Last winter Armand had StartFraction 5 Over 6 EndFraction of a row of stacked logs. At the end of the winter he had StartFraction 8 Over 15 EndFraction of the same row left. How much wood did he burn over the winter?
Armand burned StartFraction 5 Over 6 minus 8 over 15 EndFraction of the row of stacked logs. Simplifying the expression within the parentheses, we have:
StartFraction 5 Over 6 EndFraction minus StartFraction 8 Over 15 EndFraction
To subtract these fractions, we need a common denominator. The smallest number that both 6 and 15 divide into is 30, so we can rewrite the fractions with denominators of 30:
StartFraction 5 Over 6 EndFraction minus StartFraction 8 Over 15 EndFraction = StartFraction 25 Over 30 EndFraction minus StartFraction 16 Over 30 EndFraction
Now we can subtract the numerators:
StartFraction 25 Over 30 EndFraction minus StartFraction 16 Over 30 EndFraction = StartFraction 9 Over 30 EndFraction
Simplifying the fraction, we have:
StartFraction 9 Over 30 EndFraction = StartFraction 3 Over 10 EndFraction
So Armand burned 3/10 of the row of stacked logs over the winter.
At the beginning of the week, Naveen has 87 trading cards. On Monday, he gets 9 more. On Tuesday, he gives 16 away. On Wednesday, he is given 3 by a friend. On Thursday, he sells all of his cards to a collector. The collector pays him a rate of c for every card that Naveen has. If Naveen earns $124.50 from the sale, what is c, the rate that the collector pays for each card?
$1.08
$1.50
$41.50
$83.00
On Monday, Naveen has 87 + 9 = 96 trading cards.
On Tuesday, he has 96 – 16 = 80 trading cards.
On Wednesday, he has 80 + 3 = 83 trading cards.
On Thursday, he sells all 83 cards at a rate of c per card and earns $124.50.
Therefore, we can set up the equation:
83c = 124.50
Solving for c, we get:
c = 124.50 / 83 = 1.50
Therefore, the rate that the collector pays for each card is $1.50.
What is the first step in solving the equation 3.5 n + 6.4 = 42.5?
Add 6.4 to each side of the equation.
Subtract 6.4 from each side of the equation.
Multiply each side of the equation by 3.5.
Divide each side of the equation by 6.4.
Subtract 6.4 from each side of the equation.
What do the four yellow tiles in the model of the equation below represent?
3 long x tiles and 4 square 1 tiles = 2 negative 2 tiles
–4
4
–4x
4x
The four yellow tiles in the model represent 4 square 1 tiles.
Which expression is equivalent to 9 p minus 3 p + 2?
8p
14p
6 p + 2
9 p minus 1
The expression that is equivalent to 9 p minus 3 p + 2 is 6 p + 2.
Explanation:
9 p minus 3 p simplifies to 6 p. So we can rewrite the expression as:
6 p + 2
This is Daniela’s work to solve the equation 13 x + 42 = 276.
13 x + 42 = 276. 13 x = 318. x = 24 and StartFraction 6 Over 13 EndFraction.
Which property did Daniela need to use to avoid her error?
division property of equality
multiplication property of equality
subtraction property of equality
identity property of equality