#### Subtracting decimals

Subtracting decimal numbers follows the same process as addition, with the focus being on ensuring that when the calculation is set out vertically the place value parts and decimal points line up.

H | T | O | tenths | hundredths | thousandths | ||
---|---|---|---|---|---|---|---|

5 | 8 | 4 | . | 7 | 5 | 6 | |

− | 1 | 3 | 2 | . | 3 | 2 | 4 |

= | 4 | 5 | 2 | . | 4 | 3 | 2 |

Some subtractions require regrouping.

\(^4 5\hspace{-3mm}\color{red}/ \) | \(^1 4\) | 6 | . | \(^6 7\hspace{-3mm}\color{red}/ \) | \(^1 5\) | 9 | |

− | 2 | 8 | 0 | . | 2 | 8 | 7 |

= | 2 | 6 | 6 | . | 4 | 7 | 2 |

When there are different numbers of digits after the decimal point, such as in the example below, it is possible to become confused about what we should do with the space that is created by these 'ragged' decimals.

H | T | O | tenths | hundredths | ||
---|---|---|---|---|---|---|

3 | 7 | 8 | . | 5 | ||

− | 2 | 5 | 3 | . | 2 | 8 |

= |

If students have a strong understanding of place value, they will know that placing a zero to even up the lengths of the numbers doesn't alter the value of the number; it simply says that there are 'no hundredths'.

3 | 7 | 8 | . | \(^4 5\hspace{-3mm}\color{red}/ \) | \(^1 0\) | |

– | 2 | 5 | 3 | . | 2 | 8 |

= | 1 | 2 | 5 | . | 2 | 2 |