teas math
lowest common denominator
the smallest number, other than zero, that can be the denominator for two or more common fractions
3/4 is how many times greater than 1/2?
3/4=1/2X X=3/4 / 1/2 X=3/4x2/1 x=6/4=11/2 11/2
average 5 day rainfall was 1.25 in. someone lost the record for the 5th day after average was calculated. if days 1-4 were recorded as 1.5, 0.5, 2, 0.75 then what was the rainfall for day 5?
(1.5+0.5+2.0+.75+x)÷5=1.25 (4.75+x)÷5=1.25 4.75+x=6.25 x=6.25-4.75 x=1.5
meter to centimeter
1 m = 100 cm
find original price (sale price was 320, what was original price without 4% discount?)
100%-4%=96% 96%=.96 320=.96C 320/.96=C C=333.33333 or ~$333
millimeter to meter
1000 mm = 1 m
Ashley gained 14 lbs. now she is 112. what is the percent increase of her weight?
112-14=98 (14/98)x100=14.2%
how many inches in a cubic foot?
12^3=1728
150 people took an exam. 54 passed. what is the pass fail ratio?
150-54=96 54:96 reduce 9:16
ounces in a pound
16 ounces
18 is 20% of what number?
18=20%X convert 20% to .20 18=0.20X X=18/0.20 x=90
centimeters to inches
2.54 cm = 1 in
pound to ton
2000 pounds = 1 ton
How would 1.05 be displayed as a fraction?
21/20
Inches, Yards
36 inches in a yard (3ft)
what percent of 1728 is 432
432/1728=25%
60 bushes sold. three times as many pink compared to yellow. how many yellow were sold?
60=3y+y 60=4y 60/4=y y=15
Finding percent of a number (20% of 80)
Change the percent to a fraction or decimal and multiply Example: What is 20% of 80? 20/100 x 80 = 1600/100 = 16 or .20 x 80 = 16.00 = 16
The price of a 20" television changed from $450 to $400. Find the percentage change in price.
Correct answer: -11% Change in price: 450 - 400 = 50 To determine the percentage change, divide the change in price by the initial price: 50 = 0.1111 450 Multiply by 100 to determine the percentage: 0.1111 × 100 = 11.11% Because the price decreased, the change in price is negative: -11.11%, or about -11%
Determine the product of (2x/3 - 4/5) and (3/5 - x/2).
Correct answer: -x²/3 + 4x/5 - 12/25 The product of two numbers is the result of multiplying them together. (2x/3 - 4/5)(3/5 - x/2) Use FOIL (First, Outside, Inside, Last) to determine the order of operations when multiplying expressions in parentheses. (2x/3)(3/5) + (- x/2)(2x/3) + (- 4/5)(3/5) + (- 4/5)(- x/2) 6x/15 - 2x²/6 - 12/25 + 4x/10 Remember to group like terms and find a common denominator. - 2x²/6 + (4x/10 + 6x/15) - 12/25 4x/10 + 6x/15 = (4x/10)(3/3) + (6x/15)(2/2) = 12x/30 + 12x/30 = 24x/30 Simplify by dividing the numerator and denominator by 6. 24x/30 ÷ 6/6 = 4x/5 Simplify - 2x²/6 by dividing the numerator and denominator by 2. - 2x²/6 ÷ 2/2 = -x²/3 Therefore, the answer is -x²/3 + 4x/5 - 12/25.
4 1/16 ÷ 3 1/8 Which of the following options correctly simplifies the above expression?
Correct answer: 1 3/10 In order to simplify the expression, convert the mixed numbers to improper fractions. 4 1/16 = 65/16 3 1/8 = 25/8 In order to divide by a fraction, multiply it by its reciprocal. 65/16 ÷ 25/8 = 65/16 × 8/25 (65 × 8)/(16 × 25) = 520/400. Reduce the fraction to its lowest terms. 520/400 ÷ 40/40 = 13/10 Convert the improper fraction to a mixed number. 13/10 = 1 3/10
Solve the following by adding. 5/9 + 2/7 =
Correct answer: 53/63 1. Find the Least Common Denominator (LCD) of 5/9,2/7 Method 1: By Listing Multiples List out all multiples of each denominator, and find the first common one. 9 : 9,18,27,36,45,54,63 7 : 7,14,21,28,35,42,49,56,63 Therefore, the LCD is 63. Method 2: By Prime Factors List all prime factors of each denominator, and find the union of these primes. 9 : 3,3 7 : 7 Therefore, the LCD is 3×3×7=63 2. Make the denominators the same as the LCD (5×7)/(9×7) + (2×9)/(7×9) 3. Simplify - Denominators are now the same 35/63 + 18/63 4. Join the denominators (35+18)/63 5. Simplify 53/63
convert percent to decimal
Divide by 100, or move the decimal 2 places to the left. Example: 68% is equal to 0.68
convert decimal to percent
Move the decimal two places to the right and add a percent sign
when multiplying fractions, do you need to find a common denom?
NO just multiply across
absolute value
The distance a number is from zero on a number line, shown by two straight bars i.e. |x-3|
solution set of an equation i.e. |x-3|=6
The set of values that make an equation true. surrounded by brackets. |x-3|=6 x-3=6 and x-3=-6 solve both for x x=6-(-3)=9 and x=-6+3=-3 {-3,9}
cubic inch
The volume equal to a cube one inch on each side; in³
simplifying the expression
When you use the distributive property to combine like terms
a(c/b) is equal to...
a divided by b/c
simplify 1/9x3 2/3
express the mixed number as a fraction 3 2/3=(3x3+2)/3=11/3 then multiply numerators and denominators 1/9x11/3=(11x1)/(3x9)=11/27
milli to kilo
multiply by 1,000,000
convert decimal to fraction
remove the decimal and put the # over 100
x
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