Number & Algebra

Equivalent Fractions and Decimals to Hundredths

Year 3 · Year 4

✓By the end of this lesson students will be able to recognise and generate equivalent fractions.
✓By the end of this lesson students will be able to understand the place value of tenths and hundredths.
✓By the end of this lesson students will be able to represent decimals to hundredths.
✓By the end of this lesson students will be able to convert between fractions (with denominators of 10 or 100) and decimals.
✓By the end of this lesson students will be able to locate decimals on a number line.

Key concepts

Equivalent Fractions

Equivalent fractions are fractions that look different but represent the same amount or value. For example, 1/2 and 2/4 are equivalent because they both represent half of a whole. You can find equivalent fractions by multiplying or dividing both the numerator (top number) and the denominator (bottom number) by the same non-zero number.

Numerator and Denominator

In a fraction, the numerator is the top number and tells you how many parts of the whole you have. The denominator is the bottom number and tells you how many equal parts the whole is divided into.

Decimals

Decimals are another way to write parts of a whole, using a decimal point. They are based on powers of ten. For example, 0.5 means five tenths.

Tenths

When a whole is divided into 10 equal parts, each part is called a tenth. We can write one tenth as the fraction 1/10 or as the decimal 0.1. The first digit after the decimal point is in the tenths place.

Hundredths

When a whole is divided into 100 equal parts, each part is called a hundredth. We can write one hundredth as the fraction 1/100 or as the decimal 0.01. The second digit after the decimal point is in the hundredths place.

Decimal Place Value

Just like whole numbers, decimals have place value. To the left of the decimal point, we have ones, tens, hundreds, and so on. To the right of the decimal point, we have tenths, hundredths, thousandths, and so on. For example, in 3.45, the '3' is in the ones place, the '4' is in the tenths place, and the '5' is in the hundredths place.

Key facts to remember

1Equivalent fractions represent the same amount, even if they look different.
2To find an equivalent fraction, multiply or divide both the numerator and denominator by the same number (not zero).
3Decimals are another way to show parts of a whole, using a decimal point.
4The first digit after the decimal point is the tenths place (e.g., 0.1 = 1/10).
5The second digit after the decimal point is the hundredths place (e.g., 0.01 = 1/100).
61 whole can be written as 10/10 or 100/100.
71 whole can also be written as 1.0, 1.00, etc.
8Fractions with denominators of 10 or 100 can easily be converted to decimals.

Worked examples

Example 1

Show that 1/2 is equivalent to 3/6.

IStep 1: Understand what equivalent fractions mean. They represent the same amount.

IIStep 2: To show they are equivalent, we can multiply the numerator and denominator of 1/2 by the same number to see if we get 3/6.

IIIStep 3: If we multiply the denominator 2 by 3, we get 6. So, we must also multiply the numerator 1 by 3.

IVStep 4: 1 × 3 = 3 and 2 × 3 = 6.

VStep 5: So, 1/2 is equivalent to 3/6.

Answer

1/2 = 3/6

You could also draw diagrams (e.g., two identical circles, one divided into 2 parts with 1 shaded, the other divided into 6 parts with 3 shaded) to visually demonstrate they are the same amount.

Example 2

Write 0.4 as a fraction in simplest form.

IStep 1: Identify the place value of the last digit. The '4' is in the tenths place.

IIStep 2: This means 0.4 is 'four tenths'.

IIIStep 3: Write 'four tenths' as a fraction: 4/10.

IVStep 4: Simplify the fraction by dividing both the numerator and the denominator by their greatest common factor. Both 4 and 10 can be divided by 2.

VStep 5: 4 ÷ 2 = 2 and 10 ÷ 2 = 5.

Answer

2/5

Always try to simplify fractions to their simplest form if possible.

Example 3

Convert 75/100 to a decimal.

IStep 1: Look at the denominator. It is 100, which means we are dealing with hundredths.

IIStep 2: The numerator is 75, so we have 'seventy-five hundredths'.

IIIStep 3: To write this as a decimal, we need two digits after the decimal point for hundredths.

IVStep 4: Place the 75 after the decimal point. Since there are no whole numbers, we write 0 before the decimal point.

Answer

0.75

Remember that 0.75 is the same as 75 hundredths. If it was 7/100, it would be 0.07 (seven hundredths).

Common mistakes

✗Only multiplying or dividing the numerator (or denominator) when trying to find equivalent fractions.
✗Confusing tenths and hundredths, e.g., writing 0.5 as 5/100 instead of 5/10.
✗Forgetting that 0.5 and 0.50 are equivalent decimals.
✗Incorrectly placing the decimal point, e.g., writing 7 hundredths as 0.7 instead of 0.07.
✗Not simplifying fractions to their simplest form when asked.

Exam tips

★Draw diagrams (like circles or rectangles) to help you visualise and check equivalent fractions.
★When converting fractions to decimals, always check the denominator first. If it's 10, there's one decimal place. If it's 100, there are two decimal places.
★Remember your decimal place values: 'tenths' is the first spot after the decimal point, 'hundredths' is the second.
★Practice converting both ways: fractions to decimals and decimals to fractions. This will strengthen your understanding.

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