Number: Place Value, Operations, Fractions, Decimals, and Percents
What you must understand
Grade 6 number work rests on place value from millions down to thousandths, fluent multi-digit addition, subtraction, multiplication, and division, and the connections among fractions, decimals, and percents. You should be able to round whole numbers and decimals, compare and order them, find factors and multiples, identify prime and composite numbers, and apply the order of operations. Fraction skills include equivalent fractions, simplifying, comparing with unlike denominators, and adding, subtracting, multiplying, and dividing fractions and mixed numbers. Percent means "per hundred," so 35% equals 0.35 and 35/100.
Traps to watch for
- Decimal alignment: line up decimal points when adding or subtracting, but do not align points when multiplying; count decimal places in the factors instead.
- Dividing by a fraction: dividing by a fraction less than one gives a larger result, which surprises many students. Dividing by 1/2 is the same as multiplying by 2.
- Order of operations: multiplication and division before addition and subtraction, left to right within the same level; brackets first.
- Percent of a number: "of" signals multiplication, and the percent must first become a decimal or fraction.
- Rounding: look only at the digit immediately to the right of the target place.
Worked example
Find 40% of 65, then subtract 2/5 of 65 from it. Convert: 40% = 0.40, so 0.40 × 65 = 26. Also 2/5 of 65 = (65 ÷ 5) × 2 = 13 × 2 = 26. The difference is 0, because 40% and 2/5 are equivalent. Recognizing equivalent forms saves computation time and is a frequent shortcut on tests.
Rule of thumb
When a problem mixes fractions, decimals, and percents, convert everything to one form (usually decimals) before comparing or calculating, and estimate first so an unreasonable answer stands out.