Addition: Fast and Accurate Sums

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What it is

Addition puts amounts together. The numbers you add are the addends; the result is the sum (or total). Every digit has a place value: in 4,786 the 4 means 4 thousands, the 7 means 7 hundreds, the 8 means 8 tens and the 6 means 6 ones. Adding is always done place by place: ones with ones, tens with tens.

Why it matters on the exam

Addition is inside almost every numerical item: totals in word problems, averages, perimeters, percent, series and data tables. The exam is timed, so you need answers that are both right and fast. The wrong choices are usually a forgotten carry (off by 10 or 100) or a shortcut adjusted the wrong way.

How to recognize it

You are adding when you see a + sign, or words like total, in all, altogether, sum, combined, increased by, more than, or when you must find a perimeter or the total before an average.

What to look for

• How many digits each number has: line up the last digits, not the first.
• Numbers whose ends make 10 or 100 (they pair up).
• Numbers just below a round number: 98, 199, ₱1,995.
• A list that grows by the same step (5, 10, 15, …).
• Choices that differ only in one digit: check the last digit.

Words to know

• Addend: a number being added. Sum: the answer.
• Place value: what a digit is worth because of its position (ones, tens, hundreds, thousands).
• Carry (regroup): when a column adds to 10 or more, write the ones digit and move the tens digit to the next column.
• Compatible numbers: numbers that add to a round number, like 37 and 63.
• Compensation: changing a number to make it easy, then correcting the answer by the same amount.

Column addition with carrying

How to use it

1. Line up the ones digits (and the decimal points for money).
2. Add the ones column. Write the last digit; carry the rest.
3. Add the next column plus the carry. Repeat to the leftmost column.
4. Write the final carry in front.

Tandaan: Right to left, one column at a time; carry every ten.

Watch out: Forgetting the carried 1 (that gives 8,135 or 8,235 instead of 8,245). Lining up 4,786 and 459 by their first digits.

Make a ten (compatible numbers)

How to use it

1. Scan the ones digits for pairs that make 10.
2. Add each pair to a round number.
3. Add the round numbers, then any leftovers.

Tandaan: Pair to 10, pair to 100, then add.

Watch out: Using a number twice or skipping one: cross each number out as you pair it.

Left to right: add the big places first

How to use it

1. Hundreds: add them.
2. Tens: add them.
3. Ones: add them.
4. Combine the three partial sums.

Tandaan: Big places first, then combine.

Watch out: Dropping one partial sum (500 + 14 = 514 forgets the 110).

Round and adjust (compensation)

How to use it

1. Round the awkward number up to the nearest ten, hundred or thousand; note how much you added.
2. Add the round number.
3. Subtract the amount you added.

Tandaan: Rounded up? Take it back. Rounded down? Put it back.

Watch out: Adjusting the wrong way: 500 + 367 + 2 = 869 is wrong; you added 2, so take 2 away.

Adding an evenly spaced list

How to use it

1. Count the terms: (last − first) ÷ step + 1.
2. Average the first and last: (first + last) ÷ 2.
3. Multiply: average × count.

Tandaan: First plus last, times count, divided by 2.

Watch out: Counting (last − first) ÷ step and forgetting the + 1. Using the step instead of the count.

Check the sum in seconds

How to use it

1. Estimate: round each addend and add.
2. Last digit: add only the ones digits; keep the last digit.
3. Digit sum: add the digits of each addend down to one digit, add those, reduce again; the answer must reduce to the same digit.

Tandaan: Size, last digit, digit sum.

Watch out: Stopping at the estimate when two choices are both close.

Adding decimals: line up the points

How to use it

1. Line up the decimal points (not the last digits).
2. Fill empty places with 0: 8.5 = 8.50.
3. Add column by column from the right, carrying as usual.
4. Bring the point straight down.

Tandaan: Points in a column; zeros fill the gaps.

Watch out: Lining up the last digits: 8.5 + 0.75 is not 1.60.

Which addition tool do I use?

Addition table (1 to 10)

Exam techniques

Look at the choices first

Before computing, notice how the choices differ. If they differ in size, estimate. If they differ only in the last digit, add only the ones column.

When: Every multiple-choice computation.

Careful: If two choices pass the quick check, compute exactly.

Write the running total

For a long list, write the total after each number (58 → 95 → 137 → 200) instead of holding it in your head.

When: Lists of five or more numbers, or when you are tired or rushed.

Careful: Still pair to tens first when you can; it means fewer steps.

Add in pairs, even with paper

In a column of numbers, add two digits that make 10 first, then the rest.

When: Columns of money or scores.

Careful: Keep track of which digits you already used.

The traps

• Forgetting a carry. Write every carry above the next column before you add it (T1). Check with the digit sum (T6).
• Lining up the first digits of numbers with different lengths. Line up the last digits (the ones), and the decimal points for money (T1).
• Adjusting the wrong way after rounding. Rounded up → subtract the extra at the end; rounded down → add it back (T4).
• Skipping or repeating a number in a long list. Cross out each number as you use it, and count them at the end (T2).
• Counting the terms of a list as (last − first) ÷ step. Add 1: both ends count (T5).

Tandaan

• Line up the ones; add right to left; carry every ten.
• Pair numbers that make 10 or 100 first.
• Mental: big places first, then combine.
• Round and adjust: take back exactly what you added.
• Evenly spaced list: (first + last) ÷ 2 × count.
• Check: size, last digit, digit sum.

Practice this lesson

Practice questions with step-by-step solutions, written out like on paper, and the 60-second math facts sprint are in the app.

Open the lesson in the app Math facts sprint