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
What a learner can do afterwards
- 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
1 · Read
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.
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.
Break a big problem into small steps, work through them in order, then check your answer with estimation or the inverse operation.
The rewritten readings were written for this dataset.
More to read
Calculate an expression and check a solution
To evaluate an expression, replace its variables with known numbers and calculate. Identify the numbers, letters and operations before substituting. Work inside brackets first, then calculate powers if present. Next multiply or divide from left to right, then add or subtract from left to right. For 2n + 5 when n = 6, calculate 2 x 6 = 12, then 12 + 5 = 17. Substitution also checks equation solutions. If 3x - 4 = 11 gives x = 5, test it: 3 x 5 - 4 = 11.
Decimal Multiplication and Division Remix
Decimal division goes wrong most often in the decimal point, and estimation catches it. Before you divide 47.5 by 5, round to friendly numbers: 45 / 5 = 9, so the answer must sit near 9. If your calculation says 95, the point slipped and estimation sounds the alarm. Match each problem to its picture: draw the sharing story, pair the word problem with its number sentence, and tie every answer back to the basic fact underneath, like 3 x 7 = 21.
Key ideas: Create and solve real-world problems for given numerical expressions involving decimals
Big problems split into small problems. A numerical expression can mix brackets, multiplication, division, addition, and subtraction, so plan before you compute. First, list what you know and what is unknown. Next, split the job into sub-problems that each need one operation. Then write the matching expression with brackets showing the order. For a ratio story with flour and sugar at 3:2 and 12 cups of flour, sub-problem one finds one part (12 / 3 = 4) and sub-problem two scales up (2 x 4 = 8). Solve each part, then check the whole answer against a rough estimate.
Explore more
2 · Watch
به انگلیسیTake it off screen
Where it sits
Learn first
Optional connections
This opens up
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
16 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.