← SSAT® Middle Level

Number Concepts and Operations: Whole Numbers and the Four Operations

Place value, the four operations, factors and primes — the number properties that power every quick elimination on the quantitative sections.

7 topics · 30 questions

Each topic is a path, not a menu: work down it in order and every question builds on the one above. Click any of them to watch the answer draw itself.

Place Value and How Numbers Are Written

  1. How it worksHow do the columns in 4,073 split that number into thousands, hundreds, tens and ones?
  2. Worked exampleFind what the digit 7 is worth in 3,714 and what it is worth in 0.0075.
  3. Common mistakeWhy isn't 0.7 smaller than 0.65 even though it has fewer digits after the point?
Your turneasy1 of 3
A number is made of 7 thousands, 6 hundreds, 8 tens and 3 ones. What is the number?

The Four Operations and What Each One Undoes

  1. How it worksHow does division undo multiplication, drawn as a rectangle splitting back into rows?
  2. How it worksHow do the reordering rules let you rewrite 25 times 17 times 4 as something easy?
  3. Worked exampleFind 25 times 17 times 4 by reordering the factors instead of going left to right.
  4. Common mistakeWhy isn't subtraction reversible the way addition is, and what does swapping actually do?
  5. Going furtherWhat happens to a product when you double one factor and halve the other?
Your turneasy1 of 3
Find 32 times 17 times 4 by reordering the factors instead of working left to right.

Order of Operations

  1. How it worksHow does the order of operations decide what comes first in 12 - 2 times 3 + 8 divided by 4?
  2. Worked exampleFind the value of 6 + 2 times (5 - 3)2 one step at a time.
  3. Worked exampleWalk me through 20 - 3 times 4 + 18 divided by 6 and show where students usually slip.
  4. Common mistakeWhy isn't multiplication always done before division just because M comes before D?
Your turneasy1 of 3
Find the value of 12 + 2 times (9 - 3)2.

Factors, Multiples, Greatest Common Factor and Least Common Multiple

  1. How it worksHow do you list every factor of 36 by walking factor pairs in from both ends?
  2. How it worksHow does a greatest common factor differ from a least common multiple in what it counts?
  3. Worked exampleFind the greatest common factor and the least common multiple of 24 and 36.
  4. Worked exampleFind the first time buses leaving every 8 minutes and every 12 minutes depart together again.
  5. Common mistakeWhy isn't the least common multiple of two numbers always just their product?
Your turnmedium1 of 3
One number is 4 times 11 and another is 6 times 11. What is their least common multiple?

Primes, Composites and Prime Factorization

  1. How it worksHow does a factor tree break 84 apart until only primes are left at the tips?
  2. Worked exampleFind the prime factorization of 180 using a factor tree.
  3. Common mistakeWhy isn't 1 counted as a prime even though nothing but 1 and itself divides it?
Your turnhard1 of 3
A number's prime factorization is 2 raised to the power 3, times 3 raised to the power 2, times 5. What is the number?

Divisibility Rules and Remainders

  1. How it worksHow does adding up the digits of a number reveal whether 3 or 9 divides it evenly?
  2. How it worksHow do the quick tests for 2, 4, 5 and 10 read straight off the final digits?
  3. Worked exampleFind every number from 2 to 10 that divides 720 evenly, using the digit rules.
  4. Worked exampleFind the remainder when 253 is divided by 7 and show what the leftover means.
  5. Going furtherWhat happens to the remainder as you divide 1, 2, 3, 4 and so on by 5 in turn?
Your turneasy1 of 3
A number is 30 nines plus a remainder of 6. What is the number?

Even, Odd, and the Sign of a Product

  1. How it worksHow do the even and odd rules for adding and multiplying fall out of pairing objects up?
  2. How it worksHow does multiplying two negatives land on a positive, drawn as flipping direction twice?
  3. Worked exampleFind whether 17 times 23 times 46 is even or odd without multiplying anything.
  4. Worked exampleFind the sign of negative 2 times negative 3 times negative 4 times 5 by counting negatives.
  5. Common mistakeWhy isn't a negative number raised to a power always negative?
Your turneasy1 of 3
Without multiplying anything, decide whether 30 times 29 times 46 is even or odd.

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