Number & Algebra
Fractions, Decimals, and Percentages: Understanding and Operations
Grade 4 · Grade 5 · Grade 6
- ✓Understand that fractions, decimals, and percentages are different ways to represent parts of a whole.
- ✓Add and subtract fractions with common denominators.
- ✓Convert simple fractions and decimals to percentages, and vice-versa.
- ✓Calculate common percentages (e.g., 10%, 25%, 50%) of whole numbers.
- ✓Solve simple word problems involving fractions and percentages.
Key concepts
A fraction represents a part of a whole. It has two main parts: the numerator (the top number) tells you how many parts you have, and the denominator (the bottom number) tells you how many equal parts the whole is divided into. For example, in 3/4, you have 3 parts out of a total of 4 equal parts.
When fractions have the same denominator (the bottom number), adding them is easy! You just add the numerators (the top numbers) and keep the denominator the same. Remember to simplify your answer if possible.
Similar to adding, when fractions have the same denominator, you subtract the numerators and keep the denominator the same. Always check if you can simplify your final fraction.
A decimal is another way to show parts of a whole, using place value based on tens. For example, 0.5 means five tenths, and 0.25 means twenty-five hundredths. Decimals are often used for money or measurements.
A percentage is a special type of fraction that means 'out of one hundred'. The symbol for percent is %. So, 50% means 50 out of 100, or 50/100. Percentages are often used for discounts, grades, or statistics.
You can change a number from one form to another: \n- To change a fraction to a decimal: Divide the numerator by the denominator. (e.g., 1/2 = 1 ÷ 2 = 0.5)\n- To change a decimal to a percentage: Multiply the decimal by 100 and add the % sign. (e.g., 0.5 x 100 = 50%)\n- To change a percentage to a decimal: Divide the percentage by 100 and remove the % sign. (e.g., 50% ÷ 100 = 0.5)\n- To change a percentage to a fraction: Write the percentage over 100 and simplify. (e.g., 50% = 50/100 = 1/2)
To find a percentage of a number, you first convert the percentage to a decimal or a fraction, then multiply it by the number. For example, to find 25% of 80, you can think of 25% as 0.25 or 1/4.
Key facts to remember
- 1Fractions, decimals, and percentages are all ways to show parts of a whole.
- 2A percentage means 'out of one hundred'.
- 3To add or subtract fractions, their denominators (bottom numbers) must be the same.
- 4To convert a decimal to a percentage, multiply by 100 and add the % sign.
- 5To convert a percentage to a decimal, divide by 100 and remove the % sign.
- 6The whole can be represented as 1 (as a fraction or decimal) or 100% (as a percentage).
- 7Always simplify fractions to their lowest terms when possible.
Worked examples
Example 1
Add the fractions: 3/7 + 2/7
Answer
5/7
The fraction 5/7 cannot be simplified further.
Example 2
Subtract the fractions: 9/10 - 4/10
Answer
1/2
Always simplify your fractions to their lowest terms.
Example 3
What is 25% of 60?
Answer
15
Remember that 'of' in math problems often means to multiply.
Example 4
In a class of 20 students, 1/4 of them walk to school. How many students walk to school? What percentage of students walk to school?
Answer
5 students walk to school. 25% of students walk to school.
This problem combines finding a fraction of a number and converting a fraction to a percentage.
Common mistakes
- ✗Adding or subtracting the denominators when adding or subtracting fractions.
- ✗Forgetting to simplify fractions to their lowest terms.
- ✗Confusing the direction of conversion between decimals and percentages (e.g., dividing by 100 instead of multiplying, or vice versa).
- ✗Not understanding that 'of' in percentage problems usually means to multiply.
- ✗Trying to add or subtract fractions with different denominators without realizing they need to be the same.
Exam tips
- ★Always read the question carefully to understand if you need to find a fraction, decimal, or percentage, or perform an operation.
- ★Show all your steps clearly, especially when working with fractions, so your teacher can follow your thinking.
- ★Check your answers to see if they make sense. For example, if you find 50% of a number, your answer should be half of that number.
- ★Practice converting between fractions, decimals, and percentages regularly to become quick and confident.
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