---
title: "Calculations with fractions, decimals and negatives"
description: "Use the four operations with formal written methods applied to integers, decimals, proper and improper fractions, and mixed numbers, all both positive and negative"
canonical: https://lightmysky.com/learn/mathematics/calculations-with-fractions-decimals-and-negatives-mt_gNUE4B3vuk
source: https://lightmysky.com/learn/mathematics/calculations-with-fractions-decimals-and-negatives-mt_gNUE4B3vuk.md
retrieved: 2026-09-12
---

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# Calculations with fractions, decimals and negatives

Use the four operations with formal written methods applied to integers, decimals, proper and improper fractions, and mixed numbers, all both positive and negative

Subject: Mathematics · Area: Fractions · Ages 11 to 13
Page: https://lightmysky.com/learn/mathematics/calculations-with-fractions-decimals-and-negatives-mt_gNUE4B3vuk

## Ready when they can

- Add, subtract, multiply, and divide with positive and negative integers
- Apply formal written methods to calculations with decimals of any size
- Perform all four operations with proper fractions, improper fractions, and mixed numbers

## Lesson: Mixed and Improper Fractions

You already know how to add, multiply, and divide fractions. Now you will work with two ways of writing fractions bigger than one whole. A mixed number, like 2 1/4, shows a whole number next to a fraction. An improper fraction, like 9/4, shows the same amount with one fraction where the top number is bigger than the bottom number.

*(drawing: Four fourths make one whole. Nine fourths would make more than two wholes.)*

**Example.** To change an improper fraction to a mixed number, divide the top number by the bottom number. For 9/4: 9 divided by 4 is 2, remainder 1. So 9/4 = 2 1/4.

**Example.** To change a mixed number to an improper fraction, multiply the whole number by the denominator, then add the numerator. For 2 1/4: 2 x 4 = 8, then 8 + 1 = 9. Keep the same denominator, so 2 1/4 = 9/4.

**Tip.** A negative sign in front of a mixed number covers the whole thing, not just the whole number part. -1 1/2 means the same as -(3/2). Convert to an improper fraction first, keeping the negative sign, before you add, subtract, multiply, or divide.

**Recap.** Change mixed numbers and improper fractions into the same form first, keep negative signs with the whole amount, then use the written methods you already know.

## Practice

11 questions on this page, each with its working shown.

## Needs first

- [Adding Fractions (Unlike Denominators)](https://lightmysky.com/learn/mathematics/adding-fractions-unlike-denominators-mt_14T5yPXUq_)
- [Multiplying fractions (age 10+)](https://lightmysky.com/learn/mathematics/multiplying-fractions-age-10-mt_AabJisinfi)
- [Dividing fractions (unit fractions)](https://lightmysky.com/learn/mathematics/dividing-fractions-unit-fractions-mt_ifPDOYvUqm)
- [Comparing fractions (age 10+)](https://lightmysky.com/learn/mathematics/comparing-fractions-age-10-mt_PL9VkDwXfh)

## Opens up

- [Decimals and fractions (age 11+)](https://lightmysky.com/learn/mathematics/decimals-and-fractions-age-11-mt_SBkTGjiZjZ)