Jamal lives 8 blocks from school. Bethany lives 3 times as far from school as Jamal . Michael lives 4 times as far as Jamal and Bethany combined . Write a number sentence that compares how far from school Bethany lives to how far from school Michael lives.
Q2/ if you multiply both sides of an equality by 8 do you still have an equality? Give an example.
Q3/ Evaluate the expression (12_4)*(2+1). Would the value change if there were no parentheses?
I don't know..
Help me..
b = 3j
m = 4(b+j)
m = 4b+4j
m = 4b+4(b/3)
m = 16/3 b
yes
3 = 1+2
3*8 = (1+2)*8 = 8+16 = 24
(12-4)*(2+1) = 8*3 = 24
12-4*2+1 = 12-8+1 = 5
in the absence of parens, multiplication is done before addition.
That's why 3x+2 is (3*x)+2 and not 3*(x+2)
Q1/ To compare how far Bethany lives from school to how far Michael lives, we can set up a number sentence. Let's call the distance Jamal lives "x."
- Bethany lives 3 times as far from school as Jamal, so Bethany's distance is 3 * x.
- Michael lives 4 times as far as Jamal and Bethany combined, so Michael's distance is 4 * (x + 3 * x).
Therefore, the number sentence that compares how far Bethany lives to how far Michael lives is 3x < 4(x + 3x).
Q2/ If you multiply both sides of an equality by the same number, the result will still be an equality. Here's an example:
Original equation: 2x = 10
Multiply both sides by 8: 8 * (2x) = 8 * 10
16x = 80
The resulting equation 16x = 80 is still an equality.
Q3/ To evaluate the expression (12_4) * (2 + 1), we need to follow the order of operations, which is parentheses, exponents, multiplication/division (from left to right), and finally addition/subtraction (from left to right).
(12_4) refers to a special multiplication notation known as cross-multiplication. It means multiplying the digits outside the underscore by the digits inside the underscore and adding the products. So (12_4) equals 12 * 4 + 12 = 48 + 12 = 60.
Now we have the expression 60 * (2 + 1). We simplify the parentheses first:
2 + 1 = 3
So the expression becomes 60 * 3, which equals 180.
If there were no parentheses in the expression, the value would not change because multiplication is commutative:
(12_4) * (2 + 1) = 60 * (2 + 1) = 60 * 3 = 180
And without parentheses:
12_4 * 2 + 12_4 * 1 = 60 * 2 + 60 * 1 = 120 + 60 = 180
Therefore, the value would still be 180 even without parentheses.