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Grade 5 Math Formula Review

Every key Grade 5 math idea on one page — order of operations, decimals, fractions, measurement, volume, and the coordinate plane.

Operations, Expressions & Patterns

Order of operationsParentheses → ×/÷ (left→right) → +/− (left→right)

Grouping symbolsdo innermost first: ( ) inside [ ] inside { }

Write an expressiontranslate words to numbers & operations, don't solve

Coordinate patternsmake ordered pairs from two rules, then graph them

Place valueeach place is 10× the place to its right

Powers of 10× 10ⁿ moves decimal n places right; ÷ 10ⁿ moves it left

Roundinglook one place right: 5 or more rounds up

Add / subtract decimalsline up the decimal points, then compute

Multiply decimalsdecimal places in answer = sum of factors' places

Equivalent fractions× or ÷ numerator and denominator by the same number

Add / subtracta/b + c/d = (a·d + c·b) / (b·d)

Mixed numberscombine whole parts and fraction parts; regroup if needed

Estimateround each fraction to 0, ½, or 1

Multiply fractionsa/b × c/d = (a·c)/(b·d)

Fraction of a number2/3 of 12 = 2/3 × 12 = 8

Scaling× by <1 shrinks, × by >1 grows, × by 1 stays the same

Unit fraction ÷ whole(1/b) ÷ n = 1/(b·n)

Whole ÷ unit fractionn ÷ (1/b) = n·b

Convert unitsto a smaller unit ×, to a larger unit ÷

Metric prefixeskilo = 1,000 · centi = 1/100 · milli = 1/1,000

Volume (unit cubes)count the 1-unit cubes that fill the solid

Volume of a prismV = l × w × h = B × h (B = base area)

Composite solidssplit into prisms, find each volume, add them

Ordered pair (x, y)x = right from origin, y = up; origin = (0, 0)

First quadrantboth x and y are positive

Quadrilateral hierarchysquare ⊂ rectangle & rhombus ⊂ parallelogram

Classify trianglessides: equilateral/isosceles/scalene · angles: acute/right/obtuse