Mathematics Number Operations and Decimals

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Questions and Answers

What is the result of multiplying 46 by 7 when using the order of operations, including brackets, to work out simple calculations?

322

What is the decimal equivalent of the fraction 3/4?

0.75

How can you determine if a number is divisible by 6?

A number is divisible by 6 if it is divisible by both 2 and 3.

What is the result of subtracting 4.2 from 7.8?

3.6 Signup and view all the answers

What is the equivalent mixed number for the improper fraction 7/3?

2 1/3 Signup and view all the answers

How would you order the following numbers on a number line: -5, -2, 0, 1 and 4?

-5, -2, 0, 1, 4 Signup and view all the answers

Explain how Eratosthenes' 'sieve' method can be used to generate primes less than 100.

Eratosthenes' sieve method involves listing all numbers up to 100, then systematically marking as composite (not prime) the multiples of each prime number as it is encountered. The remaining unmarked numbers in the list are the primes. Signup and view all the answers

What is the relationship between a ratio and a proportion, and how can it be used to solve problems?

A ratio is a comparison of two quantities, while a proportion is an equation stating that two ratios are equal. This relationship can be used to solve problems by setting up a proportion and then solving for the unknown value. Signup and view all the answers

How can you simplify a ratio, and what are the benefits of doing so?

A ratio can be simplified by dividing both the numerator and denominator by their greatest common factor. This makes the ratio easier to work with and compare to other ratios. Signup and view all the answers

What is the distinction between rounding up and rounding down in division, and when is each approach appropriate?

Rounding up involves increasing the quotient to the next whole number, while rounding down involves decreasing the quotient to the previous whole number. The choice between rounding up and down depends on the context and the desired level of accuracy. Signup and view all the answers

How can you convert a fraction to a decimal, and what are the benefits of doing so?

A fraction can be converted to a decimal by dividing the numerator by the denominator. This conversion can make the value easier to understand and compare to other values. Signup and view all the answers

What is the difference between a simple fraction and a percentage, and how can they be used to describe different quantities?

A simple fraction represents a part of a whole, while a percentage represents a fraction of 100. Both can be used to describe proportions and quantities, but percentages are often more intuitive and easier to understand. Signup and view all the answers

Study Notes

Number Facts and Operations

Recall positive integer complements to 100
Recall multiplication facts to 10 × 10 and associated division facts
Use the order of operations, including brackets, to work out simple calculations

Decimals and Place Value

Interpret decimal notation and place value
Multiply and divide whole numbers and decimals by 10, 100, or 1000
Order decimals, including measurements, and change them to the same units
Round whole numbers to the nearest 10, 100, or 1000, and decimals to the nearest whole number or one decimal place

Multiplication and Division

Use known facts and place value to multiply and divide two-digit numbers by a single-digit number
Multiply simple decimals by one-digit numbers
Divide whole numbers and decimals by 10, 100, or 1000

Fractions, Decimals, and Percentages

Recognize the equivalence of simple fractions, decimals, and percentages
Simplify fractions by cancelling common factors
Identify equivalent fractions, and convert terminating decimals to fractions
Compare two fractions by using diagrams or converting to decimals

Negative Numbers and Integers

Recognize negative numbers as positions on a number line
Order, add, and subtract positive and negative numbers in context

Factors, Multiples, and Primes

Recognize multiples, factors, common factors, and primes (all less than 100)
Use simple tests of divisibility
Find the lowest common multiple in simple cases
Use the 'sieve' method for generating primes developed by Eratosthenes

Squares and Square Roots

Recognize squares of whole numbers to at least 20 × 20 and the corresponding square roots
Use the notation √ and ²

Addition and Subtraction of Fractions

Add and subtract two simple fractions
Find fractions of quantities (whole number answers)
Multiply a fraction by an integer

Percentages

Understand percentage as the number of parts in every 100
Use fractions and percentages to describe parts of shapes, quantities, and measures
Calculate simple fractions and percentages of quantities

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Description

Test your knowledge of basic number operations, including complements, multiplication facts, and decimal notation. Practice applying the order of operations and rounding whole numbers to the nearest 10, 100, or 1000.