Fraction of a number

Fraction of a number

Lessons

In this lesson, we will learn:

  • How to understand fraction of a number using: models with shapes, models with fraction blocks, and fraction number lines
  • The steps for multiplying a fraction with a whole number

Notes:

  • When we are looking for a fraction of a number, we are using multiplication
    • The word “of” in math usually signifies multiplication

  • We can use models with shapes to find the fraction of a number:
    • Ex. What is 15\frac{1}{5} of 15?
    • Use 15 circles to represent the whole number; divide into 5 equal parts; answer how many circles are in 1 of those parts:

Introduction to Fractions: Fraction of a Number Therefore, 15\frac{1}{5} x 15 = 3

  • We can also use models with fraction blocks to find the fraction of a number:
    • Ex. What is 23\frac{2}{3} × 5?
      • Create a fraction block with 2 of 3 equal parts shaded in. Repeat 5 times.

    Introduction to Fractions: Fraction of a Number

    • There are 10 parts shaded in, each one is worth 13\frac{1}{3} of a whole.
    • Therefore, 23\frac{2}{3} x 5 = 103\frac{10}{3} or 3 13\frac{1}{3}

  • We can also use number lines to find the fraction of a number:
    • Ex. What is 4 × 15\frac{1}{5} ?
    • Split a line (from 0 to 1) into 5 equal parts, create 4 jumps of 1 part each (15\frac{1}{5})

Introduction to Fractions: Fraction of a Number

  • Generally, the fastest way to find the fraction of a number will be to do fraction multiplication with a whole number using these steps:

    • Step 1: Put the whole number as a fraction over 1
      Step 2: Cross cancel the numbers if possible
      Step 3: Multiply the top numbers and then separately multiply the bottom numbers
      Step 4: Write your answer in lowest terms
    • Ex. What is 618\frac{6}{18} of 24?
Introduction to Fractions: Fraction of a Number
  • Introduction
    Introduction to Fraction of a Number:
    a)
    Fraction of a number using shapes

    b)
    Fraction of a number using fraction blocks

    c)
    Fraction of a number using number lines

    d)
    The 4 steps for fraction multiplication with a whole number


  • 1.
    Number Lines and Fraction of a Number
    Use the number line to complete the multiplication sentence (fill in and/or analyze):
    a)
    5 × 18\frac{1}{8} = ___

    Introduction to Fractions: Fraction of a Number

    b)
    25\frac{2}{5} x 6 = ___

    Introduction to Fractions: Fraction of a Number

    c)


    Introduction to Fractions: Fraction of a Number

    d)


    Introduction to Fractions: Fraction of a Number


  • 2.
    Fraction Blocks and Fraction of a Number
    Use fraction blocks to solve for the fraction of each number.
    a)
    4 × 16\frac{1}{6} = ?

    Introduction to Fractions: Fraction of a Number

    b)
    23\frac{2}{3} × 6 = ?

    Introduction to Fractions: Fraction of a Number

    c)
    Which model shows the answer to 19\frac{1}{9} × 5?

    Introduction to Fractions: Fraction of a Number

    d)
    Which model shows the answer to 3 x 35\frac{3}{5} × 5?

    Introduction to Fractions: Fraction of a Number


  • 3.
    Fraction Multiplication for Fraction of a Number
    Use the steps for fraction multiplication to solve.
    • Hint: (1) put whole number over 1, (2) cross cancel, (3) multiply numerators; multiply denominators, (4) write in lowest terms
    a)
    14 × 17\frac{1}{7} = ?

    b)
    311\frac{3}{11} × 11 = ?

    c)
    6 × 45\frac{4}{5} = ?

    d)
    235\frac{2}{35} × 70 = ?

    e)
    48 × 916\frac{9}{16} = ?

    f)
    Ben lives 5324\frac{53}{24} miles away from the mall. Trixie lives 6 times that distance from the mall. How many miles away from the mall does Trixie live?


  • 4.
    Figuring out Fraction Multiplication Backwards
    Fill in the blanks by working backwards.
    a)
    ? × 18\frac{1}{8} = 6

    b)
    526\frac{5}{26} × ? = 526\frac{5}{26}

    c)
    ? × 19\frac{1}{9} = 0

    d)
    ? × 34\frac{3}{4} = 6

    e)
    620\frac{6}{20} × ? = 712\frac{1}{2}


  • 5.
    Fraction of a Number Picture Problems
    Use the picture. Write the multiplication equation with a fraction and a whole number. Then, solve for the fraction of a number.
    a)

    Introduction to Fractions: Fraction of a Number

    b)

    Introduction to Fractions: Fraction of a Number

    c)

    Introduction to Fractions: Fraction of a Number


  • 6.
    Fraction of a Number: Word Problem
    Jerry Jepson Elementary School has a population of 380 students. Mrs. Kim's class has 14 girls and 10 boys.
    a)
    If 16\frac{1}{6} of the class is vegetarian, how many students are vegetarian?

    b)
    If 38\frac{3}{8} of the class has siblings, how many students have a brother or sister? How many students are only-children?

    c)
    If 738\frac{7}{38} of the school's students have pets how many students have pets? Out of these pet owners, 47\frac{4}{7} have dogs as pets; how many students have dogs?

    d)
    If 35\frac{3}{5} of the school wears glasses and 14\frac{1}{4} of Mrs. Kim's class wears glasses, what is the FRACTION of students wearing glasses in the class compared to the entire school?