times a number 11 more than half a number 5 mmore than the product of a number and 3 1/2 t

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Question 6167: how to write algebraic expression? ex;

7 less than 4 times a number

11 more than half a number
5 mmore than the product of a number and 3
1/2 the difference of a number and 15
I had this in my algebra test last month but I can't remember how to do it nor can I find it in my algebra book. Im a mom helping a child tonight but we are stumped. also im stuck on (reciprocals) 9/8, -3y/5, -2.45 and last but not least (solve) -t/12=2/3, 9a-7a=4 ???? thank you in advance for any help you provide
Answer by glabow(165) About Me  (Show Source):
You can put this solution on YOUR website!
You have three questions here. Here goes ---
Sometimes it helps to rephrase the word problem in the opposite order.
7 less than 4 times a number is the same as: a number times 4, less 7.
This is 4x-7
11 more than half a number is the same as: half a number and 11 more.
This is x%2F2%2B11
Can you now write 5 more than the product of a number and 3, which is the same as the product of a number and 3 and 5 more?
A reciprocal of a number is a second number such that when the two numbers are multiplied the answer is 1. The reciprocal of 7 is 1%2F7. The reciprocal of 1%2F7 is 7. Why? Because +%281%29%281%2F7%29=1 In fact, %28x%29%281%2Fx%29=1. So most people just say, the reciprocal of a number is 1 divided by the number. Dividing by a fraction is the same as multiplying by the reciprocal of the fraction. The general rule is reverse the numerator and the denominator and multiply. So 1 divided by a fraction is the same as 1 multiplied by the fraction "turned upside down." In general, 1%2F%28x%2Fy%29=%281%29%28y%2Fx%29
But be careful! 0 has no reciprocal! So watch out for things like +1%2F%280%2F9%29
There is no such thing as division by zero.
To answer your question, the first number 9/8 has the reciprocal 8/9. And so on.
Your third question asks to find t when -t%2F12=2%2F3
You multiply both sides by -12 which is
%28-12%29%28-t%2F12%29=%28-12%29%282%2F3%29
12t%2F12=-24%2F3
t=-8
Look closely at that first part %28-12%29%28-t%2F12%29
That's %28-12%29%28-1%2F12%29t
See the reciprocals?