← SSAT® Upper Level

Number Concepts and Operations

The first score-report subject area: the four operations, signed numbers, factors, fractions, decimals, rational numbers and estimation with no calculator.

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.

The Four Operations and Order of Operations

  1. How it worksHow does the order of operations unwrap an expression from the innermost parentheses outward?
  2. Worked exampleFind the value of 6 + 3 × (8 - 2)² ÷ 4, one operation at a time.
  3. Common mistakeWhy doesn't multiplication always come before division in the order of operations?
  4. Going furtherWhat happens to 12 - 4 - 3 when you work it right to left instead of left to right?
Your turneasy1 of 3
Write an expression, in terms of a, that means this: 6 plus the quantity 3 times (a - 5) squared, divided by 4.

Negative Numbers and Signed Arithmetic

  1. How it worksHow do two minus signs cancel in a product, drawn as a flip across zero and then a flip back?
  2. Worked exampleFind the value of -7 - (-12) + (-4) by walking each step along a number line.
  3. Worked exampleFind the values of (-2)⁵ and (-2)⁴, and show why only one of them comes out negative.
  4. Common mistakeWhy isn't -3² equal to 9 when squaring is supposed to erase the minus sign?
  5. Going furtherWhat happens to -2x < 6 when you divide both sides by that negative 2?
Your turneasy1 of 3
Walk it along a number line: what is -7 - (-16) + (-4)?

Factors, Multiples, Primes, GCF and LCM

  1. How it worksHow does a factor tree break any whole number down into one unique pile of primes?
  2. Worked exampleFind the greatest common factor and the least common multiple of 24 and 36.
  3. Worked exampleFind how many positive factors 60 has without listing every single one of them.
  4. Common mistakeWhy isn't 1 counted as a prime number when nothing divides it except itself and one?
Your turnmedium1 of 3
A whole number factors as 2 raised to the power a, times 3 raised to the power 4. Write an expression, in terms of a, for how many positive factors it has.

Operations with Fractions

  1. How it worksHow does multiplying a fraction by a disguised form of 1 change its look without changing its size?
  2. Worked exampleFind 2/3 + 3/4 - 5/6 as one fraction in lowest terms.
  3. Worked exampleWalk me through dividing 3/8 by 5/6, and show why flipping the second fraction works.
  4. Common mistakeWhy doesn't multiplying by 3/4 make a number bigger the way multiplying usually does?
  5. Worked exampleFind which is larger, 7/9 or 5/7, without turning either one into a decimal.
Your turneasy1 of 3
Give the value of 7/3 + 3/4 - 5/6 as a single number.

Decimals, Place Value and Rounding

  1. How it worksHow does place value split 0.407 into four tenths, zero hundredths and seven thousandths?
  2. Worked exampleFind the product 0.04 × 0.25 and show where the decimal point has to land.
  3. Worked exampleWalk me through rounding 3.6482 to the nearest tenth and then to the nearest hundredth.
Your turneasy1 of 3
What is 0.07 times 0.25?

Rational Numbers and the Number Line

  1. How it worksHow does long division turn any fraction into a decimal that either stops or repeats forever?
  2. Worked exampleFind the order of -2/3, -0.7, -3/5 and -0.66 from least to greatest along a number line.
  3. Common mistakeWhy isn't every decimal you can imagine writing down a rational number?
  4. Going furtherWhat happens to the repeating decimal 0.272727 when you convert it back into a fraction?
Your turnmedium1 of 3
The decimal 0.666 repeating equals a fraction with a single digit on top. What is its value as a number?

Estimation and Approximation

  1. How it worksHow does rounding one factor up and the other down keep an estimate close to the true product?
  2. Worked exampleFind a fast estimate for 6842 ÷ 68 and choose between 10, 100 and 1000.
  3. Worked exampleWalk me through estimating 48 percent of 610 closely enough to pick from five spread-out choices.
  4. Common mistakeWhy doesn't rounding both numbers up give a usable estimate when you are subtracting?
  5. Going furtherWhat changes about estimating when the five choices are 0.28, 0.30, 0.32, 0.34 and 0.36?
Your turneasy1 of 3
Estimate first, then compute: what is 48 percent of 748?

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