Fractions, Decimals and Percentages

Welcome to the World of Fractions and Decimals!

Hello there! Today, we are going to explore how we can talk about parts of a whole. Imagine you have a delicious pizza, but you have to share it with your friends. You won't have a "whole" pizza anymore; you'll have a fraction of it!

In this chapter, we will learn how fractions and decimals are actually like secret twins—they look different, but they often mean the exact same thing. Don't worry if this seems a bit tricky at first; we will take it one step at a time!

1. Equivalent Fractions: The Copycats

Equivalent fractions are fractions that look different but show the same amount. It is like saying "half a dollar" or "two quarters"—they both give you the same amount of money!

Imagine a chocolate bar:
- If you cut it into 2 pieces and eat 1, you eat \( \frac{1}{2} \).
- If you cut it into 4 pieces and eat 2, you eat \( \frac{2}{4} \).
You ate the same amount of chocolate both times!

How to find them:

To find an equivalent fraction, just multiply (or divide) the top number (numerator) and the bottom number (denominator) by the same number.

Example: \( \frac{1}{2} \) multiplied by 2 is \( \frac{2}{4} \).
Example: \( \frac{1}{2} \) multiplied by 3 is \( \frac{3}{6} \).

Quick Review: As long as you do the same thing to the top and the bottom, the fraction stays equivalent!

2. Understanding Hundredths

We already know about tenths (when we divide something into 10 pieces). Hundredths happen when we divide something into 100 tiny pieces!

Did you know? If you take one-tenth (\( \frac{1}{10} \)) and divide it into 10 even smaller bits, you get hundredths!

We write one hundredth as a fraction like this: \( \frac{1}{100} \).
We write it as a decimal like this: 0.01.

Key Takeaway:

- 10 hundredths make 1 tenth (\( 0.10 = 0.1 \)).
- 100 hundredths make 1 whole (\( 1.00 = 1 \)).

3. Adding and Subtracting Fractions

In Year 4, we only add or subtract fractions that have the same denominator (the bottom number).

This is easy because the bottom number stays the same! You only need to add or subtract the top numbers.

Addition Example: \( \frac{2}{7} + \frac{3}{7} = \frac{5}{7} \)
Subtraction Example: \( \frac{5}{8} - \frac{2}{8} = \frac{3}{8} \)

Common Mistake: Never add the bottom numbers together! If you are eating slices of a 7-slice pizza, the pizza doesn't suddenly grow to 14 slices just because you ate more.

4. Decimals: The Secret Code

Decimals are just another way of writing fractions that have 10 or 100 on the bottom. We use a decimal point to separate the whole numbers from the parts.

Place Value Chart:

Ones . Tenths Hundredths

- \( \frac{1}{10} \) is 0.1
- \( \frac{7}{10} \) is 0.7
- \( \frac{1}{100} \) is 0.01
- \( \frac{25}{100} \) is 0.25

The Famous Three:

There are some fractions and decimals that pop up all the time. It’s super helpful to remember these:

- \( \frac{1}{2} \) = 0.5
- \( \frac{1}{4} \) = 0.25
- \( \frac{3}{4} \) = 0.75

Memory Aid: Think of money! A quarter of a pound is 25p (0.25). Half a pound is 50p (0.50).

5. Dividing by 10 and 100

When we divide a number by 10 or 100, the digits don't change, but they shift to the right to become smaller.

Dividing by 10: Move the digits one place to the right.
Example: \( 21 \div 10 = 2.1 \)

Dividing by 100: Move the digits two places to the right.
Example: \( 21 \div 100 = 0.21 \)

Top Tip: Imagine the digits are sitting on a slide, sliding down past the decimal point!

6. Rounding and Comparing Decimals

Sometimes we don't need the exact decimal; we just want to know the nearest whole number.

Rounding to the nearest whole:

Look at the tenths digit (the first number after the decimal point).
- If it is 4 or less, round down.
- If it is 5 or more, round up.

Example: 4.3 rounds down to 4.
Example: 6.8 rounds up to 7.

Comparing Decimals:

When comparing decimals like 0.45 and 0.41, look at the digits from left to right. Since 5 is bigger than 1, 0.45 is the larger number.

Real-world Example: Who has more money? Someone with £0.50 or someone with £0.05? The 5 in the tenths place is much more valuable than the 5 in the hundredths place!

Final Summary

1. Equivalent fractions are the same amount with different names.
2. Adding/Subtracting fractions: Only change the top number!
3. Tenths are one place after the decimal point; hundredths are two places after.
4. Dividing by 10 or 100 slides your numbers to the right of the decimal point.
5. Rounding: 5 or more? Score! (Round up). 4 or less? Let it rest! (Round down).

You've done a great job! Fractions and decimals take practice, but once you spot them in real life (like in shop prices or measuring ingredients), they become much easier to understand.