# Khan/khan-exercises

Space/tab cleanup

1 parent a13484e commit 075f731ffc4910e7dc98af6476fd2b5908b8dd39 spicyj committed Jun 2, 2011
28 exercises/divisibility_intro.html
 @@ -6,13 +6,13 @@
- +
- randRange( 0, 1 ) ? getOddComposite( 50 ) : getEvenComposite( 50 ) + randRange( 0, 1 ) ? getOddComposite( 50 ) : getEvenComposite( 50 ) var factorization = getPrimeFactorization( NUMBER ), num_factors = round( factorization.length / 2 ), @@ -40,14 +40,14 @@
-

In other words, we are looking for a number between LOW and HIGH such that NUMBER is divisible by it.

-
-

We see that NUMBER is divisible by ANSWER.

-

NUMBER's prime factorization is NUMBER_FACTORS.

-

-

It isn't a coincidence that NUMBER's prime factorization includes ANSWER's prime factorization!

-
-
+

In other words, we are looking for a number between LOW and HIGH such that NUMBER is divisible by it.

+
+

We see that NUMBER is divisible by ANSWER.

+

NUMBER's prime factorization is NUMBER_FACTORS.

+

+

It isn't a coincidence that NUMBER's prime factorization includes ANSWER's prime factorization!

+
+
44 exercises/evaluating_expressions_1.html
 @@ -7,23 +7,23 @@
- randRange( 1, 10 ) - - if ( randRange( 0, 1 ) ) { - return randRange( 3, 10 ); - } else { - return -1 * randRange( 3, 10 ); - } - - - if ( randRange( 0, 1 ) ) { - return randRange( 3, 10 ); - } else { - return -1 * randRange( 3, 10 ); - } - + randRange( 1, 10 ) + + if ( randRange( 0, 1 ) ) { + return randRange( 3, 10 ); + } else { + return -1 * randRange( 3, 10 ); + } + + + if ( randRange( 0, 1 ) ) { + return randRange( 3, 10 ); + } else { + return -1 * randRange( 3, 10 ); + } + - (X * COEFF) + CONSTANT + (X * COEFF) + CONSTANT
@@ -35,14 +35,14 @@
-
-

Plug in X for x.

-

= (COEFF) \cdot (X) + CONSTANT

-
+
+

Plug in X for x.

+

= (COEFF) \cdot (X) + CONSTANT

+
-

= COEFF * X + CONSTANT

+

= COEFF * X + CONSTANT

-

= SOLUTION

+

= SOLUTION

136 exercises/exponents_1.html
 @@ -1,84 +1,84 @@ - Exponents 1 - + Exponents 1 + -
-

This exercise covers exponential arithmetic with, in general, integer bases raised to nonnegative integer exponents. Handles three specific cases: integers raised to positive integers (this is the most common case); nonzero integers raised to 0; and -1, 0, and 1 raised to arbitrarily large positive integers.

+
+

This exercise covers exponential arithmetic with, in general, integer bases raised to nonnegative integer exponents. Handles three specific cases: integers raised to positive integers (this is the most common case); nonzero integers raised to 0; and -1, 0, and 1 raised to arbitrarily large positive integers.

- -
- -
-
- randRangeExclude( -10, 10, [0, 1, -1] ) - BASE < 0 ? "(" + BASE + ")" : BASE - - [ undefined, undefined, 5, 4, 4, 4, 3, 3, 3, 3, 10 ] - - randRangeWeighted( 1, REASONABLE_EXPS[abs( BASE )], 1, .1 ) - round( pow( BASE, EXP ) ) - function() { - var result = BASE_STRING; - for ( var i = 1; i < EXP; i++ ) { - result += " \\cdot" + BASE_STRING; - } - return result; - }() -
+ +
+ +
+
+ randRangeExclude( -10, 10, [0, 1, -1] ) + BASE < 0 ? "(" + BASE + ")" : BASE + + [ undefined, undefined, 5, 4, 4, 4, 3, 3, 3, 3, 10 ] + + randRangeWeighted( 1, REASONABLE_EXPS[abs( BASE )], 1, .1 ) + round( pow( BASE, EXP ) ) + function() { + var result = BASE_STRING; + for ( var i = 1; i < EXP; i++ ) { + result += " \\cdot" + BASE_STRING; + } + return result; + }() +
-

BASE_STRING^{EXP}

-

SOLUTION

+

BASE_STRING^{EXP}

+

SOLUTION

-
- -
= HINT
-
= SOLUTION
-
-
+
+ +
= HINT
+
= SOLUTION
+
+
- -
-
- randRangeNonZero( -500, 500 ) - BASE < 0 ? "(" + BASE + ")" : BASE -
+ +
+
+ randRangeNonZero( -500, 500 ) + BASE < 0 ? "(" + BASE + ")" : BASE +
-

BASE_STRING^{0}

-

1

+

BASE_STRING^{0}

+

1

-
-
Anything to the 0th power equals...?
-
Anything to the 0th power equals 1.
-
-
+
+
Anything to the 0th power equals...?
+
Anything to the 0th power equals 1.
+
+
- -
-
- - random() < 0.5 ? -1 : (random() < 0.5 ? 0 : 1) - BASE === -1 ? "(-1)" : BASE - randRange( 1, 1000 ) - round( pow( BASE, EXP ) ) - function() { - if (BASE === 0) return "nonzero"; - else if (BASE === 1) return ""; - else return isEven( EXP ) ? "even" : "odd"; - }() -
+ +
+
+ + random() < 0.5 ? -1 : (random() < 0.5 ? 0 : 1) + BASE === -1 ? "(-1)" : BASE + randRange( 1, 1000 ) + round( pow( BASE, EXP ) ) + function() { + if (BASE === 0) return "nonzero"; + else if (BASE === 1) return ""; + else return isEven( EXP ) ? "even" : "odd"; + }() +
-

BASE_STRING^{EXP}

-

SOLUTION

+

BASE_STRING^{EXP}

+

SOLUTION

-
-
Cardinal(BASE) to any POWER_HINT power equals...?
-
Cardinal(BASE) to any POWER_HINT power equals SOLUTION.
-
-
-
-
+
+
Cardinal(BASE) to any POWER_HINT power equals...?
+
Cardinal(BASE) to any POWER_HINT power equals SOLUTION.
+
+
+
+
78 exercises/exponents_2.html
 @@ -1,49 +1,49 @@ - Exponents 2 - + Exponents 2 + -
-

This exercise covers exponential arithmetic with rational bases and integer (primarily negative) exponents.

+
+

This exercise covers exponential arithmetic with rational bases and integer (primarily negative) exponents.

-
-
-
- randRange( 1, 10 ) - - randRangeWeighted( 1, 10, 1, .25 ) - - random() < 0.5 - - [ undefined, 1000, 5, 4, 4, 4, 3, 3, 3, 3, 10 ] - - randRangeWeighted( 1, min( REASONABLE_EXPS[BASE_NUM], REASONABLE_EXPS[BASE_DENOM] ), 1, .1) - - random() < 0.75 - function() { - var result = BASE_NUM; - if ( BASE_DENOM !== 1 ) - result = "\\frac{BASE_NUM}{BASE_DENOM}"; - if ( BASE_NEG ) - result = "\\left(-" + result + "\\right)"; - return result; - }() - function() { - /* FIXME: implement! */ - }() - round( pow( BASE_NUM / BASE_DENOM, EXP ) ) -
+
+
+
+ randRange( 1, 10 ) + + randRangeWeighted( 1, 10, 1, .25 ) + + random() < 0.5 + + [ undefined, 1000, 5, 4, 4, 4, 3, 3, 3, 3, 10 ] + + randRangeWeighted( 1, min( REASONABLE_EXPS[BASE_NUM], REASONABLE_EXPS[BASE_DENOM] ), 1, .1) + + random() < 0.75 + function() { + var result = BASE_NUM; + if ( BASE_DENOM !== 1 ) + result = "\\frac{BASE_NUM}{BASE_DENOM}"; + if ( BASE_NEG ) + result = "\\left(-" + result + "\\right)"; + return result; + }() + function() { + /* FIXME: implement! */ + }() + round( pow( BASE_NUM / BASE_DENOM, EXP ) ) +
-

BASE_STRING^{(EXP_NEG ? "-" : "")+EXP}

-

SOLUTION

+

BASE_STRING^{(EXP_NEG ? "-" : "")+EXP}

+

SOLUTION

-
- -
-
-
-
+
+ +
+
+
+
74 exercises/linear_equations_1.html
 @@ -1,48 +1,48 @@ - Linear Equations 1 - + Linear Equations 1 + -
-
- - randRange( 2, 10 ) - randRange( 2, 10 ) - fraction( D, A ) - fraction( 1, A ) -
+ Issue #36 for reference. + --> + randRange( 2, 10 ) + randRange( 2, 10 ) + fraction( D, A ) + fraction( 1, A ) +
-
-
-

Solve for x:

-
Ax = D
+
+
+

Solve for x:

+
Ax = D
- -

SOLUTION

-
-
+ +

SOLUTION

+
+
-
- -
-

Multiply both sides by ONE_OVER_A.

-

(ONE_OVER_A) \cdot (Ax) = (ONE_OVER_A) \cdot (D)

-
-
-

Simplify.

-

x = SOLUTION

-
-
- +
+ +
+

Multiply both sides by ONE_OVER_A.

+

(ONE_OVER_A) \cdot (Ax) = (ONE_OVER_A) \cdot (D)

+
+
+

Simplify.

+

x = SOLUTION

+
+
+
46 exercises/logarithms_1.html
 @@ -14,23 +14,23 @@ function get_number( base ) { var number; do { - /* Note: This will tend to use smaller powers. */ + /* Note: This will tend to use smaller powers. */ answer = KhanUtil.randRange ( 2, 5 ); number = Math.pow( base, answer ); } while ( number > LARGEST_NUMBER ); return number; } - /* This is used for hints. Given the number you're taking a logarithim of, and - * a base, breaks the number into base x base x base... x base. - * Returns a string. */ - function get_power_string(number, base) { - var result = base; - for (var i=base; i @@ -39,30 +39,30 @@ KhanUtil.randRange( 2, 16 ) get_number(base) answer - get_power_string(number, base) + get_power_string(number, base)

log_{base}number =

-
• 1
• -
• 2
• -
• 3
• -
• 4
• -
• 5
• -
• 6
• +
• 1
• +
• 2
• +
• 3
• +
• 4
• +
• 5
• +
• 6
-

If b^e=x ,then log_{b}x=e

-

First, try to write number, the number we are taking the logarithm of, as a power of base, the base of the logarithm.

-

number can be expressed as power_string

-

number can be expressed as base^answer.

-

+

If b^e=x ,then log_{b}x=e

+

First, try to write number, the number we are taking the logarithm of, as a power of base, the base of the logarithm.

+

number can be expressed as power_string

+

number can be expressed as base^answer.

+

52 exercises/multiplication_1.html
 @@ -1,36 +1,36 @@ - Multiplication 1 - - + Multiplication 1 + + -
-
- rand( 12 ) - rand( 12 ) -
+
+
+ rand( 12 ) + rand( 12 ) +
-
-
-

A \times B = ?

-
A * B
-
-
+
+
+

A \times B = ?

+
A * B
+
+
-
- -
• • •
-
There are A rows and B columns.
-
In total, there are A * B circles.
-
+
+ +
• • •
+
There are A rows and B columns.
+
In total, there are A * B circles.
+
-
+
214 exercises/percentage_word_problems_1.html
 @@ -1,114 +1,114 @@ - Percentage Word Problems 1 - + Percentage Word Problems 1 + -
-
-
-
- KhanUtil.randRange( 1, 150 ) - KhanUtil.randRange( 2, 100 ) -
-

- What is A_SIMPLE% of B_SIMPLE? (Round to nearest whole number) -

-

round((A_SIMPLE * B_SIMPLE) / 100)

-
-

- A_SIMPLE / 100 * B_SIMPLE \approx round((A_SIMPLE * B_SIMPLE) / 100) -

-
-
-
-

- B_SIMPLE is A_SIMPLE% of what number? (Round to the hundredths place) -

-

round(((B_SIMPLE * 100) / A_SIMPLE) * 100) / 100

-
-

Let x be the number that B_SIMPLE is A_SIMPLE% of.

-

A_SIMPLE / 100 * x = B_SIMPLE

-

x=B_SIMPLE/A_SIMPLE / 100

-

x \approxround((B_SIMPLE * 100/A_SIMPLE * 100))/100

-
-
-
-
- KhanUtil.randRange( 2, 100 ) - BANK_FEWER + KhanUtil.randRange(5, 2 * BANK_FEWER + 10 ) -
-

- person(1) has BANK_MORE dollars in the bank today. Yesterday, he(1) had BANK_FEWER dollars in the bank. By what percentage did person(1)'s bank account increase over the past day? (Enter your answer as a percentage rounded to the hundredths place. For example, if your answer is 95.678%, enter 95.68 for your answer)

-

round(((BANK_MORE - BANK_FEWER) * 10000) / BANK_FEWER) / 100

-
-

The bank account grew by BANK_MORE - BANK_FEWER = BANK_MORE - BANK_FEWER dollars

-

\frac{BANK_MORE - BANK_FEWER}{BANK_FEWER} \approx round(((BANK_MORE - BANK_FEWER) * 10000) / BANK_FEWER) / 100\%

-
-
-
-

- person(1) has BANK_FEWER dollars in the bank today. Yesterday, he(1) had BANK_MORE dollars in the bank. By what percentage did person(1)'s bank account decrease over the past day? (Enter your answer as a percentage rounded to the hundredths place. For example, if your answer is 95.678%, enter 95.68 for your answer.) -

-

round(((BANK_MORE - BANK_FEWER) * 10000) / BANK_MORE) / 100

-
-

The bank account decreased by BANK_MORE - BANK_FEWER = BANK_MORE - BANK_FEWER dollars

-

\frac{BANK_MORE - BANK_FEWER}{BANK_MORE} \approx round(((BANK_MORE - BANK_FEWER) * 10000) / BANK_MORE) / 100\%

-
-
-
-
- KhanUtil.randRange( 10, 150 ) - KhanUtil.randRange( 50, 999 ) - round(YEAR_THIS * 10000 / (100 + YEAR_PERCENT_MORE)) / 100 -
-

- person(1) has YEAR_PERCENT_MORE% more money today than he(1) did this time last year. If person(1) has YEAR_THIS dollars today, how many dollars did she have this time last year? (round to the nearest cent [hundredth of a dollar])

-

YEAR_LAST

-
-

Let x be the amount of money that she had last year.

-

x + YEAR_PERCENT_MORE / 100x = YEAR_THIS

-

(100 + YEAR_PERCENT_MORE) / 100x = YEAR_THIS

-

x = \frac{YEAR_THIS}{(100 + YEAR_PERCENT_MORE) / 100}

-

x \approx YEAR_LAST

-
-
-
-

- person(1) has YEAR_PERCENT_MORE% more money today than he(1) did this time last year. If person(1) has YEAR_THIS dollars today, how many dollars did she make over this past year? (round to the nearest cent [hundredth of a dollar])

-

round((YEAR_THIS - YEAR_LAST) * 100) / 100

-
-

Let x be the amount of money that she had last year.

-

x + YEAR_PERCENT_MORE / 100x = YEAR_THIS

-

(100 + YEAR_PERCENT_MORE) / 100x = YEAR_THIS

-

x = \frac{YEAR_THIS}{(100 + YEAR_PERCENT_MORE) / 100}

-

x \approx YEAR_LAST

-

So, she had YEAR_LAST dollars last year. However, we need to know how much she has made over the past year!

-

If she had YEAR_LAST dollars last year and now has YEAR_THIS dollars this year, then she has made YEAR_THIS-YEAR_LAST \approx round((YEAR_THIS - YEAR_LAST) * 100) / 100 dollars over the course of the year.

-

So, the answer is round((YEAR_THIS - YEAR_LAST) * 100) / 100 dollars.

-
-
- -
-
- KhanUtil.randRange( 10, 25 ) - KhanUtil.randRange( 5, 100 ) - round(DOLLARS * 100 * 100 / (100 - PERCENT_OFF)) / 100 -
-
-

person(1) has DOLLARS dollars to spend at a store. The store currently has a sale where the sale price is PERCENT_OFF% off the marked price. What is the highest marked price that person(1) can afford?

-

HIGHEST_PRICE

-
-
-

Let x be the highest marked price that person(1) can afford.

-

x-(PERCENT_OFF/100)x = sale price

-

((100-PERCENT_OFF)/100)x = sale price

-

((100-PERCENT_OFF/100)x = DOLLARS

-

x = HIGHEST_PRICE dollars

-
-
-
-
+
+
+
+
+ KhanUtil.randRange( 1, 150 ) + KhanUtil.randRange( 2, 100 ) +
+

+ What is A_SIMPLE% of B_SIMPLE? (Round to nearest whole number) +

+

round((A_SIMPLE * B_SIMPLE) / 100)

+
+

+ A_SIMPLE / 100 * B_SIMPLE \approx round((A_SIMPLE * B_SIMPLE) / 100) +

+
+
+
+

+ B_SIMPLE is A_SIMPLE% of what number? (Round to the hundredths place) +

+

round(((B_SIMPLE * 100) / A_SIMPLE) * 100) / 100

+
+

Let x be the number that B_SIMPLE is A_SIMPLE% of.

+

A_SIMPLE / 100 * x = B_SIMPLE

+

x=B_SIMPLE/A_SIMPLE / 100

+

x \approxround((B_SIMPLE * 100/A_SIMPLE * 100))/100

+
+
+
+
+ KhanUtil.randRange( 2, 100 ) + BANK_FEWER + KhanUtil.randRange(5, 2 * BANK_FEWER + 10 ) +
+

+ person(1) has BANK_MORE dollars in the bank today. Yesterday, he(1) had BANK_FEWER dollars in the bank. By what percentage did person(1)'s bank account increase over the past day? (Enter your answer as a percentage rounded to the hundredths place. For example, if your answer is 95.678%, enter 95.68 for your answer)

+

round(((BANK_MORE - BANK_FEWER) * 10000) / BANK_FEWER) / 100

+
+

The bank account grew by BANK_MORE - BANK_FEWER = BANK_MORE - BANK_FEWER dollars

+

\frac{BANK_MORE - BANK_FEWER}{BANK_FEWER} \approx round(((BANK_MORE - BANK_FEWER) * 10000) / BANK_FEWER) / 100\%

+
+
+
+

+ person(1) has BANK_FEWER dollars in the bank today. Yesterday, he(1) had BANK_MORE dollars in the bank. By what percentage did person(1)'s bank account decrease over the past day? (Enter your answer as a percentage rounded to the hundredths place. For example, if your answer is 95.678%, enter 95.68 for your answer.) +

+

round(((BANK_MORE - BANK_FEWER) * 10000) / BANK_MORE) / 100

+
+

The bank account decreased by BANK_MORE - BANK_FEWER = BANK_MORE - BANK_FEWER dollars

+

\frac{BANK_MORE - BANK_FEWER}{BANK_MORE} \approx round(((BANK_MORE - BANK_FEWER) * 10000) / BANK_MORE) / 100\%

+
+
+
+
+ KhanUtil.randRange( 10, 150 ) + KhanUtil.randRange( 50, 999 ) + round(YEAR_THIS * 10000 / (100 + YEAR_PERCENT_MORE)) / 100 +
+

+ person(1) has YEAR_PERCENT_MORE% more money today than he(1) did this time last year. If person(1) has YEAR_THIS dollars today, how many dollars did she have this time last year? (round to the nearest cent [hundredth of a dollar])

+

YEAR_LAST

+
+

Let x be the amount of money that she had last year.

+

x + YEAR_PERCENT_MORE / 100x = YEAR_THIS

+

(100 + YEAR_PERCENT_MORE) / 100x = YEAR_THIS

+

x = \frac{YEAR_THIS}{(100 + YEAR_PERCENT_MORE) / 100}

+

x \approx YEAR_LAST

+
+
+
+

+ person(1) has YEAR_PERCENT_MORE% more money today than he(1) did this time last year. If person(1) has YEAR_THIS dollars today, how many dollars did she make over this past year? (round to the nearest cent [hundredth of a dollar])

+

round((YEAR_THIS - YEAR_LAST) * 100) / 100

+
+

Let x be the amount of money that she had last year.

+

x + YEAR_PERCENT_MORE / 100x = YEAR_THIS

+

(100 + YEAR_PERCENT_MORE) / 100x = YEAR_THIS

+

x = \frac{YEAR_THIS}{(100 + YEAR_PERCENT_MORE) / 100}

+

x \approx YEAR_LAST

+

So, she had YEAR_LAST dollars last year. However, we need to know how much she has made over the past year!

+

If she had YEAR_LAST dollars last year and now has YEAR_THIS dollars this year, then she has made YEAR_THIS-YEAR_LAST \approx round((YEAR_THIS - YEAR_LAST) * 100) / 100 dollars over the course of the year.

+

So, the answer is round((YEAR_THIS - YEAR_LAST) * 100) / 100 dollars.

+
+
+ +
+
+ KhanUtil.randRange( 10, 25 ) + KhanUtil.randRange( 5, 100 ) + round(DOLLARS * 100 * 100 / (100 - PERCENT_OFF)) / 100 +
+
+

person(1) has DOLLARS dollars to spend at a store. The store currently has a sale where the sale price is PERCENT_OFF% off the marked price. What is the highest marked price that person(1) can afford?

+

HIGHEST_PRICE

+
+
+

Let x be the highest marked price that person(1) can afford.

+

x-(PERCENT_OFF/100)x = sale price

+

((100-PERCENT_OFF)/100)x = sale price

+

((100-PERCENT_OFF/100)x = DOLLARS

+

x = HIGHEST_PRICE dollars

+
+
+
+
68 exercises/place_value.html
 @@ -5,56 +5,56 @@ - +
- KhanUtil.shuffle([1, 2, 3, 4, 5, 6, 7, 8, 9]).slice( 0, 4 ) + KhanUtil.shuffle([1, 2, 3, 4, 5, 6, 7, 8, 9]).slice( 0, 4 ) - DIGITS[0] - DIGITS[1] - DIGITS[2] - DIGITS[3] + DIGITS[0] + DIGITS[1] + DIGITS[2] + DIGITS[3] - 1000 * THOUSANDS + 100 * HUNDREDS + 10 * TENS + ONES + 1000 * THOUSANDS + 100 * HUNDREDS + 10 * TENS + ONES - ["thousands", "hundreds", "tens", "ones"] - randRange( 0, 3 ) + ["thousands", "hundreds", "tens", "ones"] + randRange( 0, 3 ) - DIGITS[QUESTION_TYPE] - PLACES.splice( QUESTION_TYPE, 1 ) - PLACES[0] - PLACES[1] - PLACES[2] + DIGITS[QUESTION_TYPE] + PLACES.splice( QUESTION_TYPE, 1 ) + PLACES[0] + PLACES[1] + PLACES[2]
-

What is the place value of QUESTION_PLACE in NUM?

-

SOLUTION

+

What is the place value of QUESTION_PLACE in NUM?

+

SOLUTION

-
• WRONG_1
• -
• WRONG_2
• -
• WRONG_3
• -
+
• WRONG_1
• +
• WRONG_2
• +
• WRONG_3
• +
-
-

NUM can be represented as follows.

-

= (THOUSANDS \cdot 1000) - + (HUNDREDS \cdot 100) - + (TENS \cdot 10) - + (ONES \cdot 1)

-
-

= plural( THOUSANDS, "thousand", "thousands" ) - + plural(HUNDREDS, "hundred") - + plural(TENS, "ten") - + plural(ONES, "one")

+
+

NUM can be represented as follows.

+

= (THOUSANDS \cdot 1000) + + (HUNDREDS \cdot 100) + + (TENS \cdot 10) + + (ONES \cdot 1)

+
+

= plural( THOUSANDS, "thousand", "thousands" ) + + plural(HUNDREDS, "hundred") + + plural(TENS, "ten") + + plural(ONES, "one")

-

Thus, QUESTION_PLACE is in the SOLUTION place.

+

Thus, QUESTION_PLACE is in the SOLUTION place.

8 exercises/prime_numbers.html
 @@ -28,10 +28,10 @@

Which of these numbers is prime?

PRIME

-
• WRONG_1
• -
• WRONG_2
• -
• WRONG_3
• -
• WRONG_4
• +
• WRONG_1
• +
• WRONG_2
• +
• WRONG_3
• +
• WRONG_4
31 exercises/recognizing_fractions.html
 @@ -7,8 +7,8 @@
- randRange( 1, 11 ) - randRange( 2, 12 ) + randRange( 1, 11 ) + randRange( 2, 12 )
@@ -17,25 +17,24 @@

What is the fraction's numerator?

NUMERATOR

-

Thus, the numerator is NUMERATOR.

-
+

Thus, the numerator is NUMERATOR.

+
-

What is the fraction's denominator?

-

DENOMINATOR

-
-

Thus, the denominator is DENOMINATOR.

-
-
+

What is the fraction's denominator?

+

DENOMINATOR

+
+

Thus, the denominator is DENOMINATOR.

+
+
-

Fractions help represent parts of a whole.

- -

You can think of this fraction as representing NUMERATOR out of DENOMINATOR slices of pie. In other words, the pie has been cut into DENOMINATOR slices, and we are only considering NUMERATOR of those slices.

-

The numerator is the number of slices we care about, and it is written above the fraction line. The denominator is the total number of slices, and it is written below the line.

-

- +

Fractions help represent parts of a whole.

+ +

You can think of this fraction as representing NUMERATOR out of DENOMINATOR slices of pie. In other words, the pie has been cut into DENOMINATOR slices, and we are only considering NUMERATOR of those slices.

+

The numerator is the number of slices we care about, and it is written above the fraction line. The denominator is the total number of slices, and it is written below the line.

+

70 exercises/simplifying_fractions.html
 @@ -7,12 +7,12 @@
- randRange( 3, 15 ) - randRange(2, 10) * FACTOR - randRange(2, 10) * FACTOR - getGCD( NUM, DENOM ) - getPrimeFactorization( GCD ) - toSentence( GCD_FACTORS ) + randRange( 3, 15 ) + randRange(2, 10) * FACTOR + randRange(2, 10) * FACTOR + getGCD( NUM, DENOM ) + getPrimeFactorization( GCD ) + toSentence( GCD_FACTORS )
@@ -24,35 +24,35 @@
-

There are several ways to tackle this problem.

- -

What is the GCD of NUM and DENOM?

- -

GCD(NUM, DENOM) = GCD

- -

- \dfrac{NUM}{DENOM} -

- -

- = \dfrac{NUM / GCD \cdot GCD}{ DENOM / GCD\cdot GCD} -

- -

- = \dfrac{NUM / GCD}{DENOM / GCD} \cdot \dfrac{GCD}{GCD} -

- -

- = \dfrac{NUM / GCD}{DENOM / GCD} -

-
-

You can also solve this problem by repeatedly dividing the numerator and denominator by smaller factors.

-

For example:

- -

GCD_FACTORS_SENTENCE

-
+

There are several ways to tackle this problem.

+ +

What is the GCD of NUM and DENOM?

+ +

GCD(NUM, DENOM) = GCD

+ +

+ \dfrac{NUM}{DENOM} +

+ +

+ = \dfrac{NUM / GCD \cdot GCD}{ DENOM / GCD\cdot GCD} +

+ +

+ = \dfrac{NUM / GCD}{DENOM / GCD} \cdot \dfrac{GCD}{GCD} +

+ +

+ = \dfrac{NUM / GCD}{DENOM / GCD} +

+
+

You can also solve this problem by repeatedly dividing the numerator and denominator by smaller factors.

+

For example:

+ +

GCD_FACTORS_SENTENCE

+
20 exercises/special_derivatives.html
 @@ -10,14 +10,14 @@ generateSpecialFunction("x") funcNotation("x") - + -
-
+
+

NOTATION.f = FUNC.f

-

NOTATION.ddxF = {?}

+

NOTATION.ddxF = {?}

-

FUNC.ddxF

+

FUNC.ddxF

• FUNC.wrongs[0]
• @@ -26,12 +26,12 @@
• FUNC.wrongs[3]
• FUNC.wrongs[4]
-
-
+
+
-
+

NOTATION.ddxF = FUNC.ddxF

-
-
+ +
52 exercises/subtraction_2.html
 @@ -6,33 +6,33 @@
-
- randRange(10,99) - randRange(1,9) - A%10 - (A-(A%10))/10 - (B > A_1 ? A_1+10 : A_1) - (B > A_1 ? A_2-1 : A_2) -
+
+ randRange(10,99) + randRange(1,9) + A%10 + (A-(A%10))/10 + (B > A_1 ? A_1+10 : A_1) + (B > A_1 ? A_2-1 : A_2) +
-
-
-

A - B = ?

-
A - B
-
-
-
-

First we need to make sure that all the digits in the top number are greater than or equal to the digit below it.

-

- A_1 is less then B, so we'll have to borrow. -

-

- A_2 - 1 = After_Borrow2, A_1 + 10 = After_Borrow1 -

-

All the top digits are greater than or equal to all the bottom digits, so we can start subtracting.

-

Units digit: After_Borrow1 - B = After_Borrow1-B

-

Bring down the After_Borrow2 to get (After_Borrow2*10)+After_Borrow1-B.

-
+
+
+

A - B = ?

+
A - B
+
+
+
+

First we need to make sure that all the digits in the top number are greater than or equal to the digit below it.

+

+ A_1 is less then B, so we'll have to borrow. +

+

+ A_2 - 1 = After_Borrow2, A_1 + 10 = After_Borrow1 +

+

All the top digits are greater than or equal to all the bottom digits, so we can start subtracting.

+

Units digit: After_Borrow1 - B = After_Borrow1-B

+

Bring down the After_Borrow2 to get (After_Borrow2*10)+After_Borrow1-B.

+
52 exercises/subtraction_3.html
 @@ -6,33 +6,33 @@
-
- randRange(100,999) - randRange(10,99) - digits(A) - digits(B) -
+
+ randRange(100,999) + randRange(10,99) + digits(A) + digits(B) +
-
-
-

A - B = ?

-
A - B
-
-
-
-

First we need to make sure that all the digits in the top number are greater than or equal to the digit below it.

- -

A_Array[0] is less then B_Array[0], so we'll have to borrow.

-

A_Array[1] - 1 = A_Array[1]=A_Array[1]-1, A_Array[0]+10=A_Array[0]=A_Array[0]+10

- -

A_Array[1] is less then B_Array[1], so we'll have to borrow.

-

A_Array[2] - 1 = A_Array[2]=A_Array[2]-1, A_Array[1]+10=A_Array[1]=A_Array[1]+10

-

All the top digits are greater than or equal to all the bottom digits, so we can start subtracting.

-

Units digit: A_Array[0] - B_Array[0] = A_Array[0]-B_Array[0]

-

Tens digit: A_Array[1] - B_Array[1] = A_Array[1]-B_Array[1]

-

Bring down the A_Array[2] to get A_Array[2].

-

-
+
+
+

A - B = ?

+
A - B
+
+
+
+

First we need to make sure that all the digits in the top number are greater than or equal to the digit below it.

+ +

A_Array[0] is less then B_Array[0], so we'll have to borrow.

+

A_Array[1] - 1 = A_Array[1]=A_Array[1]-1, A_Array[0]+10=A_Array[0]=A_Array[0]+10

+ +

A_Array[1] is less then B_Array[1], so we'll have to borrow.

+

A_Array[2] - 1 = A_Array[2]=A_Array[2]-1, A_Array[1]+10=A_Array[1]=A_Array[1]+10

+

All the top digits are greater than or equal to all the bottom digits, so we can start subtracting.

+

Units digit: A_Array[0] - B_Array[0] = A_Array[0]-B_Array[0]

+

Tens digit: A_Array[1] - B_Array[1] = A_Array[1]-B_Array[1]

+

Bring down the A_Array[2] to get A_Array[2].

+

+
62 exercises/subtraction_4.html
 @@ -6,38 +6,38 @@
-
- randRange(10000,99999) - randRange(100,999) - digits(A) - digits(B) -
+
+ randRange(10000,99999) + randRange(100,999) + digits(A) + digits(B) +
-
-
-

A - B = ?

-
A - B
-
-
-
-

First we need to make sure that all the digits in the top number are greater than or equal to the digit below it.

- -

For the units digit, A_Array[0] is less then B_Array[0], so we'll have to borrow.

-

A_Array[1] - 1 = A_Array[1]=A_Array[1]-1, A_Array[0] + 10 = A_Array[0]=A_Array[0]+10

- -

For the tens digit, A_Array[1] is less then B_Array[1], so we'll have to borrow.

-

A_Array[2] - 1 = A_Array[2]=A_Array[2]-1, A_Array[1] + 10 = A_Array[1]=A_Array[1]+10

- -

For the hundreds digit, A_Array[2] is less then B_Array[2], so we'll have to borrow.

-

A_Array[3] - 1 = A_Array[3]=A_Array[3]-1, A_Array[2] + 10 = A_Array[2]=A_Array[2]+10

-

All the top digits are greater than or equal to all the bottom digits, so we can start subtracting.

-

Units digit: A_Array[0] - B_Array[0] = A_Array[0]-B_Array[0]

-

Tens digit: A_Array[1] - B_Array[1] = A_Array[1]-B_Array[1]

-

Hundreds digit: A_Array[2] - B_Array[2] = A_Array[2]-B_Array[2]

-

Thousands digit: Bring down the A_Array[3] to get A_Array[3].

-

Ten thousands digit: Bring down the A_Array[4] to get A_Array[4].

-

-
+
+
+

A - B = ?

+
A - B
+
+
+
+

First we need to make sure that all the digits in the top number are greater than or equal to the digit below it.

+ +

For the units digit, A_Array[0] is less then B_Array[0], so we'll have to borrow.

+

A_Array[1] - 1 = A_Array[1]=A_Array[1]-1, A_Array[0] + 10 = A_Array[0]=A_Array[0]+10

+ +

For the tens digit, A_Array[1] is less then B_Array[1], so we'll have to borrow.

+

A_Array[2] - 1 = A_Array[2]=A_Array[2]-1, A_Array[1] + 10 = A_Array[1]=A_Array[1]+10

+ +

For the hundreds digit, A_Array[2] is less then B_Array[2], so we'll have to borrow.

+

A_Array[3] - 1 = A_Array[3]=A_Array[3]-1, A_Array[2] + 10 = A_Array[2]=A_Array[2]+10

+

All the top digits are greater than or equal to all the bottom digits, so we can start subtracting.

+

Units digit: A_Array[0] - B_Array[0] = A_Array[0]-B_Array[0]

+

Tens digit: A_Array[1] - B_Array[1] = A_Array[1]-B_Array[1]

+

Hundreds digit: A_Array[2] - B_Array[2] = A_Array[2]-B_Array[2]

+

Thousands digit: Bring down the A_Array[3] to get A_Array[3].

+

Ten thousands digit: Bring down the A_Array[4] to get A_Array[4].

+

+
4 khan-exercise.js
 @@ -20,7 +20,7 @@ var Khan = { // Load in a collection of scripts, execute callback upon completion loadScripts: function( urls, callback ) { var loaded = 0, - loading = urls.length; + loading = urls.length; // Ehhh... not a huge fan of this this.scriptWait = function( callback ) { @@ -82,7 +82,7 @@ var Khan = { // Get the problem we'll be using var problems = exercise.find(".problems").children(), - problem; + problem; // Check to see if we want to test a specific problem if ( Khan.query.problem ) {
32 utils/angles.js