The decimal, , is read as two-hundred forty-three thousandths, which translates to:

Multiply numerators, then multiply denominators. We can cross-cancel the 9 and the 3 by dividing both by 3:

To add fractions, you have to make sure that the fractions share a common denominator — that the denominator of both numbers is the same. Because these fractions do not have a common denonominator, you use the Lowest Common Multiple rule to find a common denominator. 

For these fractions, the lowest common multiple is .  and .

For the fractions to remain the same, you have to multiply the numerator and the denominator in  by  and the numerator and the denominator in  by . Once you have found the common denominator and have multiplied the numerator and denominator for each fraction, you can add the fractions.

Because the numerator is larger than the denominator, you simplify the fraction to make it a mixed number. 

There will be eighteen people at the party, including Hedwig. 

She will spend  for the large espressos.

"Buy two get one free" means that only two-thirds of the eighteen croissants - twelve of them - will be bought at the regular price, and the remaining six will be free. She will therefore spend .

The total purchase price will be . 

The change from a $100 bill will be

.

which converts as follows:

,

so

If Jim has 47 nickels, he has  in nickels. Since he has $13.85 total, he has a total of  in dimes and quarters. 

The number of dimes Jim has must leave an amount that can be made in quarters only - that is, a whole number multiple of . We try all four choices:

64 dimes:  in dimes

Amount in quarters: 

Divide this by :

, which is not a whole number. 

65 dimes:  in dimes

Amount in quarters: 

Divide this by :

, which is a whole number. 

66 dimes:  in dimes

Amount in quarters: 

Divide this by :

, which is not a whole number. 

67 dimes:  in dimes

Amount in quarters: 

Divide this by :

, which is not a whole number. 

65 dimes is the correct choice since it is the only one that allows for a whole number of quarters.

To divide numbers of unlike sign, divide their absolute values and affix a negative symbol. That is,

To divide a whole number by a decimal, move the decimal points in both numbers the same number of places until the divisor is a whole number. 

Therefore, we move the (written or implied) decimal point in each two places:

This becomes a whole number division:

Since we must affix a negative sign, the quotient is .

 of the students have chosen Swahili, so

have chosen Hausa or Yoruba.

Since  of these students have chosen Hausa,

of them have chosen Yoruba.

This is three-fifths of two-thirds, so we multiply these fractions:

Two-fifths of the students are taking Yoruba.