#NumberAndAlgebra #Core >[!info]- [Fractions, decimals and percentages | NSW Curriculum Website](https://curriculum.nsw.edu.au/learning-areas/mathematics/mathematics-k-10-2022/content/stage-4/fad6ecbfc4) >- MA4-FRC-C-01 represents and operates with fractions, decimals and percentages to solve problems ## 📖 Prior Knowledge | Content | Prior knowledge | Used for | | ------------------------------------- | -------------------------------------------------------------------------- | --------------------------------------------------- | | [[Represents Numbers B]] | - number lines<br>- decimal place value, benchmark conversions | - representing rational numbers<br>- converting FDP | | [[Multiplicative Relations A]] | - factors and multiples | - simplifying, comparing, adding fractions | | [[Multiplicative Relations B]] | - division can be recorded as a fraction | - converting FDP | | [[Representing Quantity Fractions B]] | - comparing and adding fractions with denominators of 2, 4, 8, 3, 6, 5, 10 | - comparing and adding fractions | ## [[Compare fractions using equivalence.pdf]] - Determine the highest common factor (HCF) of 2 whole numbers - Examine methods of generating equivalent fractions - Simplify fractions by using methods, including determining the HCF of the numerator and denominator or repeated simplification using common factors - Create fractions with the same denominator to compare their sizes - Compare and order fractions with different denominators ## [[Round decimals to a specified degree of accuracy using approximations.pdf]] - Round decimals to a given number of decimal places - Apply the notation ≈ as a symbol of numerical approximation - Reason why an approximation may be more appropriate than an exact answer and vice versa ## [[Identify terminating and recurring decimals.pdf]] - Use either dot or vinculum notation for recurring (repeating) decimals - Classify decimals as recurring or terminating ## [[Identify and make use of the relationship between fractions, decimals and percentages to carry out simple conversions.pdf]] - Define rational numbers as numbers that can be written in the form $\frac{a}{b}$, where $a$ and $b$ are integers and $b≠0$ - Classify fractions and percentages as rational numbers - Recognise and explain that numbers with terminating or recurring decimals are rational - Represent fractions as decimals (terminating and recurring) and percentages - Represent terminating decimals as fractions and percentages - Represent improper fractions as mixed numbers and decimals, and vice versa - Represent percentages as fractions and decimals ## [[Examine the concept of irrational numbers.pdf]] - Identify and define irrational numbers as numbers that cannot be written in the form $\frac{a}{b}$, where $a$ and $b$ are integers and $b≠0$ - Find approximations of irrational numbers using digital tools - Locate the approximate position of irrational numbers on a number line ## [[Order and compare the value of fractions, decimals and percentages.pdf]] - Locate positive and negative fractions, decimals and mixed numbers on a number line to compare their relative values - Compare and order fractions, mixed numbers, decimals (terminating and recurring) and percentages ## [[Solve problems that involve the addition and subtraction of fractions.pdf]] - Represent addition and subtraction of fractions with the same or unrelated denominators - Solve problems involving adding and subtracting fractions and mixed numbers, including finding a common denominator - Solve problems that involve subtracting a fraction from a whole number, with and without the use of digital tools ## [[Solve problems that involve the multiplication and division of fractions and decimals.pdf]] - Compare and generalise the effect of multiplying or dividing by a number with magnitude between zero and one - Represent multiplication and division of decimals - Represent multiplication and division of fractions, including mixed numbers - Multiply and divide decimals, using digital tools to solve problems - Multiply and divide fractions and mixed numbers, with and without using digital tools to solve problems - Compare initial estimates with the results of calculations - Apply knowledge of fractions and decimals of quantities to solve problems - Apply knowledge of multiplication and division of fractions and decimals to solve problems ## [[Represent one quantity as a fraction, decimal or percentage of another, with and without the use of digital tools.pdf]] - Represent one quantity as a fraction, decimal or percentage of another by considering appropriate units - Calculate percentage increases and decreases in various contexts - Examine the financial applications of percentage increase and decrease, including profit and/or loss as a percentage of cost price or selling price ## [[Solve problems that involve the use of percentages.pdf]] - Apply knowledge of percentages to calculate quantities in various contexts - Apply knowledge of percentage increases and decreases to solve problems in various contexts - Solve real-life problems involving percentages using the unitary method or other techniques - Solve financial problems involving percentages, specifically considering GST, profit and loss