Multiplication of decimals with fractions is a combination of two topics: decimals and fractions. This topic is used in everyday real-life applications such as scientific measurements, and cooking recipes. It is important to understand how to multiply decimals with fractions. In this article, we are going to understand different methods of multiplication of decimals with fractions, and some solved examples based on it.
What are Decimals?
Decimals are numbers which is a combination of a whole number and a fractional part separated by a decimal point.
Example- 0.5 which is equal to 1/2.
What are Fractions?
Fractions are a part of the whole. The fraction is a combination of the numerator and the denominator.
Example - 2/3 is a fraction where 2 is numerator and 3 is denominator.
Multiplication of Decimals with Fractions
The multiplication of decimals and fractions are used in everyday life application. It is used everywhere in our daily lives, from the grocery store to the kitchen, and even in scientific calculations.
When we multiply a decimal with a fraction, we are finding a part of a part. Before we discuss the different methods to multiply decimals with fraction let's see the basic and most commonly used method of doing this:
Steps for Multiplication of Decimals with Fractions
Step 1: first we onvert the Decimal to a Fraction
Step 2: when both decimal and the fraction are in fractional form, we multiply the Fractions
Step 3: Simplify the Result if we want
Step 4: Convert Back to a Decimal (Optional)
Different Methods to Multiply Decimals with Fractions
There are different methods of multiplication of decimals with fractions. Some of most common methods which give approximate correct answer are mentioned below:
Method 1: Convert the Decimals to a Fraction
In this method, we convert the decimal to a fraction and then perform the multiplication.
- First, we convert the decimal to a fraction.
- Now, we directly multiply the numerators.
- Multiply the denominators.
- Now, simplify the fraction if possible into lower terms.
- Convert the result back to decimals if you want.
Example: Multiply 0.75 by 3/5.
Solution:
Step 1: Convert the decimal to a fraction.
0.75 = 75/100 = 3/4.
Step 2: Multiply the numerators.
3 (from 3/4) × 3 (from 3/5) = 9.
Step 3: Multiply the denominators.
4 (from 3/4) × 5 (from 3/5) = 20.
Step 4: Simplify the fraction.
The result is 9/20, which is already in its simplest form.
Step 5: Convert back to a decimal.
9/20 as a decimal is 0.45.
So, 0.75 × 3/5 = 0.45.
Method 2: Convert the Fraction to a Decimal
In this method we convert the fraction to a decimal and then multiply two decimals to find the results.
- First, convert the fraction to a decimal.
- Now, multiply two decimals.
- If possible then simplify the answer.
Example: Multiply 0.6 by 2/3.
Solution:
Step 1: Convert the fraction to a decimal.
2/3 = 0.6667 (rounded to four decimal places).
Step 2: Multiply the two decimals.
0.6 × 0.6667 = 0.40002.
Step 3: Simplify the answer.
Round 0.40002 to 0.4.
So, 0.6 × 2/3 = 0.4
Method 3: Multiply the Decimal Directly with the Fraction
In this method, we directly multiply the decimal with the fraction. We treat the decimal as a whole number multiplied by the fraction.
- First multiply the decimal directly with the numerator of raction
- Place the result over the denominator of fraction.
- Simplify the result fraction or convert it to a decimal.
Example: Multiply 0.4 by 7/10.
Solution:
Step 1: Multiply the decimal directly with the numerator.
0.4 × 7 = 2.8.
Step 2: Place the result over the denominator.
2.8/10.
Step 3: Simplify the fraction or convert to a decimal.
2.8 ÷ 10 = 0.28.
So, 0.4 × 7/10 = 0.28.
Practice Questions on Multiplication of Decimals with Fractions
Q1: Multiply 0.5 by 4/7
Solution:
Method 1: Convert the Decimal to a Fraction
Convert the decimal to a fraction.
0.5 = 1/2.
Multiply the numerators.
1 × 4 = 4.
Multiply the denominators.
2 × 7 = 14.
Simplify the fraction.
The result is 4/14, which simplifies to 2/7.
Convert back to a decimal (if needed).
2/7 as a decimal is approximately 0.2857.
So, 0.5 × 4/7 ≈ 0.2857.
Method 2: Convert the Fraction to a Decimal
Convert the fraction to a decimal.
4/7 ≈ 0.5714 (rounded to four decimal places).
Multiply the two decimals.
0.5 × 0.5714 = 0.2857.
Simplify the answer.
The answer is 0.2857.
So, 0.5 × 4/7 ≈ 0.2857.
Method 3: Multiply the Decimal Directly with the Fraction
Multiply the decimal directly with the numerator.
0.5 × 4 = 2.
Place the result over the denominator.
2/7.
Simplify the fraction or convert it to a decimal.
2 ÷ 7 ≈ 0.2857.
So, 0.5 × 4/7 ≈ 0.2857.
Q2: Multiply 0.3 by 5/8
Solution:
Method 1: Convert the Decimal to a Fraction
Convert the decimal to a fraction.
0.3 = 3/10.
Multiply the numerators.
3 × 5 = 15.
Multiply the denominators.
10 × 8 = 80.
Simplify the fraction.
The result is 15/80, which simplifies to 3/16.
Convert back to a decimal (if needed).
3/16 as a decimal is 0.1875.
So, 0.3 × 5/8 = 0.1875.
Method 2: Convert the Fraction to a Decimal
Convert the fraction to a decimal.
5/8 = 0.625.
Multiply the two decimals.
0.3 × 0.625 = 0.1875.
Simplify the answer.
The answer is 0.1875.
So, 0.3 × 5/8 = 0.1875.
Method 3: Multiply the Decimal Directly with the Fraction
Multiply the decimal directly with the numerator.
0.3 × 5 = 1.5.
Place the result over the denominator.
1.5/8.
Simplify the fraction or convert it to a decimal.
1.5 ÷ 8 = 0.1875.
So, 0.3 × 5/8 = 0.1875.
Q3: Multiply 0.4 by 2/9
Solution:
Method 1: Convert the Decimal to a Fraction
Convert the decimal to a fraction.
0.4 = 2/5.
Multiply the numerators.
2 × 2 = 4.
Multiply the denominators.
5 × 9 = 45.
Simplify the fraction.
The result is 4/45, which is already in its simplest form.
Convert back to a decimal (if needed).
4/45 as a decimal is approximately 0.0889.
So, 0.4 × 2/9 ≈ 0.0889.
Method 2: Convert the Fraction to a Decimal
Convert the fraction to a decimal.
2/9 ≈ 0.2222 (rounded to four decimal places).
Multiply the two decimals.
0.4 × 0.2222 ≈ 0.0889.
Simplify the answer.
The answer is approximately 0.0889.
So, 0.4 × 2/9 ≈ 0.0889.
Method 3: Multiply the Decimal Directly with the Fraction
Multiply the decimal directly with the numerator.
0.4 × 2 = 0.8.
Place the result over the denominator.
0.8/9.
Simplify the fraction or convert it to a decimal.
0.8 ÷ 9 ≈ 0.0889.
So, 0.4 × 2/9 ≈ 0.0889.
Q4: Multiply 0.8 by 7/12
Solution:
Method 1: Convert the Decimal to a Fraction
Convert the decimal to a fraction.
0.8 = 4/5.
Multiply the numerators.
4 × 7 = 28.
Multiply the denominators.
5 × 12 = 60.
Simplify the fraction.
The result is 28/60, which simplifies to 7/15.
Convert back to a decimal (if needed).
7/15 as a decimal is approximately 0.4667.
So, 0.8 × 7/12 ≈ 0.4667.
Method 2: Convert the Fraction to a Decimal
Convert the fraction to a decimal.
7/12 ≈ 0.5833 (rounded to four decimal places).
Multiply the two decimals.
0.8 × 0.5833 ≈ 0.4667.
Simplify the answer.
The answer is approximately 0.4667.
So, 0.8 × 7/12 ≈ 0.4667.
Method 3: Multiply the Decimal Directly with the Fraction
Multiply the decimal directly with the numerator.
0.8 × 7 = 5.6.
Place the result over the denominator.
5.6/12.
Simplify the fraction or convert it to a decimal.
5.6 ÷ 12 = 0.4667.
So, 0.8 × 7/12 ≈ 0.4667.
Q5: Multiply 0.9 by 8/11
Solution:
Method 1: Convert the Decimal to a Fraction
Convert the decimal to a fraction.
0.9 = 9/10.
Multiply the numerators.
9 × 8 = 72.
Multiply the denominators.
10 × 11 = 110.
Simplify the fraction.
The result is 72/110, which simplifies to 36/55.
Convert back to a decimal (if needed).
36/55 as a decimal is approximately 0.6545.
So, 0.9 × 8/11 ≈ 0.6545.
Method 2: Convert the Fraction to a Decimal
Convert the fraction to a decimal.
8/11 ≈ 0.7273 (rounded to four decimal places).
Multiply the two decimals.
0.9 × 0.7273 ≈ 0.6545.
Simplify the answer.
The answer is approximately 0.6545.
So, 0.9 × 8/11 ≈ 0.6545.
Method 3: Multiply the Decimal Directly with the Fraction
Multiply the decimal directly with the numerator.
0.9 × 8 = 7.2.
Place the result over the denominator.
7.2/11.
Simplify the fraction or convert it to a decimal.
7.2 ÷ 11 ≈ 0.6545.
So, 0.9 × 8/11 ≈ 0.6545.
Q6: Multiply 0.25 by 3/4
Solution:
Method 1: Convert the Decimal to a Fraction
Convert the decimal to a fraction.
0.25 = 1/4.
Multiply the numerators.
1 × 3 = 3.
Multiply the denominators.
4 × 4 = 16.
Simplify the fraction.
The result is 3/16, which is already in its simplest form.
Convert back to a decimal (if needed).
3/16 as a decimal is 0.1875.
So, 0.25 × 3/4 = 0.1875.
Method 2: Convert the Fraction to a Decimal
Convert the fraction to a decimal.
3/4 = 0.75.
Multiply the two decimals.
0.25 × 0.75 = 0.1875.
Simplify the answer.
The answer is 0.1875.
So, 0.25 × 3/4 = 0.1875.
Method 3: Multiply the Decimal Directly with the Fraction
Multiply the decimal directly with the numerator.
0.25 × 3 = 0.75.
Place the result over the denominator.
0.75/4.
Simplify the fraction or convert it to a decimal.
0.75 ÷ 4 = 0.1875.
So, 0.25 × 3/4 = 0.1875.
Q7: Multiply 0.6 by 5/9
Solution:
Method 1: Convert the Decimal to a Fraction
Convert the decimal to a fraction.
0.6 = 3/5.
Multiply the numerators.
3 × 5 = 15.
Multiply the denominators.
5 × 9 = 45.
Simplify the fraction.
The result is 15/45, which simplifies to 1/3.
Convert back to a decimal (if needed).
1/3 as a decimal is approximately 0.3333.
So, 0.6 × 5/9 ≈ 0.3333.
Method 2: Convert the Fraction to a Decimal
Convert the fraction to a decimal.
5/9 ≈ 0.5556 (rounded to four decimal places).
Multiply the two decimals.
0.6 × 0.5556 ≈ 0.3333.
Simplify the answer.
The answer is approximately 0.3333.
So, 0.6 × 5/9 ≈ 0.3333.
Method 3: Multiply the Decimal Directly with the Fraction
Multiply the decimal directly with the numerator.
0.6 × 5 = 3.
Place the result over the denominator.
3/9.
Simplify the fraction or convert it to a decimal.
3 ÷ 9 = 0.3333.
So, 0.6 × 5/9 ≈ 0.3333.
Practice Problems on Multiplication of Decimals with Fractions
Problem: Simplify the followings:
- 0.5 × 4/3
- 1.2 × 5/8
- 0.75 × 2/3
- 2.5 × 7/10
- 0.6 × 9/5
- 3.1 × 4/9
- 0.25 × 8/7
- 1.75 × 6/11
- 0.9 × 5/2
- 2.2 × 3/5
Conclusion
It is important to learn multiplication of decimals with fraction because is used in real-world applications such as construction, scientific measurements, and cooking recipes, etc. We can easily get the result of multiplication of decimals with fractions if we follow the right steps. The method in which we first convert the decimal to a fraction, multiplying the fractions, and simplifying the result is most optimal one. It make sure that we get accurate results every time.
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