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    • ▾4th grade
      • ▸Place value of whole numbers
        • •Place value of multi-digit whole numbers
        • •Adding and subtracting multi-digit numbers
        • •Multiply and divide by 10
        • •Represent a number using base ten blocks, units, tens, and hundreds
        • •Convert between written forms of numbers
        • •Round whole numbers
        • •Estimating sums and differences by rounding
        • •Estimating products by rounding
      • ▸Multiplication and division
        • •Multiplying one-digit numbers by 10, 100, and 1000
        • •Multiplying one-digit numbers by multiples of 10, 100, and 1000
        • •Multiplying 10s
        • •Multiplication
        • •Quotients and remainders
        • •Pattern in the units digit of multiples
        • •Solve multiplication and division word problems
        • •Multi-step word problems
      • ▸Factors, multiples, and patterns
        • •Factors and multiples
        • •Divisibility tests
        • •Prime and composite numbers
        • •Number patterns
      • ▸Equivalent fractions and comparing fractions
        • •Equivalent fractions
        • •37 trick
        • •Compare fractions with unlike numerators, denominators, or both
      • ▾Fraction arithmetic
        • •Round fractions
        • •Add and subtract fractions with like denominators
        • •Add fractions with denominators of 10 or 100
        • •Multiply fractions by whole numbers
      • ▸Understand decimals
        • •Represent decimal numbers using base ten blocks
        • •Compare decimals to hundredths
      • ▸Geometry
        • •Intro to parallel and perpendicular lines
        • •Lines of symmetry
        • •Rotational symmetry
        • •Intro to angles
        • •Measuring and drawing angles
        • •Coterminal angles
        • •Naming angles
        • •Adjacent angles and the additive property of angles
      • ▸Units of measurement
        • •Converting larger units of volume to smaller ones
        • •Converting larger units of length to smaller ones
        • •Converting larger units of time to smaller ones
        • •Word problems involving measures
     › 4th grade › Fraction arithmetic

    Multiply fractions by whole numbers

    Students will learn that a fraction, such as \(4/7,\) is equal to \(4 \cdot (1/7).\) That is, \(4/7\) can be thought of as \(4\) pieces of size \(1/7.\) Then students will learn how to use this idea to multiply whole numbers by fractions. For example, \((3/7) \cdot 2\) is \(3\) pieces of size \(1/7,\) times \(2,\) which is \(6\) pieces of size \(1/7,\) which is \(6/7.\) Some problems will be expressed as \(2/3 \cdot 4,\) while others will be expressed as \(2/3\) of \(4.\) Of course, these are equivalent.

    How to Find a Fraction of a Whole Number by Math by Math with Mr. J

    Solve word problems involving multiplication of a fraction by a whole number. Start with manipulatives and pictures, then gradually move away from them.

    Do these Khan Academy exercises:

    • Interpret multiplying fraction and whole number word problems
    • Multiply mixed numbers and whole numbers
    • Multiply fractions and whole numbers with fraction models
    • Multiply fractions and whole numbers
    • Multiply unit fractions and whole numbers
    • Equivalent whole number and fraction multiplication expressions
    • Multiply fractions and whole numbers on the number line

    Conclude by leading this investigation:

    Lazy Toad Puzzles (counting, symmetry)
    by MathPickle

    4.NF.B.4: Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.

    Practice problems and additional lessons