Decimals Word Problems

Decimals word problems describe real situations, like buying groceries, measuring distance, or sharing money, using numbers that include decimal points. Instead of being handed a bare calculation like \( 14.5 - 6.25 \), you are given a short story and have to figure out which operation to use and how to set it up before you can solve anything. This makes them a great way to practice both reading comprehension and decimal arithmetic at the same time.

Before tackling these problems, it helps to be comfortable with decimal place value. If you need a refresher, review what decimals are first, since understanding tenths, hundredths, and thousandths makes every step below much easier.

Almost every decimals word problem can be solved using the same plan:

1. Read the problem twice and identify what is known and what is being asked.
2. Choose the operation (addition, subtraction, multiplication, or division) based on the situation.
3. Set up and solve the decimal calculation carefully.
4. Check the answer against the original question to make sure it makes sense.

Certain words in a problem hint at which operation to use:

Addition: total, combined, altogether, in all.
Subtraction: left, remaining, difference, how much more.
Multiplication: each, per item repeated many times, rate over a whole amount.
Division: shared equally, split into, per unit, how many groups.

For example, "Maria has \(6.5\) meters of ribbon and cuts off \(2.75\) meters" signals subtraction, while "each of the 4 friends gets an equal share of \(12.6\) meters" signals division.

A backpack costs \(\$34.99\) and a water bottle costs \(\$8.50\). How much change do you get from \(\$50\)?

First find the total cost by adding: \( 34.99 + 8.50 = 43.49 \). Then subtract that total from \(50\): \( 50 - 43.49 = 6.51 \). The change is \(\$6.51\).

Gas costs \(\$1.35\) per liter. How much do 8 liters cost?

Since each liter costs the same amount and you need a total for 8 liters, multiply: \( 1.35 \times 8 = 10.80 \). The total cost is \(\$10.80\). If the problem instead involved scaling a decimal by 10, 100, or 1000, it would use the shortcut covered in multiplying decimals by powers of 10.

Four friends share a restaurant bill of \(\$58.60\) equally. How much does each person pay?

The word "equally" signals division: \( 58.60 \div 4 = 14.65 \). Each friend pays \(\$14.65\). For more practice with this kind of division problem with decimals, see the lesson on dividing decimals by integers.

Before trusting a final answer, estimate first. Round each decimal to a friendly whole number, do the operation quickly, and compare that estimate to your exact answer. In Example 3 above, \(58.60\) rounds to about \(60\), and \(60 \div 4 = 15\), which is very close to \(14.65\), so the exact answer is reasonable. If your exact answer were far off from the estimate, such as \(1.465\) or \(146.5\), that would be a sign the decimal point landed in the wrong place.

Misaligning decimal points when adding or subtracting is one of the most frequent errors, so always line up the decimal points vertically before calculating by hand. Another common mistake is choosing the wrong operation because a number like "each" or "total" was skimmed over rather than read carefully. Finally, forgetting to attach the correct unit (dollars, meters, kilograms) to the final answer can make a technically correct number seem wrong when it's checked against the question.

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• Math 5