Class 5
Fraction - Multiplication & Division
Multiplication of fraction with whole number
Multiplying a fraction with a whole number is very simple! You are essentially taking a fraction that many times.
Steps to Multiply a Fraction with a Whole Number:
1. Write the whole number as a fraction:
Any whole number can be written as a fraction by placing it over 1.
For example, 3 becomes 3/1 .
2. Multiply the fractions:
– Multiply the numerators (top numbers).
– Multiply the denominators (bottom numbers).
3. Simplify the result, if needed:
Divide the numerator and denominator by their greatest common factor to make it smaller.
Example 1:
2/5 x 3
1. Write the whole number as a fraction:
3 = 3/1.
2. Multiply the numerators:
2 x 3 = 6 .
3. Multiply the denominators:
5 x 1 = 5 .
4. The result:
6/5
This is an improper fraction. Write it as a mixed number:
6/5 = 1 1/5.
Example 2:
4/7 x 2
1. Write the whole number as a fraction:
2 = 2/1.
2. Multiply the numerators:
4 x 2 = 8 .
3. Multiply the denominators:
7 x 1 = 7 .
4. The result:
8/7
This is an improper fraction. Write it as a mixed number:
8/5 = 1 1/7.
Key Points :
1. Whole numbers are written as fractions by putting them over 1.
2. Multiply the top numbers and bottom numbers.
3. Simplify or convert improper fractions to mixed numbers if needed.
Multiplication of two fraction
How to Multiply Two Fractions
To multiply two fractions, follow these steps:
Step 1: Multiply the Numerators
The numerator is the top number of a fraction. Multiply the numerators of both fractions to get the numerator of the answer.
For example:
2/3×4/5
Multiply the numerators: 2×4=8.
Step 2: Multiply the Denominators
The denominator is the bottom number of a fraction. Multiply the denominators of both fractions to get the denominator of the answer.
For example:
3×5 = 15
Step 3: Write the Result
The result is:
8/15
Step 4: Simplify the Fraction (If Necessary)
If the numerator and denominator have a common factor, divide both by the greatest common factor (GCF) to simplify. In this case, 8/15 is already in its simplest form.
Example with Simplification
Multiply:
6/8×3/4
- Multiply the numerators: 6×3=18.
- Multiply the denominators: 8×4=32.
- Write the result: 18/32.
- Simplify: The GCF of 18 and 32 is 2. Divide both by 2:
18/32=9/16
Multiplication of more than two fraction
Multiplying more than two fractions is just as simple as multiplying two! The process remains the same: multiply all the numerators together, then multiply all the denominators together. Let’s break it down step by step:
Steps to Multiply More Than Two Fractions
Step 1: Multiply the Numerators
The numerators are the top numbers of the fractions. Multiply all the numerators together to get the numerator of the answer.
Step 2: Multiply the Denominators
The denominators are the bottom numbers of the fractions. Multiply all the denominators together to get the denominator of the answer.
Step 3: Simplify the Fraction
If the result can be simplified, divide the numerator and denominator by their greatest common factor (GCF).
Example 1: Multiply 1/2 x 3/4 x 5/6
1. Multiply the Numerators:
1 x 3 x 5 = 15
2. Multiply the Denominators:
2 x4 x 6 = 48
3. Write the Result:
15/48
4. Simplify the Fraction:
The GCF of 15 and 48 is 3. Divide both numerator and denominator by 3:
15/48 = 5/16
So, the answer is 5/16
Example 2: Multiply 2/3 x 4/5 x 7/8
1. Multiply the Numerators:
2 x 4 x 7 = 56
2. **Multiply the Denominators**:
3 x 5 x 8 = 120
3. Write the Result:
56/ 120
4. Simplify the Fraction:
The GCF of 56 and 120 is 8. Divide both numerator and denominator by 8:
56/120 = 7/15
So, the answer is 7/ 15.
Tips for Multiplying Multiple Fractions
1. Multiply all the numerators together and all the denominators together.
2. Simplify as you go! If any numerator and denominator share common factors, you can cancel them before multiplying.
3. Check your final answer to see if it can be simplified further.
Division of two fraction
Dividing fractions might seem tricky at first, but it’s actually quite simple once you know the steps. Let’s break it down step by step:
Steps to Divide Fractions:
1. Understand the Problem: When dividing fractions, you’re asking, “How many times does one fraction fit into another?”
2. Keep, Change, Flip:
– Keep the first fraction as it is.
– Change the division sign (÷) to multiplication (×).
– Flip the second fraction upside down (this is called finding the reciprocal).
3. Multiply the Fractions: Multiply the numerators (top numbers) together and then the denominators (bottom numbers) together.
4. Simplify the Answer: If possible, simplify the resulting fraction to its lowest terms.
Example:
Let’s divide 3/4 by 2/5.
Step 1: Write the problem.
3/4 ÷ 2/5
Step 2: Keep, Change, Flip.
Keep the first fraction 3/4, change division to multiplication, and flip the second fraction 2/5 becomes 5/2.
3/4 x 5/2
Step 3: Multiply the fractions.
Multiply the numerators:
3 x 5 = 15
Multiply the denominators:
4 x 2 = 8
So, the result is:
15/8
Step 4: Simplify the answer.
15/8 is already in its simplest form, but it’s an improper fraction. You can also write it as a mixed number:
1 7/8
Key Points to Remember:
– Flip the second fraction when dividing.
– Always multiply straight across (numerators and denominators).
– Simplify your answer if needed.
Division of like and unlike fraction
Like Fractions: Fractions that have the same denominator.
Example: 2/5 , 3/5 , 4/5
– Unlike Fractions: Fractions that have different denominators.
Example: 2/5 , 3/7
Dividing Like Fractions
When dividing like fractions, the denominators are the same. Here’s how you do it:
1. Divide the Numerators: Take the numerator of the first fraction and divide it by the numerator of the second fraction.
2. Keep the Denominator the Same: Since the denominators are the same, it doesn’t change.
Example:
Divide 6/7 ÷ 3/7 .
– Divide the numerators: 6 ÷ 3 = 2
– Keep the denominator: 7
Result:
6/7 ÷ 3/7 = 2
Dividing Unlike Fractions
When dividing unlike fractions, the denominators are different. Follow these steps:
1. Keep, Change, Flip:
– Keep the first fraction as it is.
– Change the division sign (÷) to multiplication (×).
– Flip the second fraction (find its reciprocal).
2. Multiply the Fractions: Multiply the numerators and denominators as usual.
3. Simplify the Answer: Simplify the result to its lowest terms.
Example:
Divide 3/4 ÷ 2/5.
1. Keep, Change, Flip:
3/4 ÷ 2/5 = 3/4 x 5/2
2. Multiply the Fractions:
– Multiply the numerators: 3 x 5 = 15
– Multiply the denominators: 4 x 2 = 8
Result:
15/8
3. Simplify (if needed):
Convert 15/8 to a mixed number:
1 7/8
Key Points to Remember
– Like Fractions: Divide the numerators, keep the denominator.
– Unlike Fractions: Use the “Keep, Change, Flip” method, then multiply.