Number and Operations - Grade 6 Numeracy
Number and Operations tests fluency and reasoning with whole numbers, decimals, fractions, mixed numbers, percents, factors, multiples, and order of operations. Expect questions that ask you to calculate, estimate, compare, and explain whether an answer is reasonable.
Core rules
- Place value extends to thousandths. Multiply or divide decimals as if they were whole numbers, then use estimation to place the decimal point.
- Fractions, decimals, and percents are three names for the same value: 3/4 = 0.75 = 75%.
- Add and subtract fractions only after finding a common denominator. Multiply numerators and denominators. Divide by multiplying by the reciprocal, or by using a common denominator.
- Convert mixed numbers to improper fractions before multiplying or dividing; regroup when subtracting.
- Percent means “per 100.” Find a percent of a number by converting to a decimal or fraction, for example 20% of 45 = 0.20 × 45.
- Order of operations: brackets first, then exponents, then multiplication and division left to right, then addition and subtraction left to right.
- Estimate before calculating and check that the answer is reasonable.
Worked example
Calculate 3/4 ÷ 1/6. Reasoning: Division asks how many sixths fit into three quarters. Use a common denominator: 3/4 = 9/12 and 1/6 = 2/12. So 9/12 ÷ 2/12 means 9 twelfths divided into groups of 2 twelfths, which is 9 ÷ 2 = 4 1/2. Check: 4 1/2 × 1/6 = 9/2 × 1/6 = 9/12 = 3/4. Answer: 4 1/2.
Traps that cost marks
- Adding denominators, such as writing 1/2 + 1/3 = 2/5.
- Dividing fractions without the reciprocal, or flipping the wrong fraction.
- Misplacing the decimal point after multiplying decimals.
- Working strictly left to right in an expression that contains multiplication and addition.
- Finding a percent of the wrong base, such as using a new price instead of the original.
- Forgetting to regroup when subtracting mixed numbers.