Dividing Fractions
What are the different parts of a fraction named? Where do they go?
Numerator (top), denominator (bottom)
|a| or two straight lines around a number/variable.
What is a positive number?
What is a negative number?
Any number that is greater than 0 is a positive number.
Any number less than 0 is a negative number.
What is the difference between an expression and an equation? Give an example of each for points.
Expressions do not have an equals sign. ex: x+4, 4+3, etc.
Equations are math sentences that do use an equals sign. ex: x+4=8, 4+3=7, etc.
What is the golden rule of solving equations?
Write out this equation, then solve.
"Two-thirds divided by one fifth."
2/3 ÷ 1/5
2/3 x 5/1 = 10/3 or 3 and 1/3
The number's absolute value is always the number because absolute value is a number's amount away from zero. Absolute value is always positive, so a negative number's absolute value is just that number as a positive.
Where does a negative number go on a horizontal number line?
To the left of 0.
What is the difference between an algebraic equation and a numerical equation? Give an example of each.
An algebraic equation is an equation that has variables or an unknown number. ex: x+2=5.
A numerical equation only uses numbers. ex: 3+2=5.
Use the distributive property to write this as an equivalent expression.
6(x+2)
6x+12
What is the math term for "Copy Dot Flip"?
Multiplying by the Reciprocal
Is this a true statement? Why or why not?
|-20| is greater than 18.
Yes. The absolute value of -20 is 20, which is greater than 18.
Where does a positive number go on a vertical number line? What is a real life example of this?
A positive number goes above 0 on a number line. A real life example of this could be sea level or temperature.
How do you solve a one step equation? Write out the steps that you remember.
1. Use the inverse operation
2. Do it to both sides
3. Check your answer by plugging what you got for x back into the original equation.
When you see a number right up against a parentheses, what operation are you supposed to do? Give an example.
Multiplication.
ex: 6(x+1) is the same thing as (6)(x+1) or 6*(x+1). Imagine there is a little dot between the number and the parentheses.
Write this equation, then solve. You need to show all work to get points.
"Five-twelfths divided by three-sevenths."
5/12 ÷ 3/7
5/12 x 7/3 = 35/36
|-2/3| is greater than |4/5|.
No. The absolute value of -2/3 is 2/3, which is less than 4/5.
2/3 = 0.667, 4/5 = 0.8, which means 4/5 is greater than 2/3.
Answer each part. All must be correct to get points.
a. A negative number times a positive number =
b. A negative number times a negative number =
c. A positive number times a positive number =
a. negative
b. positive
c. positive
Solve this equation. Show all work to get points.
x+18 = 25
x = 7
5(x-8)
5x-40.
Step 1: Write the equation.
33 1/3 ÷ 6 2/3
Step 2: Change to improper fractions
100/3 ÷ 20/3
Step 3: Copy dot flip
100/3 * 3/20 = 100/20 = 5
Step 4: Include units with answer.
There was 5 liters of paint in each bucket.
|-13|+ 14 -|12|+10 = 15
No. |-13| = 13, |12|=12, so the equation would be 13+14-12+10, which gets you 25, not 15.
Solve this equation. Also, what is adding a negative number the same thing as? You need both parts of this to get points.
-4 + 5 - 3 + -2.
Adding a negative number is the same thing as subtracting a positive.
Solve this equation. Show all work to get points.
x/4 = 5.
x = 20.
Working backwards, expand this equivalent expression out in factored form.
4x+16
4(x+4)