12 Questions
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
What is the equivalent mixed number for the improper fraction 7/3?
2 1/3
How would you order the following numbers on a number line: -5, -2, 0, 1 and 4?
-5, -2, 0, 1, 4
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.
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.
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.
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.
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.
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.
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
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.
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