Fractions and Decimals

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Overview

Developing a strong understanding of fractions and decimals is crucial for your success in year 6 maths. Fractions and decimals are not just abstract numbers; they have practical applications in everyday life, such as cooking, measurements, and financial calculations. By mastering them, you’ll enhance your problem-solving skills and be well-equipped for future mathematical challenges. Let’s dive in and explore a bit more together!

Learning Outcomes

By the end of this article, you will:

• Be able to add and subtract fractions with unlike denominators confidently.
• Understand how to determine a fraction of a whole.
• Be able to multiply fractions.
• Be able to divide fractions.
• Discover how to multiply a decimal number by a power of 10 and efficiently shift the decimal point.
• Learn the technique of dividing a decimal number by a power of 10 and correctly adjust the decimal placement.
• Develop the skill to multiply decimals, paying attention to the decimal point positioning in the final answer.

Adding and Subtracting Fractions with Unlike Denominators

In year 5, you learned how to add or subtract fractions when the denominators were equal. But what if the denominators are different? Let’s look at a couple of examples…

Add: \(\frac{1}{2}+ \frac{2}{3}\)
Although the denominators are different, we can use the concept of equivalent fractions to change them to 6, which is the LCM of 2 and 3 (the two denominators).

\(\frac{1}{2}= \frac{3}{6}\)

\(\frac{2}{3}= \frac{4}{6}\)

Therefore, \(\frac{1}{2}+ \frac{2}{3}=\frac{3}{6}+ \frac{4}{6}=\frac{3+4}{6}=\frac{7}{6}\)

Subtract: \(\frac{5}{6}- \frac{3}{4}\)
Here, the common denominator should be 12, which is the LCM of 6 and 4 (the two denominators).

\(\frac{5}{6}= \frac{10}{12}\)

\(\frac{3}{4}= \frac{9}{12}\)

Therefore, \(\frac{5}{6}- \frac{3}{4}=\frac{10}{12}- \frac{9}{12}=\frac{10-9}{12}=\frac{1}{12}\)

Try this: Add – \(\frac{3}{8}+ \frac{4}{5}\)

Fraction of a Whole

Fractions can be used to determine a part of a whole. For instance, imagine there are 30 students in a class, and 3/5 of them are boys. How many boys are there in the class? This can be found by calculating 3/5 of 30. To do this, divide 30 into 5 equal parts and combine 3 of those parts.

\(30\div 5=6\) and \(6\times 3=18\). So, we say, “three-fifth of 30 is 18”, and there are 18 boys in the class.

Here’s another question for you: In a group of 35 people, 1/7 are adults. How many adults are in the group?

Multiplying Fractions

To multiply two or more fractions, multiply the numerators to get the numerator of the answer fraction. Likewise, multiply the denominators to get the denominator of the answer fraction. Remember, you should always look to simplify the numbers before you multiply. Take, for example, multiplying \(\frac{2}{3}\) and \(\frac{9}{16}\). You should simplify the 2 from the top with the 16 from the bottom and the 9 from the top with the 3 from the bottom, as shown below.


Therefore, \(\frac{2}{3}\times \frac{9}{16} = \frac{1}{1}\times \frac{3}{8} = \frac{1\times 3}{1\times 8}\ = \frac{3}{8}\ \)

Your turn now: Multiply – \(\frac{4}{7}\times \frac{21}{10}\)

Dividing Fractions

To divide fraction A by fraction B, change the division to multiplication and swap the numerator and the denominator of the divisor fraction (B). Then, multiply in the same way as mentioned above. Here’s an example:

\(\frac{3}{4}\div \frac{9}{8} = \frac{3}{4}\times \frac{8}{9} = \frac{2}{3}\)

Multiplying a Decimal Number by a Power of 10