# Word problems for decimals and integers

### Word problems for decimals and integers

#### Lessons

In this lesson, we will learn:

• How to approach word problems for multiplying decimals with integers
• How to approach word problems for dividing decimals by integers
• How to approach word problems for decimals and integers where you need to first multiply, then divide (or vice versa)

Notes:

• What happens when we multiply or divide decimals with integers?
• When multiplying or dividing a decimal by a positive integer, the answer will be positive.
• When multiplying or dividing a decimal by a negative integer, the answer will be negative.
• You can decide if your answer will be positive or negative before you multiply/divide or after you finish multiplying/dividing (it doesn’t matter, just don’t forget to do it!)

• When you multiply decimals with integers, the number of decimal places in your answer (the product) will be the same as the number of decimal places in the multiplicand (the decimal)

• When you divide decimals by integers, the number of decimal places in your answer (the quotient) is decided by the decimal point in your dividend (the decimal). You must line up the dividend’s decimal point with the quotient’s decimal point in the long division format.

• 1.
Multiplying decimals with negative integers
If you return your library book late, there will be a fine! The library will add a deduction onto your account of - $0.25 every day until you return it. a) How much total deductions will be on your account if you return your book a week late? b) How much total deductions will be on your account if you return your book 8 weeks late? • 2. Dividing decimals with positive integers What is the better deal? Option A: 5 apples for$5.75

Option B: 8 apples for \$8.64

• 3.
Multiplying and dividing decimals by integers (Part 1)
A sinkhole is a hole in the ground that is formed when the surface layer of the earth collapses.

Scientists are using robots that each carry 58.364m of rope to climb as far down into the earth as possible. When the first robot reaches its maximum depth, it is at -58.364m into the earth.
a)
If it takes 3 robots to reach the bottom of the sinkhole, what is the total depth of the sinkhole?

b)
If the robots only had half of their rope length, to what depth would they have travelled?

• 4.
Multiplying and dividing decimals by integers (Part 2)
Bamboo plants are the fastest growing plants on Earth! They say they can grow up to 91cm in one day (that's almost as tall as a three-year-old kid)!

Jenna measured her bamboo plant to grow about 89.784cm in one day. Assuming that the bamboo plant is growing at the same rate all day long, how much did it grow in 4 hours?

• 5.
Multiplying and dividing decimals by integers (Part 3)
A group of meteorologists are studying temperatures around the world. The chart shows how much temperature change (either getting hotter or colder) they measured in each city over a certain amount of time:
 City Temperature Change Time London -10.8 °C 4 hours New York +13.56 °C 5 hours Tokyo -11.709 °C 3 hours Dubai +14.92 °C 5 hours
a)
Calculate the rate of temperature change (in °C / hour; by dividing the temperature change by the time).

b)
Which city had the fastest rate of temperature change and was it getting colder or hotter?

c)
On the same day, another meteorologist in Barcelona observes that the rate of temperature change during a period of 6 hours was -1.654 °C / hour. How much did the temperature change during that time?