Math problems

-math-problems.md

This is a collection of multi-step story problems and fraction problems for my daughter to use as practice.

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fractions.txt

reduce/simplify
8/10
3/15
5/15

make proper
7/3
20/8 // non-reduced
24/8 // whole number

simple addition
2/7 + 3/7
3/20 + 7/20 // non-reduced
5/8 + 7/8 // improper

single denominator change addition
1/2 + 1/4
1/4 + 7/12 // non-reduced
3/4 + 7/12 // improper, non-reduced

double denominator change addition
1/2 + 1/3
1/2 + 3/5 // improper
3/4 + 3/5 // improper

smallest/largest
1/2 2/3 3/8 5/12
3/4 8/12 15/24 17/20

ice-cream.txt

Suzy, Anastasia and Olivia want to buy a big tub of ice cream for
$4.30.  If Olivia has $1.30 and Suzy has $1.60, how much does
Anastasia need to cover the rest?

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After Olivia, there will be $4.30 - $1.30 = $3.00 remaining.  After
Suzy there will be $3.00 - $1.60 = $1.40 left for Anastasia to pay.

picture-frame.txt

Suzy is framing a picture, which is 20 cm wide and 25 cm tall.  Her
frame is 28 cm by 36 inches.  How much far from the left edge should
she place the picture so that it is centered in the frame?  How far
from the top edge?

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There will 28 - 20 = 8 extra cm of width.  So she should place the
picture 8 / 2 = 4 cm from the left edge.

There will be 36 - 25 = 11 extra cm of height.  So she should place
the picture 11 / 2 = 5.5 cm from the top edge.

rocket-trip.txt

Suzy is preparing for a trip to Mars.  She needs 2.5 gallons of water
for each day of travel and she has packed 4,500 pounds of it. The trip
is 150 million miles, and she will travel at 25,000 miles per hour.

1) What additional fact do you need to solve this problem?

2) Can you express that fact as a ratio (with units)?

3) There are two more ratios in the problem.  What are they?

4) Did she pack too little, too much, or the right amount of water?

5) How much is she off?

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1) How much one gallon of water weight in pounds.

2) 8 pounds / 1 gallon.

3) 25,000 miles / 1 hour, 2.5 gallons / 1 day.

4) She packed too little.

5) She should pack 500 more pounds.

The trip will be 150,000,000 / 25,000 = 6000 hours long, or
6000 / 24 = 250 days long.  She will need to bring 250 * 2.5 = 625
gallons or 625 * 8 = 5,000 pounds of water.

Assuming 7.5 gallons consumed per day (instead of 2.5, because I can't
write clearly), then she will need to bring 250 * 7.5 = 1875 gallons
or 1875 * 8 = 15,000 pounds of water.

taxi-ride.txt

Suzy is going to the movies.  She has $30, and the movie ticket only
costs $7.50, but she has to take a taxi to get there.  The fare
includes a base fee of $2.00 as soon as you get in, plus $2.50 per
mile traveled. If the theatre is 5 miles away and she tips the driver
$3, how much money will she have to buy popcorn?

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The taxi ride will cost $2 + (5 * $2.50) + $3 = $17.50.  Plus the cost
of the movie ticket is $17.50 + $7.50 = $25.  So she will have
$30 - $25 = $5 for popcorn.

water-balloons.txt

Suzy is filling up water baloons for a party. It takes her 12 seconds
to fill one ballon.  How many minutes will it take to fill up the 50
balloons she needs?

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She can fill up 60 / 12 = 5 baloons per minute.  So it will take
50 / 5 = 10 minutes to fill up all the balloons.

She will need 12 * 50 = 600 seconds to fill up all the balloons. So it
will take 600 / 60 = 10 minutes to fill up all the balloons.