Decimal Word Problems Study Guide (page 2)
Introduction to Decimal Word Problems
How many times can you subtract 7 from 83, and what is left afterwards? You can subtract it as many times as you want, and it leaves 76 every time.
Certain situations can seem complicated, but underneath, they are really not that difficult. This lesson will focus on the basics of decimals and decimal word problems, so that they will not seem as difficult the next time around.
Decimal Place Value
Decimals are based on place value. Each place value is named by the distance it is from the decimal point. Commonly used decimal places are shown in the following figure.
Remember, decimals and fractions are very closely related. Take these examples:
To round a decimal to a certain place value, look to the decimal place to the right of the place that you are rounding. If the digit to the right is 4 or less, keep the number in the place value and drop the numbers to the right. For example, to round the number 2.354 to the nearest hundredth, look to the number 4 in the thousandths place. Because this number is 4 or less, keep the 5 in the hundredths place and drop the digit to the right. The rounded decimal becomes 2.35.
To round the number 6.178 to the nearest tenth, look to the 7 in the hundredths place. Because this number is 5 or greater, round the 1 in the tenths place to 2 and drop the digits to the right. The rounded number becomes 6.2.
Remember that our money system is based on dollars and cents. When rounding with money, always round to the nearest hundredth, unless told otherwise.
Adding and Subtracting Decimals
To add or subtract decimals, line up the decimal points and then add or subtract as you would whole numbers. For example, to add 12.26 + 14.11, line up the decimal points vertically and add.
When you are adding or subtracting, if one number goes out more decimal places than another, trailing zeros can be added to the right of the decimal point to make the problem easier. For example, when adding 2.3 and 4.15 you may line up the numbers as follows and add a zero after the 3 in 2.3:
As always, be sure to line up the decimal points when adding and subtracting.
To multiply decimals, multiply the decimals as you would whole numbers. Then, count the number of decimal places in each number being multiplied to find the total number of decimal places. Move the decimal this many places from the right in the answer to find the correct decimal place.
- Multiply 6.23 by 5.4.
Because there are two decimal places in the first value and one in the second, move the decimal point 2 + 1 = 3 places from the right for the final answer. The final answer is 33.642.
To divide decimals, move the decimal point in the divisor to the right so that the divisor is a whole number. Then, move the decimal point in the dividend the same number of places. Line up the decimal points vertically so that the quotient has a decimal point lined up with the dividend.
To divide 13.44 by 2.1, set up the division and change 2.1 to the whole number 21 by moving the decimal point one place to the right. Then, move the decimal point of the dividend one place to the right to make 13.44 into 134.4. Next, divide 134.4 by 21 as shown in the following figure.
- The quotient is 6.4.
Decimal Word Problems
The following examples use the basic properties of decimals in math word problems. Read and work through each problem to get an idea of how to approach decimal word problems, and then try your hand at the practice problems following them. Do not worry; answer explanations are given to help you through any rough spots.
Ted and Kristen are shopping for pens and notebooks. The pens cost $0.50 each and the notebooks are $1.50 each. Ted buys 2 pens and 1 notebook and pays with a $5 bill. Kristen buys 3 pens and 2 notebooks and pays with a $10 bill. What is the total amount of change they get back?
Read and understand the question. This problem asks for the total amount of change that two people get back while shopping for pens and notebooks. The cost of each pen and notebook is given, along with the money they have to spend.
Make a plan. Use the strategy of making a table to keep track of how much each person spent. Then, subtract this amount from the money they used to pay for the items to find how much change they got back. Add the amounts of change to find the total.
Carry out the plan. Make a table of the amounts spent.
Because they paid with a $5.00 bill and a $10.00 bill for a total of $15.00, they get back $15 – $7 = $8 in change.
Check your answer. To check your answer, figure out the total number of pens and notebooks bought, and subtract this amount from $15. A total of 5 pens were bought for a total cost of $2.50. A total of 3 notebooks were purchased for a total of $4.50. This is a total of $2.50 + $4.50 = $7.00, leaving $15 – $7 = $8 in change between both people. This solution is checking.
The individual times for four runners on the same team in a track relay event were 29.3 seconds, 35.8 seconds, 41.1 seconds, and 31.2 seconds. What was the total time for the team?
Read and understand the question. This question is looking for the total time it took a team to finish a race. The individual times are given.
Make a plan. Add each of the individuals' times together to find the total amount of time for the relay team.
Carry out the plan. Add the times vertically and line up the decimal points.
The team completed the race in 137.4 seconds.
Check your answer. Check your answer by subtracting each number from 137.4 until you reach zero seconds: 137.4– 29.3 – 35.8 – 41.1 – 31.2 = 0. This problem is checking.
Find practice problems and solutions for these concepts at Decimal Word Problems Practice Questions.
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