Page 61 - Year 10 Knowledge Organiser

Maths: FOUNDATION: Fractions and Percentages: 3 of 4 Maths: FOUNDATION: Equations and Inequalities: 4 of 4

What you need to know: What you need to know: What you need to know: What you need to know: You need to be able to:

Fractions, Decimals and Percentages Comparing FDP Ordering FDP Reading and writing inequalities x > 2 is shown as: x ≥ 3 is shown as: • Read an inequality.
You need to be able to convert between fractions, decimals and To be able to compare values we need to To be able to order FDP we need to • Represent an inequality
percentages. get them in the same format. write them all in the same format. The list of integers for -2 ≤ x < 1 is -1, 0, 1 on a number line.
Example: Order from smallest to • Solve one-step equations
Percentages: Example: Which is greater, 78% or 0.8? largest If x is between two values, use two circles: and inequalities.
We can either change the 0.8 into a Check the symbols
percentage or the 0.78 into a decimal. carefully, if they have the • Solve two-step equations
You can choose to convert them all line underneath, they and inequalities.
0.8 = 80% to fractions, decimals or include the end value. • Solve equations
Which is greater 78% or 80%? percentages as long as you convert and inequalities with
Decimals: 80% is greater so the answer is 0.8. them all into the same. Solving one-step equations and inequalities Solving with unknowns on both sides brackets.
To solve any equation or inequality we need to do the To solve an equation or inequality with unknowns on • Solve equations and
Example: Which is greater 17 0.87? Changing them to percentages: inverse of the operation that we see. both sides, we need to collect all of the same terms inequalities with
20 1 1
= 25% 0.19 = 19% 0.3 = 30% = 20% together, still by looking at the inverse.
4 5 unknowns on both sides.
Fractions: 17 85 87
= 0.87 = From smallest to biggest
20 100 100
19%, 20%, 25%. 25%, 30%
87 is bigger than 85 so the answer is 0.87 Top Tips:
Answer:

0.19, , , 26%, 0.3
1 1
5 4 Always add or subtract the smaller
Solving two-step equations and inequalities Solving equations with brackets: number of terms to avoid getting a
These are some conversions that you You need to be able to: To solve a two-step equation or inequality we need to We must expand the brackets first then solve by doing negative number at the end.
the inverse of the operations. We use the same method
complete 2 inverse calculations in a specific order.
need to learn. for inequalities.
Top tips- to convert: • Convert between simple fractions, decimals and percentages. The inequality sign always points
• Percentages to decimals divide by 100 • Convert between recurring decimals and percentages. to the smaller number.
• Decimals to percentages multiply by 100 • Compare fractions, decimals and percentages.
• Percentages to fractions put over 100 • Order fractions, decimals and percentages by converting. Extension Grade 5+: Dividing by a
• Fractions make sure the denominator is 100 negative flips the inequality sign.