Problem 63 - Algebra 1: Concepts and Skills

Question

ADDING DECIMALS Add. $$ 46+7.55 $$

Step-by-Step Solution

Answer

The sum of 46 and 7.55 is 53.55.

Step 1: Convert the whole number to a decimal

The whole number 46 can be written as a decimal by adding .00, that gives us 46.00. This allows us to align the numbers properly for addition.

Step 2: Align the numbers

Line up the numbers by their decimal points. It would look like this: \[ 46.00 \] \[ +7.55 \]

Step 3: Perform the addition

Add the numbers column by column as usual, starting from the right. If a column adds up to more than 10, carry the value to the next column to the left. Keep the decimal point aligned in the answer. After adding, one gets \[ 53.55 \]

Key Concepts

Decimal Addition

When adding decimals, it's crucial to handle numbers with care since decimals represent fractions of a whole. Think of it as putting together pieces of a cake, where a decimal point helps to make sure you are combining the right size of slices.

Aligning Decimal Points

Visualizing decimals on a place value chart can be helpful, imagine each number has its own address - units, tenths, hundredths, and so on. Aligning decimal points ensures each 'neighbor' lines up correctly before you invite them to the calculation 'party'. It's like making sure all your friends are gathered at the same spot before starting a fun activity!

Carrying Over in Addition

Consider carrying over as a helpful friend who sees if you have too much to handle and offers to take some load off your hands. It's a useful technique that simplifies the addition process, by transferring excess to the neighboring column - just remember to say thank you by adding it to the next!