Factor is 2(13+3x)
Simplify is 26+6x
To solve the first four problems shown in the picture, you must find out what number was multiplied by the original to get the new number in the second fraction.
In the case of problem 1, 5 was multiplied by 4 to get 20. So, to make the fractions proportional, you multiply the numerator by 4 as well. This would be: 4/5=16/20.
Do this for the next 3 problems.
Now, to solve problem 5, both 3 and 5 can go into 15, so it doesn't really matter what you choose. I will go with 5, as it is the larger number and will be easier to solve with.
3:5=?:15, or 3/5=?/15 is the problem here. You can do the rest of this problem using the same technique I used to help you solve the first three problems.
Problem 6 is the same thing, but instead of enlarging the number, you are decreasing. It is done in the same way, but using division instead of multiplication.
10 cm wide is reduced to 4 cm wide. 30 cm long is reduced to ? cm long. This can be written as: 10/30=4/?
But because 10 isn't divisible by 4 evenly, you can use ratios to answer this. In the original diagram, there is 1cm in length for every 3cm in width. So if there are 4cm in length, multiply that by 3 to get width. 4x3=12. The length of the reduced diagram would be 12cm.
For question 7, you know that in 2 hours, a wood stove burns 4 logs. Assuming that all logs in the problem are same-sized, you can simply multiply 4 by 4, as 2 goes into 8 four times, and 4 logs are used up every 2 hours.
For question 8, you must divide $2.20, or 2.2, by 5. This would be: 2.2/5=0.44
A single stamp is worth $0.44, so multiply that number by 7 to get the price of 7 stamps.
I cannot answer question 9 as it seems to be a multi-part question that includes a diagram that is not shown in the photo.
However, if you need help solving problem 9, feel free to post the rest of the page as another question and if I am not too late, I will try to help. I hope I helped out :-)
Answers: Rational, Integer
A rational number is anything we can write as a ratio or fraction of two whole numbers. In this case, -3 = -3/1 is the fraction of -3 over 1. This is why -3 is rational. This means it is not irrational. The literal definition of "irrational" means "not rational", which contradicts the previous statement of it being rational.
An integer is any positive or negative whole number. The value 0 is included as well. So -3 is also an integer. Any integer is a rational number, but not the other way around (eg: 2/3 is rational but not an integer).
The set of whole numbers is usually defined in your book to be {0, 1, 2, 3, 4, ...} which is the set of positive numbers without any decimal or fractional parts. The value 0 is included. We see that -3 is not in this set. So -3 is not in the set of whole numbers.
The set of natural numbers is {1, 2, 3, 4, ...} which is essentially the set of whole numbers, but kick out 0. This set is also known as the set of counting numbers. Like before, we don't see -3 in here so -3 is not in the set of natural numbers.
