Lesson 38: Adding and Subtracting Decimal Numbers and Whole Numbers

New Concept

Squaring a number means multiplying the number by itself. Finding the square root of a number is the inverse of squaring a number.

"Seven squared" is $7 \times 7$, which is 49.

The principal square root of 81 is 9.

What’s next

This is your introduction to these foundational concepts. Soon, we'll apply them in worked examples and challenge problems involving area, perimeter, and order of operations.

Property

To add or subtract a whole number and a decimal, write the whole number with a decimal point and align the decimal points vertically. This ensures that you are combining digits with the same place value, like ones with ones and tenths with tenths.

Examples

• $15. + 9.5 + 15. + 9.5 = 49.0$
• $25.75 - 8.00 = 17.75$
• Find the total cost of a 5 dollars snack and a 2.50 dollars drink: $5.00 + 2.50 = 7.50$ dollars.

Explanation

Think of a whole number as a celebrity trying to sneak into the decimal party. To fit in, it needs a disguise: a decimal point and a zero cape! By writing 7 as 7.0, you can line it up perfectly with other decimals like 3.14. This trick ensures everyone lines up correctly, preventing mathematical chaos and making your calculations neat and tidy.

Property

Finding the principal square root of a number is the inverse operation of squaring a number. The symbol $\sqrt{\phantom{0}}$ asks, 'What positive number, when multiplied by itself, gives you the number inside?'

Examples

• $\sqrt{81} = 9$
• $\sqrt{100} - \sqrt{49} = 10 - 7 = 3$
• A square-shaped garden has an area of 144 square feet. The length of one side is $\sqrt{144} = 12$ feet.

Explanation

Think of squaring as building a square patio. If you know one side is 7 feet, you square it to find the area is 49 square feet. The square root does the reverse! If you only know the patio's area is 49 square feet, the square root, $\sqrt{49}$, is your magic tool to find out that one side must be 7 feet long.

Property

A number is a perfect square if its square root is a whole number. The first four perfect squares are 1, 4, 9, and 16.

Examples

• The number 64 is a perfect square because $\sqrt{64} = 8$, which is a whole number.
• The first five perfect squares are $1^2=1$, $2^2=4$, $3^2=9$, $4^2=16$, and $5^2=25$.
• Simplify the expression: $\sqrt{4} + \sqrt{9} = 2 + 3 = 5$.

Explanation

Perfect squares are the 'cool kids' of numbers. When you take their square root, you get a nice, clean whole number—no messy decimals allowed! They are the result of a whole number getting squared (e.g., $5 \times 5 = 25$). This makes them super predictable and satisfying to work with, like perfectly fitting a puzzle piece into place every single time.