Division fraction word problems?

Question

1) on their vacation, the Reikos spent 1/4 of their money on gas, 1/4 on food and lodging and 1/8 on tourist attractions. What fraction of their money did they spend?If they started with $840.000, how much money  they have left? 

 

2) In febuarary 1993, Canada's Kate Pace won the gold medal at the World Alpine Ski Championships. Her winning time was 1 min 27.38 s. She finished 28/100 of a second ahead of Astrid Leodemal of Norway. What was Astrids time? 

 

3) About 2/5 of Canada's gold production comes from Ontario. About 3/10 comes from Quebec and 1/10 from Bristish Columbia. What fraction of Canada's gold production comes from the rest of the country? Give answer in lowest terms. 

Answer 1

1)

 

Let x = the total amount of money they started off

 

Amount spent on gas = (1/4)x

 

 

They spent a fraction of what is left.

 

Amount spent on food & lodging = (1/4)[x - (1/4)x]

                                                = (1/4)(3/4)x

                                               = (3/16)x

 

 

They spend a fraction of what is left.

 

Amount spent on tourist attractions = (1/8)[(x - (1/4)x) - (3/16)x]

                                                    = (9/128)x

                                                          

 

If we add up all the amounts they spent off, we get fraction of the money they spent.

 

(1/4)x + (3/16)x + (9/128)x = (65/128)x

 

 

The spent 65/128 of their entire money.

 

 

If they started with $840,

 

(65/128)(840) = 426.56

 

 

They spent $426.56

 

 

What they have left is

 

$840 - $426.56 = $413.44

 

 

 

2)

 

Convert minutes to seconds, since seconds is the dominant unit.

 

1 min = 60 sec

 

 

Kate's winning time = 60 sec + 27.38 sec = 87.38 sec

 

She finished 28/100 of a second ahead of Astrid.  We can convert this fraction to a decimal for easy calculation.

 

28/100 = 0.28

 

 

She finished 0.28 of a second ahead of Astrid.  So her time would be less than Astrid's since she finished first.

 

 

Astrid's time = Kate's time + 0.28 × (Kate's time)

 

                   = 87.38 + 0.28(87.38)

 

                  = 111.85 sec

 

 

3)

 

All of these place are from the same country.

 

Add the fractions that come from these specific areas,

 

2/5 + 3/10 + 1/10 =

 

4/10 + 3/10 + 1/10 =

 

8/10 =

 

4 / 5

 

 

This means that 1/5 of gold production comes from the rest of country.

 

 

 

 

 

Answer 2

Hi Cyrill,

 

1) You need to add the fractions to get the fraction of their money that they spent.  Adding fractions requires a common denominator and then you add the numerators.

 

1/4 + 1/4 + 1/8. . . 8 is the lowest common denominator and so you need to multiply the first two fractions by 2/2:

 

2/8 + 2/8 + 1/8 = 5/8 and they have 3/8 left (5/8 + 3/8 = 1)

 

They started with 840,000 so the remaining money = 3/8 x 840,000 = 3 x 105,000 = $315,000

 

2) Kate's time was 1 min and 27 and 38 hundredths of a second.  Astrid took 28 hundredths of a second slower. . .

 

38/100 + 28/100 = 64/100 = 0.64

 

So Astrid's time was 1 min 27.64 seconds

 

3)This is similar to question 1. . . you have to add the fractions after finding the lowest common denominator and then subtract from 1 to the get production from the rest of the county.  I'll let you do this yourself.

 

Have fun.

 

Dan