Fractions Decimals Percentages

numberandalgebra core

Fractions, decimals and percentages | NSW Curriculum Website

• 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 - decimal place value, benchmark conversions	- representing rational numbers - 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 $b\ne 0$
• 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 $b\ne 0$
• 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