Number & Operations — Fractions
Understanding Fractions: Operations and Decimals
Grade 4
- ✓By the end of this lesson students will be able to add and subtract fractions with like denominators.
- ✓By the end of this lesson students will be able to multiply a fraction by a whole number.
- ✓By the end of this lesson students will be able to convert fractions with denominators 10 or 100 to decimal notation.
- ✓By the end of this lesson students will be able to compare decimals to the hundredths place.
Key concepts
Equivalent fractions are different ways to name the same amount. For example, 1/2 is equivalent to 2/4 because they represent the same portion of a whole. We can find equivalent fractions by multiplying or dividing both the numerator and the denominator by the same non-zero number. This is useful when working with fractions and decimals.
When adding fractions that have the same denominator, you add the numerators and keep the denominator the same. Think of it as combining parts of the same size from the same whole.
When subtracting fractions that have the same denominator, you subtract the numerators and keep the denominator the same. Think of it as taking away parts of the same size from the same whole.
To multiply a fraction by a whole number, you multiply the whole number by the numerator of the fraction and keep the denominator the same. This is like having multiple copies of the fraction.
Decimals are another way to write fractions with denominators of 10 or 100. The first digit after the decimal point is the tenths place, and the second digit is the hundredths place. For example, 3/10 is written as 0.3, and 25/100 is written as 0.25.
To compare two decimals, look at the digits from left to right, starting with the largest place value. If the tenths digits are different, the decimal with the larger tenths digit is greater. If the tenths digits are the same, compare the hundredths digits. Remember that comparisons are valid only when the decimals refer to the same whole.
Key facts to remember
- 1To add or subtract fractions, their denominators must be the same.
- 2When adding or subtracting fractions with like denominators, only add or subtract the numerators. The denominator stays the same.
- 3To multiply a fraction by a whole number, multiply the whole number by the numerator. The denominator stays the same.
- 4Fractions with denominators of 10 or 100 can be written as decimals.
- 5The first digit after the decimal point is the tenths place; the second is the hundredths place.
- 6You can compare decimals by looking at the digits from left to right, starting with the tenths place.
- 7A mixed number combines a whole number and a fraction (e.g., 1 3/5).
Worked examples
Example 1
Solve: 3/8 + 2/8
Answer
5/8
This is like combining 3 pieces and 2 pieces of an 8-piece pizza.
Example 2
Multiply: 4 × 2/5
Answer
8/5 or 1 3/5
This means you have four groups of 2/5.
Example 3
Write 7/10 and 34/100 as decimals, then compare them using <, >, or =.
Answer
0.7 > 0.34
Remember that 0.7 is the same as 0.70. Adding a zero to the end of a decimal does not change its value.
Common mistakes
- ✗Adding or subtracting denominators when adding or subtracting fractions.
- ✗Forgetting to keep the denominator the same when multiplying a fraction by a whole number.
- ✗Confusing the tenths and hundredths places when writing or comparing decimals (e.g., writing 7/10 as 0.07 instead of 0.7).
- ✗Incorrectly comparing decimals, for example, thinking 0.34 is greater than 0.7 because 34 is greater than 7.
Exam tips
- ★Always check if fractions have like denominators before adding or subtracting.
- ★Draw visual models (like fraction bars or circles) to help understand fraction operations.
- ★When converting fractions to decimals, remember that 7/10 is 0.7, not 0.07.
- ★To compare decimals, you can add a zero to the end of a tenths decimal to make it a hundredths decimal (e.g., 0.7 = 0.70) to make comparison easier.
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