# Multiplication of Fractions As Parts of A Group

Multiplication of fractional numbers can be represented as parts of a group.

Background information: Multiplication of a fractional number with a whole number, may be thought of as a fractional part OF a group. 3/5 OF 10 Can be thought of as how much would be in THREE small groups, if the ten were divided into five equal groups. 1/5 + 1/5 + 1/5 + 1/5 + 1/5 = ONE GROUP (of ten).

3/5 OF 10 represented with Cuisenaire rods:

If white = one, then orange = 10

Think what rod could be used five times to match an orange?

Use this rod to be 1/5 of ten and then use repeated addition and add two more red rods.

Place them on top of the orange rod to compare them.

These three red rods represent 3/5 of orange (10) or 6 (white).

Activity: Illustrate multiplication of a fractional number and whole number by dividing a group into equal parts and select the fractional number of parts.

Solve problems like the following:

1/3 x 9 |
1/4 x 12 |

1/3 x 12 |
1/5 x 15 |

2/5 x 10 |
3/4 x 12 |

3/5 x 15 |
1/5 x 5 |

1/5 x 20 |
3/5 x 10 |

1/4 x 12 |
2/3 x 18 |

3/4 x 12 |
3/4 x 16 |

2/3 x 12 |
2/3 x 21 |

Dr. Robert Sweetland's Notes ©