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Grade 5 · Common Core Math

Five units. One notebook.
Real math, worked by hand.

This is a worksheet you can actually do something with — read the idea, study a worked example, then solve problems and check your own work right here.

5units to master
15practice problems
0required logins
UNIT 01

Adding & Subtracting Fractions

Different denominators can't be added directly — first find a common denominator, then add the numerators.

The rule: To add or subtract fractions with unlike denominators, rewrite both fractions using the least common denominator (LCD), then add or subtract just the numerators. The denominator stays the same.
1/4 + 1/6 → 3/12 + 2/12 → 5/12

  • Q1 1/3 + 1/6 = ? (answer as a fraction like a/b)

    The LCD of 3 and 6 is 6. Rewrite 1/3 as 2/6, then add 2/6 + 1/6.

  • Q2 5/8 − 1/4 = ?

    The LCD of 8 and 4 is 8. Rewrite 1/4 as 2/8, then subtract.

  • Q3 2/5 + 1/2 = ?

    The LCD of 5 and 2 is 10. Rewrite both fractions over 10ths.
UNIT 02

Decimal Place Value & Operations

Decimals extend place value to tenths, hundredths, and thousandths. Line up the decimal points before adding or subtracting.

The rule: When adding or subtracting decimals, stack the numbers so the decimal points line up vertically. Add zeros as placeholders if needed, then add or subtract like whole numbers.
3.6 + 2.45 → 3.60 + 2.45 → 6.05

  • Q4 4.7 + 3.25 = ?

  • Q5 9.03 − 4.6 = ?

  • Q6 What is 0.6 × 10? (think about how multiplying by 10 shifts the decimal point)

UNIT 03

Multi-Digit Multiplication & Division

Break big multiplication into smaller steps, and remember division can leave a remainder.

The rule: For multi-digit multiplication, multiply by each place value separately, then add the partial products. For division, find how many times the divisor fits, subtract, and bring down the next digit.
23 × 14 → 23×10=230, 23×4=92 → 322

  • Q7 34 × 12 = ?

  • Q8 156 ÷ 12 = ?

  • Q9 A box holds 24 pencils. How many boxes are needed for 300 pencils, if leftover pencils still need a box? (round up)

    300 ÷ 24 = 12.5. Since boxes can't be split, round up to the next whole box.
UNIT 04

Order of Operations

When an expression has more than one operation, the order you solve in changes the answer — so everyone follows the same order.

The rule (PEMDAS): Solve Parentheses first, then Exponents, then Multiplication and Division (left to right), then Addition and Subtraction (left to right).
3 + 4 × (2+1) → 3 + 4 × 3 → 15

  • Q10 5 + 2 × (6 − 4) = ?

  • Q11 (3 + 5) × 2 − 4 = ?

  • Q12 18 ÷ (3 + 3) + 1 = ?

UNIT 05

Volume of Rectangular Prisms

Volume measures how much space a 3D shape takes up, counted in cubic units.

The rule: Volume of a rectangular prism = length × width × height. The answer is always in cubic units (like cm³ or in³) because three dimensions are multiplied together.
L=4, W=3, H=2 → 4 × 3 × 2 → 24 cubic units

  • Q13 A box is 5 in long, 4 in wide, and 3 in tall. What is its volume?

  • Q14 A cube has sides of 6 cm. What is its volume?

    All sides of a cube are equal, so volume = side × side × side.

  • Q15 A fish tank is 10 in long, 6 in wide, and 8 in tall. How many cubic inches of water fill it completely?