Using fractions
Fractions show parts of whole numbers, for example, the fraction \(\frac{1}{4}\) shows a number that is 1 part out of 4, or a quarter.
\(\frac{1}{4}\) is the same as \(1 \div 4\).
Fractions are one way of showing numbers that are parts of a whole. Other ways are A number that uses powers of 10 as place value. In the example of 0.82, the 8 represents tenths and the 2 represents hundredths. and A proportion representing parts per hundred, for example 9% is 9 out of 100, or 9/100.. You can also convert between fractions, decimals and percentages. Like whole numbers and decimals, fractions can be either positive or negative. For example, \(3 \frac{1}{5}\) or \(- \frac{1}{4}\).
Equivalent fractions
Equivalent fractions are fractions that are worth exactly the same even though they are written differently. \(\frac{1}{4}\) is worth the same as \(\frac{2}{8}\) because \(\frac{2}{8}\) will A fraction is simplified when there are no more common factors shared by the numerator and denominator. For example, the fraction 8/10 will simplify to 4/5 by removing a common factor of 2. to \(\frac{1}{4}\) by dividing the numerator and denominator by 2.
Working out equivalent fractions
Equivalent fractions are made by multiplying or dividing the The bottom part of a fraction. For ⅝, the denominator is 8, which represents 'eighths'. and The top part of a fraction. For ⅝ , the numerator is 5. of the fraction by the same number.
For example, to find fractions that are equivalent to \(\frac{1}{3}\), multiply the numerator and denominator by the same number.
Multiplying or dividing both parts of a fraction by the same number will always create equivalent fractions. There are an Never ends, repeats forever. amount of equivalent fractions that can be found because there are an infinite amount of numbers to multiply by.
Question
\(\frac{3}{8}\:\) is equivalent to \(\frac{?}{24}\). Find the missing number.
Look at the two fractions to see what An amount that each number or numbers will be multiplied by. has been used. In this case, the denominators are both known: 8 and 24. 8 has been multiplied by 3 to get a new denominator of 24. This means the numerator also has to be multiplied by 3:
\(3 \times 3 = 9\)
The answer is \(\frac{9}{24}\).
More guides on this topic
- NEW: Whole numbers
- NEW: Order of operations and negative numbers
- NEW: Decimals
- NEW: Converting between fractions, decimals and percentages
- NEW: Higher – How to convert recurring decimals
- NEW: How to round numbers
- NEW: What is accuracy in maths?
- NEW: What are fractions?
- NEW: How to add, subtract, multiply and divide fractions
- NEW: Multiples and factors
- NEW: Highest Common Factor and Lowest Common Multiple
- NEW: Laws of indices
- NEW: Negative and fractional indices
- NEW: Standard form
- NEW: Calculations using standard form
- Whole numbers - AQA
- Approximation - AQA
- Decimals - AQA
- Multiples and factors - AQA
- Laws of indices - AQA
- Converting between fractions, decimals and percentages - AQA
- Standard form - AQA
- Surds - AQA
- Financial mathematics - AQA