Addition and Subtraction - Pre-Algebra
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When a plus and minus sign meet, the sign becomes negative. When adding two negative numbers, we treat as an addition problem and add a minus sign in the end. Answer is 
.
When a plus and minus sign meet, the sign becomes negative. When adding two negative numbers, we treat as an addition problem and add a minus sign in the end. Answer is
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Just subtract normally. Answer is 
.
Just subtract normally. Answer is
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When two minus signs meet, the sign becomes positive. It becomes an addition problem. Answer is 
.
When two minus signs meet, the sign becomes positive. It becomes an addition problem. Answer is
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This is the same as adding two negative numbers. We treat as an addition problem and add the minus sign in the end. Answer is 
.
This is the same as adding two negative numbers. We treat as an addition problem and add the minus sign in the end. Answer is
Solve:
Solve:
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The numbers are positive. Just add. The sum is 
.
The numbers are positive. Just add. The sum is
Solve:
Solve:
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A plus and minus sign becomes a minus sign. This is just a subtraction problem. Answer is 
.
A plus and minus sign becomes a minus sign. This is just a subtraction problem. Answer is
Solve:
Solve:
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Two minus signs become a plus sign. This is an addition problem. Answer is 
.
Two minus signs become a plus sign. This is an addition problem. Answer is
Solve:
Solve:
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When a plus and minus sign meet, the operation becomes minus sign. We subtract normally. Answer is 
.
When a plus and minus sign meet, the operation becomes minus sign. We subtract normally. Answer is
Simplify:
Simplify:
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Combine like terms: 
. Remember you can only combine terms that have the same variables, for example 
and 
, but not 
and 
Combine like terms:
Simplify the expression.
Simplify the expression.
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Re-write the expression to group like terms together.
Simplify.
Re-write the expression to group like terms together.
Simplify.
What is 
simplified?
What is
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To simplify a problem like the example above we must combine the like-termed variables.
Like terms are the terms that share the same variable(s) to the same power. In this example the like term is 
.
To combine like terms the variable 
stays the same and you add the numbers in front.
Perform the necessary addition, 
, to get 
.
We have the simplified version of the equation, 
.
To simplify a problem like the example above we must combine the like-termed variables.
Like terms are the terms that share the same variable(s) to the same power. In this example the like term is
To combine like terms the variable
Perform the necessary addition,
We have the simplified version of the equation,
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According to the rules in _Order of Operations, w_e work through this problem by solving from left to right since there is only addition and subtraction.
Step 1: Subtract 6 from 4:
Step 2: Everytime you add the same number with an opposite sign, the answer will be 0:
Step 3: Subtract 4 from 0:
Step 4: When you subtract a positive number from a negative number, you are actually adding two negative numbers. One way to remember this is to remember the phrase "leave, change, change." You leave the sign of the first number, then you change the operation from subtraction to addition, then you change the sign of the second number from positive to negative:
According to the rules in _Order of Operations, w_e work through this problem by solving from left to right since there is only addition and subtraction.
Step 1: Subtract 6 from 4:
Step 2: Everytime you add the same number with an opposite sign, the answer will be 0:
Step 3: Subtract 4 from 0:
Step 4: When you subtract a positive number from a negative number, you are actually adding two negative numbers. One way to remember this is to remember the phrase "leave, change, change." You leave the sign of the first number, then you change the operation from subtraction to addition, then you change the sign of the second number from positive to negative:
Simplify:
Simplify:
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Group like terms, and then add or subtract their values from one another.
Note: subtracting a negative number is the same as adding a positive number.
Add or subtract like terms from left to right.
Group like terms, and then add or subtract their values from one another.
Note: subtracting a negative number is the same as adding a positive number.
Add or subtract like terms from left to right.
Solve 
if
.
Solve
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Plug the given variables into the equation:
Plug the given variables into the equation:
Add 
.
Add
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Add the ones digit.
The ones digit is the ones digit of the final answer. Since there is a one in the tens digit, this is the carry over for the next calculation.
Add the tens digit with the carryover.
Combine all the numbers. The answer is 
.
Add the ones digit.
The ones digit is the ones digit of the final answer. Since there is a one in the tens digit, this is the carry over for the next calculation.
Add the tens digit with the carryover.
Combine all the numbers. The answer is
Simplify:
Simplify:
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Explanation:
Combine like terms: 
. Remember you can only combine terms that have the same variables, for example 
and 
, but not 
and 
Explanation:
Combine like terms:
Above is the menu at a coffee shop.
Dale has a coupon that entitles him to a free butter croissant with the purchase of one large drink of any kind. The coupon says "limit one per coupon".
He decides to purchase a small espresso, a small iced coffee, and two butter croissants. Disregarding tax, how much will he pay for them?
Above is the menu at a coffee shop.
Dale has a coupon that entitles him to a free butter croissant with the purchase of one large drink of any kind. The coupon says "limit one per coupon".
He decides to purchase a small espresso, a small iced coffee, and two butter croissants. Disregarding tax, how much will he pay for them?
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The coupon only entitles him to one free croissant with a large drink. Since Phil only orders small drinks, he will not use the coupon, and he will pay for the drinks and both croissants. He will therefore pay:
The coupon only entitles him to one free croissant with a large drink. Since Phil only orders small drinks, he will not use the coupon, and he will pay for the drinks and both croissants. He will therefore pay:
Above is the menu at a coffee shop.
Andy has a coupon which he can use to get either a free butter croissant with the purchase of a large drink or one dollar off a butter croissant with the purchase of a small drink. The coupon says "limit one per coupon".
Andy orders one large cappucino, one small cappucino, and two butter croissants. Disregarding tax, how much will he spend?
Above is the menu at a coffee shop.
Andy has a coupon which he can use to get either a free butter croissant with the purchase of a large drink or one dollar off a butter croissant with the purchase of a small drink. The coupon says "limit one per coupon".
Andy orders one large cappucino, one small cappucino, and two butter croissants. Disregarding tax, how much will he spend?
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Andy will get one of the butter croissants for free, since he is also purchasing a large drink. He will pay for one large cappucino, one small cappucino, and one butter croissant; add their prices:
Andy will get one of the butter croissants for free, since he is also purchasing a large drink. He will pay for one large cappucino, one small cappucino, and one butter croissant; add their prices:
Above is the menu at a coffee shop.
Julia has a coupon which she can use to get either one dollar off the price of a butter croissant with the purchase of a large drink or fifty cents off the price of a butter croissant with the purchase of a small drink. The coupon says "limit 4".
Julia orders five small cappucinos and five butter croissants. Disregarding tax, how much will she spend?
Above is the menu at a coffee shop.
Julia has a coupon which she can use to get either one dollar off the price of a butter croissant with the purchase of a large drink or fifty cents off the price of a butter croissant with the purchase of a small drink. The coupon says "limit 4".
Julia orders five small cappucinos and five butter croissants. Disregarding tax, how much will she spend?
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Julia will be able to save on four of the five butter croissants, since the coupon allows discounts on up to four; since she is only buying small drinks, the four croissants will be fifty cents off each. Therefore, we can add the regular prices of the drinks:
The five small cappucinos: 
The five butter croissants: 
The total before discount: 
Then subtract a total discount of 
:
Julia will be able to save on four of the five butter croissants, since the coupon allows discounts on up to four; since she is only buying small drinks, the four croissants will be fifty cents off each. Therefore, we can add the regular prices of the drinks:
The five small cappucinos:
The five butter croissants:
The total before discount:
Then subtract a total discount of
Write solution as an improper fraction.
Write solution as an improper fraction.
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When adding or subtracting fractions, you must find the common denominator. This is best done by finding the least common multiple of the denominators, in this case 5 and 3. What is the lowest number that is divisible by both 5 and 3? Often, the easiest solution is to multiply the denominators together. This works most often with single digit numbers. Anything larger and you will have to find the least common multiple another way.
The LCM of 5 and 3 is 15 (5 x 3). Now you know that both fractions must have 15 on the bottom. Now, to convert 4/5 to ?/15, you must recognize how many times 5 goes into 15 (3), and multiply the numerator by that number. Therefore:
Do the same with the other side.
Now that the denominators match, all that's left is to add the numerators together.
This solution is already an improper fraction (the numerator is larger than the denominator), therefore you may leave the fraction as is.
When adding or subtracting fractions, you must find the common denominator. This is best done by finding the least common multiple of the denominators, in this case 5 and 3. What is the lowest number that is divisible by both 5 and 3? Often, the easiest solution is to multiply the denominators together. This works most often with single digit numbers. Anything larger and you will have to find the least common multiple another way.
The LCM of 5 and 3 is 15 (5 x 3). Now you know that both fractions must have 15 on the bottom. Now, to convert 4/5 to ?/15, you must recognize how many times 5 goes into 15 (3), and multiply the numerator by that number. Therefore:
Do the same with the other side.
Now that the denominators match, all that's left is to add the numerators together.
This solution is already an improper fraction (the numerator is larger than the denominator), therefore you may leave the fraction as is.