NYS Math Grade 4 cheat sheet

Grade 4 Mathematics - Core Facts, Formulas, and Decision Rules

• Place value: each place is 10 times the place to its right, so 3 in the thousands place equals 30 hundreds; a digit in the hundreds place is worth 100 times the same digit in the ones place.

• Standard forms: 5,082 = expanded form 5,000 + 80 + 2 = word form "five thousand eighty-two"; a zero in a place holds that place open.

• Rounding rule: find the digit in the rounding place, look at the digit to its right; 0–4 keeps it, 5–9 increases it by 1, and all digits to the right become zero.

• Compare multi-digit numbers by comparing digits from the leftmost place value; the first place where digits differ decides the comparison (>, <, =).

• Multiplication: factors × factors = product; division: dividend ÷ divisor = quotient, and quotient × divisor + remainder = dividend with remainder less than the divisor.

• Area of a rectangle = length × width; perimeter of a rectangle = 2 × (length + width); area is measured in square units, perimeter in linear units.

• Equivalent fractions: multiplying or dividing numerator and denominator by the same nonzero number gives an equivalent fraction (1/2 = 2/4 = 4/8).

• Add or subtract fractions with like denominators by combining only the numerators and keeping the denominator; compare fractions with the same numerator by the size of the denominators (larger denominator means smaller fraction).

• A decimal with denominator 10 or 100 converts directly: 0.7 = 7/10 and 0.35 = 35/100; compare decimals place by place, so 0.5 > 0.45.