Number and Operations
What Number and Operations covers
This domain tests whether you can move confidently among whole numbers, fractions, decimals, and percentages, and whether you can choose the correct operation in a short word problem. Expect place value, rounding, factors and multiples, equivalent fractions, ordering numbers, and the four operations with regrouping. The exam also checks that you apply the conventional order of operations rather than calculating left to right.
Core rules to keep straight
- Place value: each position is ten times the one on its right. In 4,708.26 the 7 is worth 700, the 2 is worth 0.2, and the 6 is worth 0.06.
- Fractions need a common denominator before you add or subtract; multiply numerators and denominators when multiplying; invert the second fraction when dividing.
- To compare decimals, line up decimal points and compare place by place; adding zeros on the right does not change value.
- Percent means “per 100.” To convert a percent to a decimal, divide by 100; to convert a decimal to a percent, multiply by 100.
- Order of operations: brackets, indices/powers, multiplication and division left to right, then addition and subtraction left to right.
- A factor divides a number exactly; a multiple is the result of multiplying by a whole number.
Worked example
Find 3/4 + 5/6, then write the answer as a decimal. The least common denominator of 4 and 6 is 12. Convert: 3/4 = 9/12 and 5/6 = 10/12. Add the numerators: 9 + 10 = 19, so the sum is 19/12 = 1 7/12. To convert, divide 19 by 12: 12 goes once with remainder 7, giving 1.5833…, or about 1.58. Checking reasonableness: both fractions are less than 1, but their sum is greater than 1, which fits.
Traps that cost marks
Adding denominators (3/4 + 5/6 ≠ 8/10) is the most common fraction error. In decimals, misaligning place columns can turn 3.6 + 0.45 into an incorrect total; write 0.45 under 3.60 so the tenths and hundredths match. In order of operations, 8 + 2 × 3 = 14, not 30. Reading “of” as a signal to multiply, as in 1/2 of 18 = 9, is correct; reading a remainder as the answer is not. Always check whether the question asks for a fraction, decimal, or percentage.