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Math - Algebra 1 > C3 Fractions and Decimals > Flashcards

C3 Fractions and Decimals Flashcards

1
Q

Reciprocal

A

two numbers whose product is 1, also called the multiplicative inverse

4/3 is the reciprocal of 3/4 when multiplied together the product is 1.

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2
Q

increasing the terms of a fraction: what are the steps?

A

multiply both the numerator and the denominator by the same number

example:

3/4 x 2 = 6/8

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3
Q

cross multiplication for comparing fractions: what are the steps?

A
  1. Multiply the numerator of the first fraction by the denominator of the second fraction and jot down the answer.
  2. Multiply the numerator of the second fraction by the denominator of the first fraction and jot down the answers.

STEPS: 1X2 3X­4​​​

  1. Compare the two numbers, the larger number is the larger fraction

Note: only work with two fractions at a time, determine the which one is the greatest and then toss the smallest one and compare the greatest with the next one.

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4
Q

multiplying fractions: what are the steps?

A
  1. Change the mixed numbers into improper fractions
  2. Multiply the numerators together and the denominators together
  3. Reduce all the way

Tip: you can also make multiplying easier by first canceling out equal factors in the numerators an the denominators (on the diagnal) of each fraction.

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5
Q

dividing fractions: what are the steps

A

multiply the first fraction by the reciprical of the second fraction.

  1. Change the mixed numbers into improper fractions
  2. Flip the second fraction, placing the denominator on top and the numerator on the bottom. (THE RECIPRICAL)
  3. Change the division sign to multiplication
  4. Continue as with multiplication of fractions
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6
Q

adding fractions with same denominator: what are the steps?

A

add the numerators and leave the denominator unchanged

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7
Q

adding fractions with different denominators the easy way; what are the 3 steps?

A
  1. multiply the numerator of each fraction by the denominator(s) of the other fraction(s), add the results of each multiplication, place the sum as the new numerator.
  2. multiply all the denominators together, the product of the denominators is your new denominator
  3. reduce as neccessary
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8
Q

adding fractions with different denominator the traditional way; what are the 3 steps?

A
  1. find the least common multiple (LCM) of the two denominators
  2. Increase the terms of each fractions so that the denominator of each equals the LCM.
  3. Add the new fractions (add the numerators and leave the denominator unchanged)
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9
Q

subtracting fractions with the same denominator; what are the steps?

A

subtract the numerator of the second fraction from the numerator of the first fraction and leave the denominator unchanged

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10
Q

subtracting fractions with different denominators the easy way; what are the 3 steps?

A
  1. cross multiply the two fractions (numerator of first by denominator of 2nd and vice versa) and subtract the second number from the first for you new numerator.
  2. multiply all the denominators together to get the new denominator
  3. put the new numerator over the denominator to get your answer
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11
Q

subtracting fractions with different denominators the traditional way; what are the 3 steps?

A
  1. find the least common multiple (LCM) of the two denominators
  2. Increase the terms of each fractions so that the denominator of each equals the LCM.
  3. Subtract the new fractions (subtract the numerators and leave the denominator unchanged)
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12
Q

convert mixed number to improper fraction: what are the steps?

A
  1. multiply the denominator of the fractional part by the whole number, and add the result to the numerator.
  2. use this result as your new numerator, and place it over the existing denominator
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13
Q

converting improper fraction to a mixed number: what are the steps?

A
  1. divide the numerator (dividend) by the denominator (divisor)
  2. the quotent (answer) becomes the whole number part
  3. the remainder (answer) becomes the new numerator
  4. the denominator of the improper fractions is still the denominator
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14
Q

ratio

A

is a mathematical comparison of two numbers, based on division

2:3 is the same as 2 to 3 and 2/3

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15
Q

adding decimals: what are the steps

A
  1. arrange the numbers in a column and line up the decimal points
  2. add as usaul, column by column, from right to left
  3. Place the decimal point in the answer in line with the other decimal points vertically
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16
Q

subtraction decimals: what are the steps?

A
  1. arrange the numbers in a column and line up the decimal points
  2. Subtract as usual, column by column from right to left
  3. When you’re done, place the decimal point in the answer in line with the other decimal points in the problem.
17
Q

multiplying decimals: what are the steps?

A
  1. perform the multiplication as you do for whole numbers.
  2. when you are done, count the digits to the right of the decimal point in each factor, and add the result.
  3. Place the decimal point in your answer so that your answer has the same number of digits after the decimal point
18
Q

dividing decimals: what are the steps

A
  1. Turn the divisor the into a whole number by moving the decimal point all the way to the right
  2. Then move the decimal point in the dividend the same number of places to the right (add zeros as necessary, it does not change the value).
  3. Place the decimal point in the quotient directly above the decimal point in the dividend
  4. Divide as normal, being careful to line up the quotient properly so that the decimal point falls into place.
19
Q

decimals to fraction conversion: what are the steps?

A
  1. Place the decimal number as the numerator and the number 1 in the denominator
  2. Move the decimal point in the numerator one place to the right, then add a 0 behind the 1 in the denominator
  3. Repeat step 2 until the decimal point is moved all the way to the right and the numerator is a whole number

Note: converting decimals greater than 1 to a fraction the result is expressed as a mixed number e.g. 4.51 is 4 and 51/100.

20
Q

fraction to decimal conversion: what are the steps

A
  1. Divide the numerator by the denominator using decimal division
  2. Attach enough zeros to the numerator (dividend) so that you can continue dividing until you find the decimal is either a terminating decimal or a repeating decimal
21
Q

percent definition

A

percent means “out of 100”

Example: 50 out of a 100 means 50%

22
Q

change a percent to a decimal: steps?

A

drop the % sign and move the decimal point two places to the left

Examples:

2.5% = 0.025

4% = 0.04

36% = 0.36

111% = 1.11

23
Q

change decimal to percent: what are the steps

A

move the decimal point two places to the right and add a % sign

  1. 07 = 7%
  2. 21 = 21%
  3. 375 = 37.5%
  4. 75 = 275%
24
Q

convert percents to fractions: what are the steps

A
  1. place the percentage number in the numerator
  2. use the number 100 as your denominator
  3. reduce the fraction or change to mixed number as necessary

Example;

217% is 217/100 converted to 2 and 17/100

8% is 8/100 reduced to 2/25

25
Q

convert fractions to percents: what are the steps

A
  1. convert the fraction to a decimal
  2. convert the decimal to a percent
26
Q

flip trick for solving tough looking percent problems

A

move the percent sign from one number to the other number and flip the order of the numbers

Example:

88% of 50 flip to 50% of 88; easy 44

7% of 200 flip to 200% of 7; easy 2x7 = 14

27
Q

scientific notation: uses a process called?

A

powers of ten expressed as exponents

100 = 1

101 = 10

102 = 100

103 = 1,000

104 = 10,000

105 = 100,000

106 = 1,000,000

28
Q

multiplying powers of 10 in exponential form: what are the steps?

Solve: 1014 x 1015 =

A

add their exponents

1014 x 1015 = 1014 + 15 = 1029

29
Q

scientific notation: every number can be written in scientific notation as a _______ of two numbers.

  • A decimal greater than or equal to ___ and less than ____.
  • A power of ___ written as an exponent
A

scientific notation: every number can be writting in scientific notation as a product of two numbers.

  • A decimal greater than or equal to 1 and less than 10.
  • A power of 10 written as an exponent
30
Q

convert numbers to scientific notation

what are the steps to change the following numbers to scientific notation?

360,000,000 and 0.00006113

A
  1. Write the number as a decimal (if it isn’t already one)
  • 360,000,000.0
  • 0.00006113
  1. Move the decimal point just enough places to change this number to a new number that’s between 1 and 10.
  • 360,000,000.0 becomes 3.6
  • 0.00006113 becomes 6.113
  1. Multiply the new number by 10 raised (x 100) to the number of places you moved the decimal point in step 2. (if moved the decimal to the left it is a positve exponent. If moved to the right it is a negative exponent)
  • 3.6 x 108
  • 6.113 x 10-5
31
Q

why does scientific notation always use a decimal between 1 and 10?

A

Order of Magnitude: is a simple way to keep track of roughly how large or small a number is so you can compare numbers more easily.

32
Q

what is the order of magnitude of the following numbers

  1. 600,000 = 6 x 105
  2. 0.00095 = 9.5 x 10-4
A
  1. 600,000 = 6 x 105 (order of magnitude is 5 )
  2. 0.00095 = 9.5 x 10-4 (order of magnitude is -4 )
33
Q

the number of digits to the right of the decimal point in the numerator tells you the number of _____** in the power of **___\_ that is written in the denominator.

A

the number of digits to the right of the decimal point in the numerator tells you the number of zeros** in the power of **ten that is written in the denominator

34
Q

to simplify a complex fraction, you first work at creating ______ _____ or _____ in the numerator and the denominator, independently, and then you divide the numerator by the denominator

A

to simplify a complex fraction, you first work at creating improper fractions or integers in the numerator and the denominator, independently, and then you divide the numerator by the denominator

35
Q

when dividing variables instead of writing a negative exponent in the numerator what should you do?

A

if a variable is greater in the denominator, then the difference between the two powers is preferably written as a positive power of the base–in the denominator–instead of with a negative exponent in the numerator

18a3b12 / 3a7b4 = 6a3-7b12-4 = 6a-4b8 = 6b8 / a4

Math - Algebra 1 (9 decks)

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