---
title: "Advanced Multi-Step Problems"
description: "Make sense of complex multi-step problems involving ratio, proportion, algebra, negative numbers, and all four operations with fractions and decimals by analysing given and unknown quantities, plannin"
canonical: https://lightmysky.com/learn/mathematics/advanced-multi-step-problems-mt_FieL-vVTI_
source: https://lightmysky.com/learn/mathematics/advanced-multi-step-problems-mt_FieL-vVTI_.md
retrieved: 2026-10-19
---

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# Advanced Multi-Step Problems

Make sense of complex multi-step problems involving ratio, proportion, algebra, negative numbers, and all four operations with fractions and decimals by analysing given and unknown quantities, planning solution strategies, and evaluating reasonableness using estimation and inverse operations

Subject: Mathematics · Area: Mathematical Thinking · Ages 10 to 11
Page: https://lightmysky.com/learn/mathematics/advanced-multi-step-problems-mt_FieL-vVTI_

## Ready when they can

- Break down a three-step ratio problem into sub-problems and plan a solution pathway
- Identify which quantities are known/unknown in an algebraic word problem and set up equations
- Use estimation to check whether a decimal division answer is reasonable before finalising

## Lesson: Breaking Down Big Problems

Some problems mix a lot together: ratios, unknown numbers, fractions, decimals, even negative numbers. A problem like this can feel too big to start. The trick is to break it into smaller steps. First find what you already know, then spot what you still need to find, and plan your steps before you calculate anything. You already split big problems into steps. The number to find is the unknown, often called x.

*(drawing: Work through a big problem in this order: knowns, unknowns, plan, solve, check.)*

**Example.** A juice recipe mixes orange and mango juice in a ratio of 2:3. Priya makes 50 litres in total. Step 1: add the ratio parts, 2 + 3 = 5. Step 2: divide the total by the parts, 50 ÷ 5 = 10 litres per part. Step 3: multiply each part, orange = 2 × 10 = 20 litres, mango = 3 × 10 = 30 litres.

Once you have an answer, don't stop there. Round the numbers and estimate to see if your answer is about the right size. You can also work backwards with the inverse operation to test it. If 40 ÷ 8 = 5, then 5 × 8 should bring you back to 40.

**Recap.** Break a big problem into small steps, work through them in order, then check your answer with estimation or the inverse operation.

## Practice

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

## Needs first

- [Finding knowledge gaps](https://lightmysky.com/learn/learning-to-learn/finding-knowledge-gaps-mt_2uHYdoxD0H)
- [Unequal sharing and grouping](https://lightmysky.com/learn/mathematics/unequal-sharing-and-grouping-mt_FnUJMXPUZX)
- [Complex Multi-Step Problems](https://lightmysky.com/learn/mathematics/complex-multi-step-problems-mt_GpltXPoaoc)
- [Multi-step problems: choosing operations](https://lightmysky.com/learn/mathematics/multi-step-problems-choosing-operations-mt_RXnyhCRYXA)

## Opens up

- [Using a Calculator Well](https://lightmysky.com/learn/mathematics/using-a-calculator-well-mt_FZE80D2jS_)