Changing Improper Fractions and Mixed Numbers - ANSWERSImproper fractions can be converted to mixed numbers by following these steps:
Write division
... [Show More] problem with numerator divided by denominator.
Divide to determine quotient and remainder.
Write mixed number with the quotient as the whole number and the remainder as the numerator over the same denominator.
Changing Mixed Numbers Into Improper Fractions - ANSWERSMixed numbers can also be converted to improper fractions by following these steps:
Multiply the whole number by the denominator of the fraction.
To the product given by step 1, add the number of the numerator.
Write the result of step 2 as the numerator of the improper fraction. The denominator of the improper fraction should be the denominator of the original fraction.
Simplify the improper fraction by diving the numerator and denominator by all common factors.
Discrete Data - ANSWERSHas distinct values, can be counted, has unconnected points (dots)
Continuous data - ANSWERSHas values within a range, measured (not counted) does not have gaps between data points. (connected lines or curves)
Sign rule for Multiplication and division - ANSWERS1. +# x +# = +#
2. -# x -# = +#
A product or division of two numbers of the same sign will result in a positive number
3. -# x +# = -#
4. +# x -# = -#
A product or division of two numbers of different signs will result in a negative number
Prime Number - ANSWERSA prime number is a number that has exactly two positive factors; 1 and itself.
Composite Number - ANSWERSA number that is not prime. It has 2 or more positive factor, including 1 and itself.
Prime Factorization - ANSWERSWriting the number as a product of only prime numbers.
Greatest Common Factor (GCF) - ANSWERSThe larges number that divides all the given numbers evenly.
Multiples of a number - ANSWERSNumbers that can be obtained by multiplying the given number by 1, 2, 3, 4, etc.
Least Common Multiple (LCM) - ANSWERSthe smallest positive number that can be divided by the given numbers
Centigrade/Fahrenheit Conversions - ANSWERSC = (F - 32) X 5/9
F = (C X 9/5) + 32
Unit Conversions for Household Measures of Volume - ANSWERS1 tablespoon = 3 teaspoons
1 oz = 2 tablespoons
1 cup = 8 oz
1 pint = 2 cups
1 quart = 1 pints
1 gallon = 4 quarts
Common Metric Conversions - ANSWERS1 L = 1000 mL
1kg = 1000 g
1 g = 1000 mg
1 mg = 1000 mcg
Conversions between Household and Metric Units - ANSWERS1 cc (Cubic Centimeter) = 1 mL
1 oz = 30 mL
1 L = 1.057 qt
1 tsp = 5 mL
1 kg = 2.2 lbs
1 oz = 28.35 g
Like Terms - ANSWERSTerms that have the same variable raised to the same power; they can be combined using addition and subtraction
Addition/Subtraction Principle - ANSWERSWe can add or subtract the same number to both sides of an equation and the resulting expression remains equal.
Multiplication/Division Principle - ANSWERSWe can multiply or divide the same number to both sides of an equation and the resulting expression remains equal. (Divide by 0 is not allowed)
Butterfly Method - ANSWERSCross Multiply, if a/b = c/d then a x d = b x c
Slope-Intercept Equation - ANSWERSy = mx + b
Where "m" is the slope, "b" is the y-intercept, and "x" and "y" follow the coordinate formula (x,y)
Slope of a line - ANSWERSThe slope of a line is the ratio of the vertical change between two points on the line to the horizontal change between those two points.
rise: (y2 - y1) / run: (x2 - x1)
Reducing Fractions Using Prime Factorization - ANSWERSThe steps to reduce a fraction through prime factorization are as follows:
List the prime factors of both the numerator and denominator.
Cancel the factors that are common to both the numerator and denominator.
Multiply across the numerator and denominator.
6/8
6/8 = 2x3/2x2x2x
2x3/2x2x2x = 3/2x2
3/2x2 = 3/4
Reducing Fractions Using Common Factors - ANSWERSThe steps for the common factors method are as follows:
Divide numerator and denominator by a common factor.
Continue to divide by common factors.
Write the reduced factor.
-28/42
-28/42 = (-28/7) / (42/7) = -4/6
Reduce -4/6 = (-4/2)/(6/2) = -2/3
Least Common Denominator - ANSWERSThe least common multiple of the denominators of two or more fractions.
Let's determine the least common denominator of 13 and −27.
Ask "do 3 and 7 have a factor in common?" No.
So, this is situation 1. Multiply 3×7=21. 21 is the least common multiple of the numbers 3 and 7, therefore it is the least common denominator for 13 and −27.
21 is the LCD for 13 and −27
Transforming Fractions - ANSWERSDivide the least common denominator by the current denominator.
Multiply both the numerator and the denominator by this integer.
Let's now transform 1/3 and −2/7 each into their equivalent fractions that share a common denominator of 21 , which we found in the example above.
First, convert 1/3 to an equivalent fraction with a denominator of 21 .
Divide the LCD (the new denominator) by the current denominator.
21÷3=7
Multiply the numerator and denominators by 7 .
(1×7)/(3×7)=721
Adding Fractions with the Same Denominator - ANSWERSAdd or subtract the numerators of all the fractions in the expression
Keep the same denominator! (The temptation to add the two denominators is very strong—resist.)
If necessary, reduce the answer.
Adding Fractions with Different Denominators - ANSWERSFind the least common denominator (LCD).
Use the LCD to find the equivalent fractions and rewrite the expression.
Add or subtract the numerators of all the fractions in the expression.
Keep the denominator the same—do not add them.
If necessary, reduce the answer.
Adding and Subtracting Mixed Number Fractions - ANSWERSChange the mixed numbers* to improper fractions*.
Find the least common denominator (LCD) if the fractions have different denominators and convert to equivalent fractions with the LCD.
Add or subtract the numerators of all the fractions in the expression.
Keep the denominator the same.
Change improper fractions to a mixed number (if needed).
If necessary, reduce the fraction to lowest form.
Subtract the following mixed numbers:
8 5/6 − 5 1/2
Step 1: Change the mixed number to an improper fraction.
8 5/6 = 53/6
and
5 1/2=11/2
Step 2: Find equivalent fractions with the least common multiple.
Convert the fractions to equivalent fractions with the LCM. The least common multiple is 6 , therefore:
53/6 does not need to change
Multiply the numerator and denominator of 11/2 by 3
53/6 − 11/2 = 53/6 − 33/6
Step 3: Subtract like fractions.
Next, subtract the fractions.
53 / 6−336=206
Step 4: To complete the problem, convert any improper fractions to lowest terms.
20/6 = 3 2/6
Finally, reduce the fraction to its lowest form.
3 2/6 = 3 1/3
Multiplying Fractions - ANSWERSMultiply the numerators to obtain a new numerator.
Multiply the denominators to obtain a new denominator.
Write the answer in fraction form and reduce it to the lowest terms, if necessary.
Change any improper fractions to mixed numbers.
*Mixed Number Fractions:*
Change any mixed numbers to improper fractions.
Multiply the numerators to obtain a new numerator.
Multiply the denominators to obtain a new denominator and write the answer in fraction form.
Change the improper fraction back to a mixed number.
Reduce the mixed number to the lowest terms, if necessary.
Dividing Fractions - ANSWERSChange the division sign ( ÷ ) to a multiplication sign ( × ).
Write the reciprocal of the second fraction.
Multiply the numerators.
Multiply the denominators.
Write the answer in the form of a fraction.
Reduce the fraction to the lowest terms, if necessary.
*Mixed Number Fractions:*
Change any mixed numbers to improper fractions.
Change the division sign ( ÷ ) to a multiplication sign ( × ).
Write the reciprocal of the second fraction.
Multiply the numerators and denominators as usual.
Change the improper fraction to a mixed number.
Reduce the fraction to the lowest terms, if necessary.
Coefficient - ANSWERSIn algebra, constants* often take the form of coefficients*. A coefficient is a number by which a variable is being multiplied. Coefficients are written in front of variables. So, in 16x , 16 is the coefficient and x is the variable.
If a variable is without a number in front of it, the coefficient is 1 . Though it is not written, there is essentially an invisible 1 in front of any variable without a numerical coefficient.
Steps for Combining Terms - ANSWERSIdentify Like Terms
Move Terms Next to Each other
Add or Subtract
Distributive Property - ANSWERSDistribute the term outside the parentheses to each of the terms inside the parentheses
a(b + c) = ab + ac
Distribution of Negative Numbers - ANSWERSWhen in doubt, change all subtraction operations to the addition of negative numbers.
Principle of Equality - ANSWERSIf you perform equivalent operations to both sides of an equation, the result will always be an equivalent equation.
Steps for Solving an Equation With Complex Expressions - ANSWERSSubstitute any variable's known value for the variable itself
Simplify expressions on either side of the equation following order of operations:
Distribute
Combine Like terms
Add and subtract constants
Complete any other process that serves to simplify the expression
Move terms across the equation, using the Addition and Subtraction Principles of Equality:
Move all constants to one side of the equation
Get all terms with the variable to be solved on the opposite side of the equation
Simplify the expressions on either side of the equation:
Combine like terms on one side, if necessary
Add and subtract constants on the other side, if necessary
Isolate the lone variable on one side of the equation, using the Multiplication and Division Principles of Equality:
The variable will be across from its value
Check your answer:
Plug in your solution to the original equation. Perform the arithmetic on both sides of the equation. If the two sides of the equation are equal, you have successfully solved the equation!
Butterfly Method in Algebraic Equations - ANSWERSExample
Solve the following algebraic equation: 23/21 x j = 25/13 .
Write the algebraic equation in the form ax/b=c/d
Remember that a/b(x)=ax/b since x can be converted into x/1 .
Now draw "butterfly wings" around the opposite terms.
Multiply the numbers in each of the butterfly wings:
Getting and equation into Slope-Intercept Form - ANSWERSFirst, make sure the y [Show Less]