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Equation Solving and Percentage Calculations

This lesson covers trial and improvement method for solving equations, converting amounts to percentages, and understanding ratio concepts in mathematics.

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Equation Solving and Percentage Calculations

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  1. Key Stage 3MathematicsKey FactsLevel 6

  2. Level 6 Number and Algebra Week 1 • Trial and improvement based on algebra • Expressing amounts as a percentage • Equivalence between Fractions, Decimals and Percentages. • Ratio

  3. Solve the equation x³ + x = 20 Using trial and improvement discover the value of x to the nearest tenth. NB – You will not get the exact solution We are looking for the nearest tenth.

  4. Solve the equation x³ + x = 20 Using trial and improvement and give your answer to the nearest tenth

  5. Solve the equation x³ + x = 20 Using trial and improvement and give your answer to the nearest tenth

  6. Solve the equation x³ + x = 20 Using trial and improvement and give your answer to the nearest tenth

  7. Now Try: Solve the equation x³ + x = 8 Using trial and improvement and give your answer to the nearest tenth Remember you will not get the exact answer.

  8. Amounts as a % • Fat in a mars bar 28g out of 35g. What percentage is this? Write as a fraction • =28/35 Convert to a percentage (top ÷ bottom x 100) • 28 ÷ 35 x 100 = 80% top ÷ bottom converts a fraction to a decimal Multiply by 100 to make a decimal into a percentage

  9. Amounts as a % • Now try these: • 36g out of 180g • 12 children out of 96 • £15 out of £60

  10. A percentage is a fraction out of 100

  11. Now try to make your own triangles using the following please: • 3/10 • 12.5% • 0.28

  12. The ratio of boys to girls in a class is 3:2 Altogether there are 30 students in the class. How many boys are there?

  13. The ratio of boys to girls in a class is 3:2 Altogether there are 30 students in the class. How many boys are there? The ratio 3:2 represents 5 parts(add 3 + 2) Divide 30 students by the 5 parts (divide) 30 ÷ 5 = 6 Multiply the relevant part of the ratio by the answer (multiply) 3 × 6 = 18 boys

  14. Now try these: The ratio of boys to girls in a year group is 4:3 Altogether there are 210students in the year group. How many boys are there? The ratio of flour, sugar and butter in a recipe is 1:3:5 Altogether there are 360g of ingredients used. How much sugar was used?

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