Decimals, fractions and Introductory Algebra are covered in 9th grade math (KS3 Maths in the UK). This review sheet gives concise explanations of these topics and gives practice questions.

When multiplying decimals, be careful about where to place the decimal.

How do you know how many decimal places your answer will have?

If you multiply 5.4 and 7.3, how many decimal places will your answer have?

**Practice questions:**

8.3 x 2.4

3.89 x 4.5

2.111²

4 x 3.2

7.1 x 5.3 x 1.2

**Fractions:**

**Multiplying Fractions:**

If there is a mixed number or whole number, convert it to a fraction. When multiplying fractions, multiply the numerators together to form the answer numerator, and multiply the denominators together to form the answer denominator. This means, multiply the top numbers together and the bottom numbers together. It is important to simplify your answer. If the answer is a “top-heavy” fraction, convert it to a whole number and the fraction remainder. Make sure that any fraction is simplified to the lowest possible terms. Remember that when simplifying, both the top and bottom numbers must be divided by the same number.

**Dividing Fractions:**

If there is a mixed number or whole number, convert it to a fraction. When dividing fractions, you need to cross multiply. Multiply the numerator of the first number with the denominator of the second number to form the numerator of your answer. Multiply the denominator of the first number with the numerator of the second to form the denominator in your answer. As with multiplying, make sure to simplify your answers.

**Practice Questions:**

**– 5/7 x 3/4**

1 1/3 x 2/5

3 ÷ 4/5

(1/2 x 9/10 ) ÷ 1/4

4 1/4 ÷ 2

**Introductory Algebra:**

Be able to match the following terms with definitions: equation, expression, formula, function, identity, term.

Understand the Letter Symbol Rules. For example, when symbols are added together, they can be simplified as a multiplication (x + x + x can be simplified as 3x; x multiplied by x, on the other hand, is written as x²).

Be comfortable with simplifying expressions. Combine like terms. This means you need to be able to use the distributive property (for example, 2(x-2) is the same as 2x-4).

You should be able to evaluate variable expressions; that means that if you are given the values of the unknown symbols, you can solve the problem. Or, if you are given the answer to the expression, you can find the value of the symbol.

**Sample Problems:**

If John has a certain amount of money, and Edward has £5 less than John, how much does Edward have? If Nick has twice as much as John, how much does he have?

Solve y – 3 x 2 if y=5

Find the value of y if y ÷2 + 3=11

Simplify the following expressions: x + x + x + x – 5 + 2 ; 3x – 4 + x -7; 1 + 2(k – 2)

Distribute these expressions in order to simplify: -1 (4k + 2); (5 x 3y) x 2