Lesson 51: Adding Numbers with More Than Three Digits, Checking One-Digit Division

New Concept

We can check a division answer by multiplying the numbers outside the division box:

What’s next

Next, you'll apply this checking method to division problems and also practice adding numbers with more than three digits.

Property

When using pencil and paper to add numbers that have more than three digits, we add in the ones column first. Then we add in the tens column, the hundreds column, the thousands column, and so on. When the sum of the digits in a column is a two-digit number, we record the second digit below the line and write the first digit above the next column to the left.

Example

Example 1: A hiker takes two routes measuring $52,176$ feet and $79,685$ feet. The total round trip is $131,861$ feet.

Example 2: A business owner spent $4850$ dollars on a computer, $395$ dollars on software, and $45$ dollars on a mouse. The total cost is $5290$ dollars.

Explanation

Think of it like stacking Legos, but with numbers! You line up your numbers by place value and add each column from right to left. If a column's total is ten or more, you just carry the 'ten' part over to its neighbors on the left.

Property

To check a division problem, you multiply the quotient, which is the answer you found, by the divisor, which is the number you are dividing by. The result of this multiplication should equal the dividend, the number that was originally being divided. This confirms your division is correct because multiplication and division are inverse operations.

Example

Example 1: First, divide $24$ by $4$ to get $6$. $\frac{6}{4) \overline{24}}$. Then check the answer by multiplying: $6 \times 4 = 24$. The product matches.
Example 2: First, divide $49$ by $7$ to get $7$. $\frac{7}{7) \overline{49}}$. Then check the answer by multiplying: $7 \times 7 = 49$. The product matches.

Explanation

Division and multiplication are a team with opposite powers! Division breaks numbers apart, and multiplication puts them back together. If you can use multiplication to perfectly rebuild the original number, you know your division mission was a success!

Property

To solve a word problem, first read carefully to find the key numbers and the main question. Next, decide which mathematical operation is needed, such as addition for totals, subtraction for differences, or multiplication for equal groups. Finally, write a number sentence or equation using this information, and solve it to find the answer. This translates the story into math.

Example

Example 1: In a class, there are 5 teams, and each team has 7 players. How many players are there in total? Equation: $5 \text{ teams} \times 7 \text{ players per team} = 35 \text{ players}$.
Example 2: A recipe calls for 8 apples for each pie. If a baker makes 6 pies, how many apples does he need? Equation: $8 \text{ apples per pie} \times 6 \text{ pies} = 48 \text{ apples}$.

Explanation

Solving a word problem is like being a detective. You must read the story for clues (the numbers), figure out the action (the operation), write down your case file (the equation), and crack the case by finding the final answer! Every problem tells a story.