Year 5 · Equivalent Fractions and Mixed Numbers · Summary
Year 5 Equivalent Fractions and Mixed Numbers: summary and key words
Part of the Year 5 equivalent fractions and mixed numbers chapter. Chapter overview · whole chapter on one page
Chapter summary
| Skill | Method |
|---|---|
| Equivalent fractions | Multiply or divide the top and the bottom by the SAME number: |
| Simplify | Divide the top and the bottom by a common factor (the HCF does it in one go). Simplest form: the only common factor is 1. |
| Compare and order | Same denominator: bigger numerator = bigger fraction. Otherwise change to a common denominator first. Write the original fractions in the answer. |
| Improper to mixed | Divide the top by the bottom: whole number = answer, new top = remainder. |
| Mixed to improper | Whole × bottom + top, over the same bottom: 2 |
| Fractions as division | The fraction line means divide: 3 ÷ 4 = |
| Add and subtract fractions | Same denominator: add or subtract the numerators and keep the denominator. Different: common denominator first. Simplify, and write answers over 1 as mixed numbers. |
| Mixed numbers | Add (or subtract) the wholes and the fractions. If the fraction part is 1 or more, carry a whole. If you cannot take the fraction away, change to improper fractions. |
| Fraction × whole number | Multiply the numerator and keep the denominator: 3 × |
| Fraction of an amount | Divide by the denominator, multiply by the numerator: |
| Reasoning | Spot the mistake by doing it yourself. Never add the denominators. “Prove it” needs working and a sentence. One counter-example breaks “always”. |
Can you…?
- I can find equivalent fractions by multiplying or dividing the top and the bottom by the same number, including tenths and hundredths.
- I can simplify a fraction by dividing by a common factor.
- I can compare and order fractions by changing them to a common denominator.
- I can change improper fractions to mixed numbers and mixed numbers to improper fractions.
- I can write a division as a fraction, such as 3 ÷ 4 =
3 4 - I can add and subtract fractions with the same denominator and with denominators that are multiples of one another.
- I can add and subtract mixed numbers, including when I cross a whole number.
- I can multiply fractions and mixed numbers by whole numbers.
- I can find a fraction of an amount, and find the whole when I know a fraction of it.
- I can solve word problems with bar models and explain my reasoning.
Key terms
- Fraction
- A number that shows equal parts of a whole, such as
3 8 - Numerator
- The top number of a fraction. It says how many parts we have.
- Denominator
- The bottom number of a fraction. It says how many equal parts the whole is cut into.
- Equivalent fractions
- Fractions that are worth the same amount, like
1 2 4 8 - Simplify
- To write a fraction with smaller numbers by dividing the top and the bottom by a common factor.
- Common factor
- A number that divides exactly into two or more numbers.
- Highest common factor (HCF)
- The biggest number that divides exactly into two numbers.
- Simplest form
- A fraction whose top and bottom have no common factor except 1.
- Common denominator
- A bottom number that the denominators of two or more fractions all go into.
- Unit fraction
- A fraction with a numerator of 1, such as
1 5 - Improper fraction
- A fraction with a top number bigger than or equal to the bottom number, such as
7 4 - Mixed number
- A whole number and a fraction together, such as 1
3 4 - Fraction wall
- A picture of bricks that shows fractions of one whole, row by row.
- Ascending
- In order from the smallest to the largest.
- Descending
- In order from the largest to the smallest.
- Tenths and hundredths
- A tenth is one of 10 equal parts and a hundredth is one of 100 equal parts. 1 tenth = 10 hundredths.
- Counter-example
- One example that shows a statement is false.
- Bar model
- A drawing of bars that shows the parts and the whole of a problem.